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Cluster analysis

Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some specific sense defined by the analyst) to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning.

Cluster analysis refers to a family of algorithms and tasks rather than one specific algorithm. It can be achieved by various algorithms that differ significantly in their understanding of what constitutes a cluster and how to efficiently find them. Popular notions of clusters include groups with small distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated as a multi-objective optimization problem. The appropriate clustering algorithm and parameter settings (including parameters such as the distance function to use, a density threshold or the number of expected clusters) depend on the individual data set and intended use of the results. Cluster analysis as such is not an automatic task, but an iterative process of knowledge discovery or interactive multi-objective optimization that involves trial and failure. It is often necessary to modify data preprocessing and model parameters until the result achieves the desired properties.

Besides the term clustering, there is a number of terms with similar meanings, including automatic classification, numerical taxonomy, botryology (from βότρυς grape), typological analysis, and community detection. The subtle differences are often in the use of the results: while in data mining, the resulting groups are the matter of interest, in automatic classification the resulting discriminative power is of interest.

Cluster analysis was originated in anthropology by Driver and Kroeber in 1932 and introduced to psychology by Joseph Zubin in 1938 and Robert Tryon in 1939 and famously used by Cattell beginning in 1943 for trait theory classification in personality psychology.

Definition
The notion of a "cluster" cannot be precisely defined, which is one of the reasons why there are so many clustering algorithms. There is a common denominator: a group of data objects. However, different researchers employ different cluster models, and for each of these cluster models again different algorithms can be given. The notion of a cluster, as found by different algorithms, varies significantly in its properties. Understanding these "cluster models" is key to understanding the differences between the various algorithms. Typical cluster models include:
 * Connectivity models: for example, hierarchical clustering builds models based on distance connectivity.
 * Centroid models: for example, the k-means algorithm represents each cluster by a single mean vector.
 * Distribution models: clusters are modeled using statistical distributions, such as multivariate normal distributions used by the expectation-maximization algorithm.
 * Density models: for example, DBSCAN and OPTICS defines clusters as connected dense regions in the data space.
 * Subspace models: in biclustering (also known as co-clustering or two-mode-clustering), clusters are modeled with both cluster members and relevant attributes.
 * Group models: some algorithms do not provide a refined model for their results and just provide the grouping information.
 * Graph-based models: a clique, that is, a subset of nodes in a graph such that every two nodes in the subset are connected by an edge can be considered as a prototypical form of cluster. Relaxations of the complete connectivity requirement (a fraction of the edges can be missing) are known as quasi-cliques, as in the HCS clustering algorithm.
 * Signed graph models: Every path in a signed graph has a sign from the product of the signs on the edges. Under the assumptions of balance theory, edges may change sign and result in a bifurcated graph. The weaker "clusterability axiom" (no cycle has exactly one negative edge) yields results with more than two clusters, or subgraphs with only positive edges.
 * Neural models: the most well-known unsupervised neural network is the self-organizing map and these models can usually be characterized as similar to one or more of the above models, and including subspace models when neural networks implement a form of Principal Component Analysis or Independent Component Analysis.

A "clustering" is essentially a set of such clusters, usually containing all objects in the data set. Additionally, it may specify the relationship of the clusters to each other, for example, a hierarchy of clusters embedded in each other. Clusterings can be roughly distinguished as:
 * Hard clustering: each object belongs to a cluster or not
 * Soft clustering (also: fuzzy clustering): each object belongs to each cluster to a certain degree (for example, a likelihood of belonging to the cluster)

There are also finer distinctions possible, for example:

 * Strict partitioning clustering: each object belongs to exactly one cluster
 * Strict partitioning clustering with outliers: objects can also belong to no cluster; in which case they are considered outliers
 * Overlapping clustering (also: alternative clustering, multi-view clustering): objects may belong to more than one cluster; usually involving hard clusters
 * Hierarchical clustering: objects that belong to a child cluster also belong to the parent cluster
 * Subspace clustering: while an overlapping clustering, within a uniquely defined subspace, clusters are not expected to overlap

Algorithms
As listed above, clustering algorithms can be categorized based on their cluster model. The following overview will only list the most prominent examples of clustering algorithms, as there are possibly over 100 published clustering algorithms. Not all provide models for their clusters and can thus not easily be categorized. An overview of algorithms explained in Wikipedia can be found in the list of statistics algorithms.

There is no objectively "correct" clustering algorithm, but as it was noted, "clustering is in the eye of the beholder." The most appropriate clustering algorithm for a particular problem often needs to be chosen experimentally, unless there is a mathematical reason to prefer one cluster model over another. An algorithm that is designed for one kind of model will generally fail on a data set that contains a radically different kind of model. For example, k-means cannot find non-convex clusters. Most traditional clustering methods assume the clusters exhibit a spherical, elliptical or convex shape.

Connectivity-based clustering (hierarchical clustering)
Connectivity-based clustering, also known as hierarchical clustering, is based on the core idea of objects being more related to nearby objects than to objects farther away. These algorithms connect "objects" to form "clusters" based on their distance. A cluster can be described largely by the maximum distance needed to connect parts of the cluster. At different distances, different clusters will form, which can be represented using a dendrogram, which explains where the common name "hierarchical clustering" comes from: these algorithms do not provide a single partitioning of the data set, but instead provide an extensive hierarchy of clusters that merge with each other at certain distances. In a dendrogram, the y-axis marks the distance at which the clusters merge, while the objects are placed along the x-axis such that the clusters don't mix.

Connectivity-based clustering is a whole family of methods that differ by the way distances are computed. Apart from the usual choice of distance functions, the user also needs to decide on the linkage criterion (since a cluster consists of multiple objects, there are multiple candidates to compute the distance) to use. Popular choices are known as single-linkage clustering (the minimum of object distances), complete linkage clustering (the maximum of object distances), and UPGMA or WPGMA ("Unweighted or Weighted Pair Group Method with Arithmetic Mean", also known as average linkage clustering). Furthermore, hierarchical clustering can be agglomerative (starting with single elements and aggregating them into clusters) or divisive (starting with the complete data set and dividing it into partitions).

These methods will not produce a unique partitioning of the data set, but a hierarchy from which the user still needs to choose appropriate clusters. They are not very robust towards outliers, which will either show up as additional clusters or even cause other clusters to merge (known as "chaining phenomenon", in particular with single-linkage clustering). In the general case, the complexity is $$\mathcal{O}(n^3)$$ for agglomerative clustering and $$\mathcal{O}(2^{n-1})$$ for divisive clustering, which makes them too slow for large data sets. For some special cases, optimal efficient methods (of complexity $$\mathcal{O}(n^2)$$) are known: SLINK for single-linkage and CLINK for complete-linkage clustering.

Centroid-based clustering
In centroid-based clustering, each cluster is represented by a central vector, which is not necessarily a member of the data set. When the number of clusters is fixed to k, k-means clustering gives a formal definition as an optimization problem: find the k cluster centers and assign the objects to the nearest cluster center, such that the squared distances from the cluster are minimized.

The optimization problem itself is known to be NP-hard, and thus the common approach is to search only for approximate solutions. A particularly well-known approximate method is Lloyd's algorithm, often just referred to as "k-means algorithm" (although another algorithm introduced this name). It does however only find a local optimum, and is commonly run multiple times with different random initializations. Variations of k-means often include such optimizations as choosing the best of multiple runs, but also restricting the centroids to members of the data set (k-medoids), choosing medians (k-medians clustering), choosing the initial centers less randomly (k-means++) or allowing a fuzzy cluster assignment (fuzzy c-means).

Most k-means-type algorithms require the number of clusters – k – to be specified in advance, which is considered to be one of the biggest drawbacks of these algorithms. Furthermore, the algorithms prefer clusters of approximately similar size, as they will always assign an object to the nearest centroid. This often leads to incorrectly cut borders of clusters (which is not surprising since the algorithm optimizes cluster centers, not cluster borders).

K-means has a number of interesting theoretical properties. First, it partitions the data space into a structure known as a Voronoi diagram. Second, it is conceptually close to nearest neighbor classification, and as such is popular in machine learning. Third, it can be seen as a variation of model-based clustering, and Lloyd's algorithm as a variation of the Expectation-maximization algorithm for this model discussed below.

Centroid-based clustering problems such as k-means and k-medoids are special cases of the uncapacitated, metric facility location problem, a canonical problem in the operations research and computational geometry communities. In a basic facility location problem (of which there are numerous variants that model more elaborate settings), the task is to find the best warehouse locations to optimally service a given set of consumers. One may view "warehouses" as cluster centroids and "consumer locations" as the data to be clustered. This makes it possible to apply the well-developed algorithmic solutions from the facility location literature to the presently considered centroid-based clustering problem.

Model-based clustering
The clustering framework most closely related to statistics is model-based clustering, which is based on distribution models. This approach models the data as arising from a mixture of probability distributions. It has the advantages of providing principled statistical answers to questions such as how many clusters there are, what clustering method or model to use, and how to detect and deal with outliers.

While the theoretical foundation of these methods is excellent, they suffer from overfitting unless constraints are put on the model complexity. A more complex model will usually be able to explain the data better, which makes choosing the appropriate model complexity inherently difficult. Standard model-based clustering methods include more parsimonious models based on the eigenvalue decomposition of the covariance matrices, that provide a balance between overfitting and fidelity to the data.

One prominent method is known as Gaussian mixture models (using the expectation-maximization algorithm). Here, the data set is usually modeled with a fixed (to avoid overfitting) number of Gaussian distributions that are initialized randomly and whose parameters are iteratively optimized to better fit the data set. This will converge to a local optimum, so multiple runs may produce different results. In order to obtain a hard clustering, objects are often then assigned to the Gaussian distribution they most likely belong to; for soft clusterings, this is not necessary.

Distribution-based clustering produces complex models for clusters that can capture correlation and dependence between attributes. However, these algorithms put an extra burden on the user: for many real data sets, there may be no concisely defined mathematical model (e.g. assuming Gaussian distributions is a rather strong assumption on the data).

Density-based clustering
In density-based clustering, clusters are defined as areas of higher density than the remainder of the data set. Objects in sparse areas – that are required to separate clusters – are usually considered to be noise and border points.

The most popular density-based clustering method is DBSCAN. In contrast to many newer methods, it features a well-defined cluster model called "density-reachability". Similar to linkage-based clustering, it is based on connecting points within certain distance thresholds. However, it only connects points that satisfy a density criterion, in the original variant defined as a minimum number of other objects within this radius. A cluster consists of all density-connected objects (which can form a cluster of an arbitrary shape, in contrast to many other methods) plus all objects that are within these objects' range. Another interesting property of DBSCAN is that its complexity is fairly low – it requires a linear number of range queries on the database – and that it will discover essentially the same results (it is deterministic for core and noise points, but not for border points) in each run, therefore there is no need to run it multiple times. OPTICS is a generalization of DBSCAN that removes the need to choose an appropriate value for the range parameter $$\varepsilon$$, and produces a hierarchical result related to that of linkage clustering. DeLi-Clu, Density-Link-Clustering combines ideas from single-linkage clustering and OPTICS, eliminating the $$\varepsilon$$ parameter entirely and offering performance improvements over OPTICS by using an R-tree index.

The key drawback of DBSCAN and OPTICS is that they expect some kind of density drop to detect cluster borders. On data sets with, for example, overlapping Gaussian distributions – a common use case in artificial data – the cluster borders produced by these algorithms will often look arbitrary, because the cluster density decreases continuously. On a data set consisting of mixtures of Gaussians, these algorithms are nearly always outperformed by methods such as EM clustering that are able to precisely model this kind of data.

Mean-shift is a clustering approach where each object is moved to the densest area in its vicinity, based on kernel density estimation. Eventually, objects converge to local maxima of density. Similar to k-means clustering, these "density attractors" can serve as representatives for the data set, but mean-shift can detect arbitrary-shaped clusters similar to DBSCAN. Due to the expensive iterative procedure and density estimation, mean-shift is usually slower than DBSCAN or k-Means. Besides that, the applicability of the mean-shift algorithm to multidimensional data is hindered by the unsmooth behaviour of the kernel density estimate, which results in over-fragmentation of cluster tails.

Grid-based clustering
The grid-based technique is used for a multi-dimensional data set. In this technique, we create a grid structure, and the comparison is performed on grids (also known as cells). The grid-based technique is fast and has low computational complexity. There are two types of grid-based clustering methods: STING and CLIQUE. Steps involved in grid-based clustering algorithm are:
 * 1) Divide data space into a finite number of cells.
 * 2) Randomly select a cell ‘c’, where c should not be traversed beforehand.
 * 3) Calculate the density of ‘c’
 * 4) If the density of ‘c’ greater than threshold density
 * 5) Mark cell ‘c’ as a new cluster
 * 6) Calculate the density of all the neighbors of ‘c’
 * 7) If the density of a neighboring cell is greater than threshold density then, add the cell in the cluster and repeat steps 4.2 and 4.3 till there is no neighbor with a density greater than threshold density.
 * 8) Repeat steps 2,3 and 4 till all the cells are traversed.
 * 9) Stop.

Recent developments
In recent years, considerable effort has been put into improving the performance of existing algorithms. Among them are CLARANS, and BIRCH. With the recent need to process larger and larger data sets (also known as big data), the willingness to trade semantic meaning of the generated clusters for performance has been increasing. This led to the development of pre-clustering methods such as canopy clustering, which can process huge data sets efficiently, but the resulting "clusters" are merely a rough pre-partitioning of the data set to then analyze the partitions with existing slower methods such as k-means clustering.

For high-dimensional data, many of the existing methods fail due to the curse of dimensionality, which renders particular distance functions problematic in high-dimensional spaces. This led to new clustering algorithms for high-dimensional data that focus on subspace clustering (where only some attributes are used, and cluster models include the relevant attributes for the cluster) and correlation clustering that also looks for arbitrary rotated ("correlated") subspace clusters that can be modeled by giving a correlation of their attributes. Examples for such clustering algorithms are CLIQUE and SUBCLU.

Ideas from density-based clustering methods (in particular the DBSCAN/OPTICS family of algorithms) have been adapted to subspace clustering (HiSC, hierarchical subspace clustering and DiSH ) and correlation clustering (HiCO, hierarchical correlation clustering, 4C using "correlation connectivity" and ERiC exploring hierarchical density-based correlation clusters).

Several different clustering systems based on mutual information have been proposed. One is Marina Meilă's variation of information metric; another provides hierarchical clustering. Using genetic algorithms, a wide range of different fit-functions can be optimized, including mutual information. Also belief propagation, a recent development in computer science and statistical physics, has led to the creation of new types of clustering algorithms.

Evaluation and assessment
Evaluation (or "validation") of clustering results is as difficult as the clustering itself. Popular approaches involve "internal" evaluation, where the clustering is summarized to a single quality score, "external" evaluation, where the clustering is compared to an existing "ground truth" classification, "manual" evaluation by a human expert, and "indirect" evaluation by evaluating the utility of the clustering in its intended application.

Internal evaluation measures suffer from the problem that they represent functions that themselves can be seen as a clustering objective. For example, one could cluster the data set by the Silhouette coefficient; except that there is no known efficient algorithm for this. By using such an internal measure for evaluation, one rather compares the similarity of the optimization problems, and not necessarily how useful the clustering is.

External evaluation has similar problems: if we have such "ground truth" labels, then we would not need to cluster; and in practical applications we usually do not have such labels. On the other hand, the labels only reflect one possible partitioning of the data set, which does not imply that there does not exist a different, and maybe even better, clustering.

Neither of these approaches can therefore ultimately judge the actual quality of a clustering, but this needs human evaluation, which is highly subjective. Nevertheless, such statistics can be quite informative in identifying bad clusterings, but one should not dismiss subjective human evaluation.

Internal evaluation
When a clustering result is evaluated based on the data that was clustered itself, this is called internal evaluation. These methods usually assign the best score to the algorithm that produces clusters with high similarity within a cluster and low similarity between clusters. One drawback of using internal criteria in cluster evaluation is that high scores on an internal measure do not necessarily result in effective information retrieval applications. Additionally, this evaluation is biased towards algorithms that use the same cluster model. For example, k-means clustering naturally optimizes object distances, and a distance-based internal criterion will likely overrate the resulting clustering.

Therefore, the internal evaluation measures are best suited to get some insight into situations where one algorithm performs better than another, but this shall not imply that one algorithm produces more valid results than another. Validity as measured by such an index depends on the claim that this kind of structure exists in the data set. An algorithm designed for some kind of models has no chance if the data set contains a radically different set of models, or if the evaluation measures a radically different criterion. For example, k-means clustering can only find convex clusters, and many evaluation indexes assume convex clusters. On a data set with non-convex clusters neither the use of k-means, nor of an evaluation criterion that assumes convexity, is sound.

More than a dozen of internal evaluation measures exist, usually based on the intuition that items in the same cluster should be more similar than items in different clusters. For example, the following methods can be used to assess the quality of clustering algorithms based on internal criterion:

 * Davies–Bouldin index
 * The Davies–Bouldin index can be calculated by the following formula:

DB = \frac {1} {n} \sum_{i=1}^{n} \max_{j\neq i}\left(\frac{\sigma_i + \sigma_j} {d(c_i,c_j)}\right) $$
 * where n is the number of clusters, $$c_i$$ is the centroid of cluster $$i$$, $$\sigma_i$$ is the average distance of all elements in cluster $$i$$ to centroid $$c_i$$, and $$d(c_i,c_j)$$ is the distance between centroids $$c_i$$ and $$c_j$$. Since algorithms that produce clusters with low intra-cluster distances (high intra-cluster similarity) and high inter-cluster distances (low inter-cluster similarity) will have a low Davies–Bouldin index, the clustering algorithm that produces a collection of clusters with the smallest Davies–Bouldin index is considered the best algorithm based on this criterion.

 * Dunn index
 * The Dunn index aims to identify dense and well-separated clusters. It is defined as the ratio between the minimal inter-cluster distance to maximal intra-cluster distance. For each cluster partition, the Dunn index can be calculated by the following formula:

D = \frac{\min_{1 \leq i < j \leq n} d(i,j)}{\max_{1 \leq k \leq n} d^{\prime}(k)} \,, $$
 * where d(i,j) represents the distance between clusters i and j, and d '(k) measures the intra-cluster distance of cluster k. The inter-cluster distance d(i,j) between two clusters may be any number of distance measures, such as the distance between the centroids of the clusters. Similarly, the intra-cluster distance d '(k) may be measured in a variety of ways, such as the maximal distance between any pair of elements in cluster k. Since internal criterion seek clusters with high intra-cluster similarity and low inter-cluster similarity, algorithms that produce clusters with high Dunn index are more desirable.

 * Silhouette coefficient
 * The silhouette coefficient contrasts the average distance to elements in the same cluster with the average distance to elements in other clusters. Objects with a high silhouette value are considered well clustered, objects with a low value may be outliers. This index works well with k-means clustering, and is also used to determine the optimal number of clusters.

External evaluation
In external evaluation, clustering results are evaluated based on data that was not used for clustering, such as known class labels and external benchmarks. Such benchmarks consist of a set of pre-classified items, and these sets are often created by (expert) humans. Thus, the benchmark sets can be thought of as a gold standard for evaluation. These types of evaluation methods measure how close the clustering is to the predetermined benchmark classes. However, it has recently been discussed whether this is adequate for real data, or only on synthetic data sets with a factual ground truth, since classes can contain internal structure, the attributes present may not allow separation of clusters or the classes may contain anomalies. Additionally, from a knowledge discovery point of view, the reproduction of known knowledge may not necessarily be the intended result. In the special scenario of constrained clustering, where meta information (such as class labels) is used already in the clustering process, the hold-out of information for evaluation purposes is non-trivial.

A number of measures are adapted from variants used to evaluate classification tasks. In place of counting the number of times a class was correctly assigned to a single data point (known as true positives), such pair counting metrics assess whether each pair of data points that is truly in the same cluster is predicted to be in the same cluster.

As with internal evaluation, several external evaluation measures exist, for example:
 * Purity: Purity is a measure of the extent to which clusters contain a single class. Its calculation can be thought of as follows: For each cluster, count the number of data points from the most common class in said cluster. Now take the sum over all clusters and divide by the total number of data points. Formally, given some set of clusters $$M$$ and some set of classes $$D$$, both partitioning $$N$$ data points, purity can be defined as:

\frac{1}{N}\sum_{m\in M}\max_{d\in D}{|m \cap d|} $$
 * This measure doesn't penalize having many clusters, and more clusters will make it easier to produce a high purity. A purity score of 1 is always possible by putting each data point in its own cluster. Also, purity doesn't work well for imbalanced data, where even poorly performing clustering algorithms will give a high purity value. For example, if a size 1000 dataset consists of two classes, one containing 999 points and the other containing 1 point, then every possible partition will have a purity of at least 99.9%.

 * Rand index
 * The Rand index computes how similar the clusters (returned by the clustering algorithm) are to the benchmark classifications. It can be computed using the following formula:

RI = \frac {TP + TN} {TP + FP + FN + TN} $$
 * where $$TP$$ is the number of true positives, $$TN$$ is the number of true negatives, $$FP$$ is the number of false positives, and $$FN$$ is the number of false negatives. The instances being counted here are the number of correct pairwise assignments. That is, $$TP$$ is the number of pairs of points that are clustered together in the predicted partition and in the ground truth partition, $$FP$$ is the number of pairs of points that are clustered together in the predicted partition but not in the ground truth partition etc. If the dataset is of size N, then $$TP + TN + FP + FN = \binom{N}{2}$$.

One issue with the Rand index is that false positives and false negatives are equally weighted. This may be an undesirable characteristic for some clustering applications. The F-measure addresses this concern, as does the chance-corrected adjusted Rand index.
 * F-measure
 * The F-measure can be used to balance the contribution of false negatives by weighting recall through a parameter $$\beta \geq 0$$. Let precision and recall (both external evaluation measures in themselves) be defined as follows:

P = \frac {TP } {TP + FP } $$

R = \frac {TP } {TP + FN} $$
 * where $$P$$ is the precision rate and $$R$$ is the recall rate. We can calculate the F-measure by using the following formula:

F_{\beta} = \frac {(\beta^2 + 1)\cdot P \cdot R } {\beta^2 \cdot P + R} $$
 * When $$\beta=0$$, $$F_{0}=P$$. In other words, recall has no impact on the F-measure when $$\beta=0$$, and increasing $$\beta$$ allocates an increasing amount of weight to recall in the final F-measure.
 * Also $$TN$$ is not taken into account and can vary from 0 upward without bound.

 * Jaccard index
 * The Jaccard index is used to quantify the similarity between two datasets. The Jaccard index takes on a value between 0 and 1. An index of 1 means that the two dataset are identical, and an index of 0 indicates that the datasets have no common elements. The Jaccard index is defined by the following formula:

J(A,B) = \frac {|A \cap B| } {|A \cup B|} = \frac{TP}{TP + FP + FN} $$
 * This is simply the number of unique elements common to both sets divided by the total number of unique elements in both sets.
 * Note that $$TN$$ is not taken into account.

 * Dice index
 * The Dice symmetric measure doubles the weight on $$TP$$ while still ignoring $$TN$$:

DSC = \frac{2TP}{2TP + FP + FN} $$
 * Fowlkes–Mallows index
 * The Fowlkes–Mallows index computes the similarity between the clusters returned by the clustering algorithm and the benchmark classifications. The higher the value of the Fowlkes–Mallows index the more similar the clusters and the benchmark classifications are. It can be computed using the following formula:

FM = \sqrt{ \frac {TP}{TP+FP} \cdot \frac{TP}{TP+FN} } $$
 * where $$TP$$ is the number of true positives, $$FP$$ is the number of false positives, and $$FN$$ is the number of false negatives. The $$FM$$ index is the geometric mean of the precision and recall $$P$$ and $$R$$, and is thus also known as the G-measure, while the F-measure is their harmonic mean. Moreover, precision and recall are also known as Wallace's indices $$B^I$$ and $$B^{II}$$. Chance normalized versions of recall, precision and G-measure correspond to Informedness, Markedness and Matthews Correlation and relate strongly to Kappa.

 * Chi Index is an external validation index that measure the clustering results by applying the chi-squared statistic. This index scores positively the fact that the labels are as sparse as possible across the clusters, i.e., that each cluster has as few different labels as possible. The higher the value of the Chi Index the greater the relationship between the resulting clusters and the label used.
 * The mutual information is an information theoretic measure of how much information is shared between a clustering and a ground-truth classification that can detect a non-linear similarity between two clusterings. Normalized mutual information is a family of corrected-for-chance variants of this that has a reduced bias for varying cluster numbers.
 * Confusion matrix
 * A confusion matrix can be used to quickly visualize the results of a classification (or clustering) algorithm. It shows how different a cluster is from the gold standard cluster.

Cluster tendency
To measure cluster tendency is to measure to what degree clusters exist in the data to be clustered, and may be performed as an initial test, before attempting clustering. One way to do this is to compare the data against random data. On average, random data should not have clusters.

 * Hopkins statistic
 * There are multiple formulations of the Hopkins statistic. A typical one is as follows. Let $$X$$ be the set of $$n$$ data points in $$d$$ dimensional space. Consider a random sample (without replacement) of $$m \ll n$$ data points with members $$x_i$$. Also generate a set $$Y$$ of $$m$$ uniformly randomly distributed data points. Now define two distance measures, $$u_i$$ to be the distance of $$y_i \in Y$$ from its nearest neighbor in X and $$w_i$$ to be the distance of $$x_i \in X$$ from its nearest neighbor in X. We then define the Hopkins statistic as:

H=\frac{\sum_{i=1}^m{u_i^d}}{\sum_{i=1}^m{u_i^d}+\sum_{i=1}^m{w_i^d}} \,, $$
 * With this definition, uniform random data should tend to have values near to 0.5, and clustered data should tend to have values nearer to 1.
 * However, data containing just a single Gaussian will also score close to 1, as this statistic measures deviation from a uniform distribution, not multimodality, making this statistic largely useless in application (as real data never is remotely uniform).

Biology, computational biology and bioinformatics

 * Plant and animal ecology
 * Cluster analysis is used to describe and to make spatial and temporal comparisons of communities (assemblages) of organisms in heterogeneous environments. It is also used in plant systematics to generate artificial phylogenies or clusters of organisms (individuals) at the species, genus or higher level that share a number of attributes.

 * Transcriptomics
 * Clustering is used to build groups of genes with related expression patterns (also known as coexpressed genes) as in HCS clustering algorithm. Often such groups contain functionally related proteins, such as enzymes for a specific pathway, or genes that are co-regulated. High throughput experiments using expressed sequence tags (ESTs) or DNA microarrays can be a powerful tool for genome annotation – a general aspect of genomics.

 * Sequence analysis
 * Sequence clustering is used to group homologous sequences into gene families. This is a very important concept in bioinformatics, and evolutionary biology in general. See evolution by gene duplication.

 * High-throughput genotyping platforms
 * Clustering algorithms are used to automatically assign genotypes.

 * Human genetic clustering
 * The similarity of genetic data is used in clustering to infer population structures.

Medicine

 * Medical imaging
 * On PET scans, cluster analysis can be used to differentiate between different types of tissue in a three-dimensional image for many different purposes.

 * Analysis of antimicrobial activity
 * Cluster analysis can be used to analyse patterns of antibiotic resistance, to classify antimicrobial compounds according to their mechanism of action, to classify antibiotics according to their antibacterial activity.

 * IMRT segmentation
 * Clustering can be used to divide a fluence map into distinct regions for conversion into deliverable fields in MLC-based Radiation Therapy.

Business and marketing

 * Market research
 * Cluster analysis is widely used in market research when working with multivariate data from surveys and test panels. Market researchers use cluster analysis to partition the general population of consumers into market segments and to better understand the relationships between different groups of consumers/potential customers, and for use in market segmentation, product positioning, new product development and selecting test markets.

 * Grouping of shopping items
 * Clustering can be used to group all the shopping items available on the web into a set of unique products. For example, all the items on eBay can be grouped into unique products (eBay does not have the concept of a SKU).

World Wide Web

 * Social network analysis
 * In the study of social networks, clustering may be used to recognize communities within large groups of people.

 * Search result grouping
 * In the process of intelligent grouping of the files and websites, clustering may be used to create a more relevant set of search results compared to normal search engines like Google. There are currently a number of web-based clustering tools such as Clusty. It also may be used to return a more comprehensive set of results in cases where a search term could refer to vastly different things. Each distinct use of the term corresponds to a unique cluster of results, allowing a ranking algorithm to return comprehensive results by picking the top result from each cluster.

 * Slippy map optimization
 * Flickr's map of photos and other map sites use clustering to reduce the number of markers on a map. This makes it both faster and reduces the amount of visual clutter.

Computer science

 * Software evolution
 * Clustering is useful in software evolution as it helps to reduce legacy properties in code by reforming functionality that has become dispersed. It is a form of restructuring and hence is a way of direct preventative maintenance.

 * Image segmentation
 * Clustering can be used to divide a digital image into distinct regions for border detection or object recognition.

 * Evolutionary algorithms
 * Clustering may be used to identify different niches within the population of an evolutionary algorithm so that reproductive opportunity can be distributed more evenly amongst the evolving species or subspecies.

 * Recommender systems
 * Recommender systems are designed to recommend new items based on a user's tastes. They sometimes use clustering algorithms to predict a user's preferences based on the preferences of other users in the user's cluster.

 * Markov chain Monte Carlo methods
 * Clustering is often utilized to locate and characterize extrema in the target distribution.

 * Anomaly detection
 * Anomalies/outliers are typically – be it explicitly or implicitly – defined with respect to clustering structure in data.

 * Natural language processing
 * Clustering can be used to resolve lexical ambiguity.

 * DevOps
 * Clustering has been used to analyse the effectiveness of DevOps teams.

Social science

 * Sequence analysis in social sciences
 * Cluster analysis is used to identify patterns of family life trajectories, professional careers, and daily or weekly time use for example.

 * Crime analysis
 * Cluster analysis can be used to identify areas where there are greater incidences of particular types of crime. By identifying these distinct areas or "hot spots" where a similar crime has happened over a period of time, it is possible to manage law enforcement resources more effectively.

 * Educational data mining
 * Cluster analysis is for example used to identify groups of schools or students with similar properties.

 * Typologies
 * From poll data, projects such as those undertaken by the Pew Research Center use cluster analysis to discern typologies of opinions, habits, and demographics that may be useful in politics and marketing.

Others

 * Field robotics
 * Clustering algorithms are used for robotic situational awareness to track objects and detect outliers in sensor data.

 * Mathematical chemistry
 * To find structural similarity, etc., for example, 3000 chemical compounds were clustered in the space of 90 topological indices.

 * Climatology
 * To find weather regimes or preferred sea level pressure atmospheric patterns.

 * Finance
 * Cluster analysis has been used to cluster stocks into sectors.

 * Petroleum geology
 * Cluster analysis is used to reconstruct missing bottom hole core data or missing log curves in order to evaluate reservoir properties.

 * Geochemistry
 * The clustering of chemical properties in different sample locations.

Specialized types of cluster analysis

 * Automatic clustering algorithms
 * Balanced clustering
 * Clustering high-dimensional data
 * Conceptual clustering
 * Consensus clustering
 * Constrained clustering
 * Community detection
 * Data stream clustering
 * HCS clustering
 * Sequence clustering
 * Spectral clustering

Techniques used in cluster analysis

 * Artificial neural network (ANN)
 * Nearest neighbor search
 * Neighbourhood components analysis
 * Latent class analysis
 * Affinity propagation

Data projection and preprocessing

 * Dimension reduction
 * Principal component analysis
 * Multidimensional scaling

Other

 * Cluster-weighted modeling
 * Curse of dimensionality
 * Determining the number of clusters in a data set
 * Parallel coordinates
 * Structured data analysis
 * Linear separability

title: Cluster analysis


text:
Rudolph Schoenheimer

Rudolf Schoenheimer (May 10, 1898 – September 11, 1941) was a German-American biochemist who developed the technique of isotope labelling/tagging of biomolecules, enabling detailed study of metabolism. This work revealed that all the constituents of an organism are in a constant state of chemical renewal.

Born in Berlin, after graduating in medicine from the Friedrich Wilhelm University there, he learned further organic chemistry at the University of Leipzig and then studied biochemistry at the University of Freiburg where he rose to be Head of Physiological Chemistry.

He spent the 1930-31 academic year at the University of Chicago. In 1933, following the rise of the Nazis to power he emigrated from Germany to the Columbia University to join the department of Biological Chemistry. Working with David Rittenberg, from the radiochemistry laboratory of Harold C. Urey and later together with Konrad Bloch, they used stable isotopes to tag foodstuffs and trace their metabolism within living things.

He further established that cholesterol is a risk factor in atherosclerosis.

He suffered from manic depression all of his life, which led to him in 1941 committing suicide using cyanide. He had been honoured with the request to give the Dunham Lecture at Harvard before his death. It was read for him following his death.

Early life and education
Rudolf Schoenheimer was born in Berlin, Germany on 10 May 1898. He was the son of Gertrude Edel and Hugo Schoenheimer, who was a physician. He was Jewish, however his family converted to Christianity. He attended local schools in Berlin before graduating from the Dorotheen-Stadtische Gymnasium in 1916. Following his graduation Schoenheimer was drafted into the German army. He served in the artillery on the western front for two years during world war 1. Following his service in the war, he began his study of medicine at the University of Berlin. In 1922 he received his M.D. His M.D dissertation was titled "Über die experimentelle Cholesterinkrankheit der Kaninchen" ("About the experimental cholesterol disease of rabbits"). He then spent a year working at the Moabit Hospital in Berlin as a pathologist. He continued his scientific research during this time and studied the production of atherosclerosis in animals through administering cholesterol.

In 1924, Schoenheimer began his 3-year study at the University of Leipzig, in a program aimed at advancing his knowledge in chemistry. The program was aided by the Rockefeller Foundation and taught by Karl Thomas, professor of physiological chemistry at the University of Leipzig. During his time at Leipzig, Schoenheimer was able to develop a method of synthesising peptides.

Career
After his studies at Leipzig had ended, he began a year of work at the Moabit Hospital in Berlin as the resident pathologist. During this time, he began his research and studies on the issue of atherosclerosis. His first published works, dated during this period were in on the development of atherosclerosis in experimental animals when administered cholesterol. He also spent time working in the laboratory of Peter Rona at the Berlin Municipal Hospital.

In 1926, Schoenheimer was invited by Ludwig Aschoff to join the faculty at the University of Freiburg. There he worked as an assistant professor. The investigation of pathological material was part of his work duties. During this time, he also researched atherosclerosis and the role of dietary cholesterol in its development. He became the active in 1927, and then the titular, head of his division in 1931.

In 1930, until 1931, Schoenheimer was in the United States as the Douglas Smith Fellow at the University of Chicago. During this time Schoenheimer came into contact with the Josiah Macy Jr Foundation. Later in 1931, The Macy Foundation, with Ludwig Kast as its president, started supporting Schoenheimer in his atherosclerosis studies. Following his fellowship, he returned to the University of Freiburg, taking the position of head of the Pathological Chemistry department.

Columbia University: 1933-1934
In April 1933, Schoenheimer emigrated to the United States in response to the Nazi regime's policy for the dismissal of Jewish faculty in universities. He was offered work at Columbia University as an assistant professor, where he continued his research on metabolism and cholesterol synthesis, alongside Walter M. Sperry and David Rittenberg.

In 1933, Germany entered a political crisis and saw the rise of Hitler and the Nazi Party, which led Schoenheimer into emigrating to the United States. Schoenheimer had Jewish heritage which he was conscious of despite his Family having converted to Christianity. Schoenheimer had joined a Jewish Youth Movement and was actively involved in the Zionist Organisation following WW1. Due to the situation in Germany at the time and the Nazi Policy dismissing Jewish faculty, Schoenheimer was unlikely to remain living in Germany. Ludwig Kast was informed of this situation and contacted U.S universities, Cornell and Columbia on behalf of Schoenheimer. Hans T. Clarke, the Chairman of the Biological Chemistry Department at the University of Columbia, invited Schoenheimer to work at the University. He began work in the Department of Biological Chemistry as a research assistant. The Josiah Macy Foundation provided his salary and research support whilst he worked at Columbia. At Columbia Schoenheimer was among others that shared similar interests in Biochemistry and wanted it to move in the direction of organic chemistry.

Scientific work
Schoenheimer's scientific work contributed to biochemistry and metabolic studies, with his most significant work being the application of isotopes to the study of intermediary metabolism. Schoenheimer's earlier scientific work in the 1920s centered on the physiology and pathology of sterols.

Early work: 1924-1933
In 1926, while at the University of Leipzig, Schoenheimer developed a method of synthesising peptides. From 1903 to 1909, Emil Fischer's scientific work had prompted the synthesis of many peptides, however there were limitations to his method. Fischer used a halogen acyl amino acid halide coupling method. A suitable method was needed, which involved an amino blocking group being removed by a nonhydrolyptic process. This method was first proposed by Rudolph Schoenheimer, as he utilised earlier findings by Michel Bergmann which demonstrated that with a mixture of hydrogen iodide and phosphonium iodide, p-toluenesulfonyl amino acids could be detosylated reductively. Schoenheimer used the azide coupling method introduced by Theodor Curtius, and the acid chloride method introduced by Emil Fischer in order to make several peptides.

In 1929, Schoenheimer investigated how different sterols impacted cholesterol deposition in rabbits. It had been assumed that only plants were able to synthesize complex compounds whilst animals were forced to obtain these compounds indirectly from plants. It was assumed also that there would only small chemical changes were necessary when modifying these compounds to suit specific needs. Previous cholesterol-balance studies indicated that under specific conditions, animals could possess the ability to form cholesterol, as it has been discovered that sometimes negative balances are present in metabolic studies, wherein more sterol is excreted than consumed. These observations did not demonstrate whether cholesterol present in the animal body was due to synthesis or whether it had all actually come from vegetable food. The transformation of plant sterols into cholesterol within the body of an animal requires the sterol to be absorbable. This is the notion Schoenheimer investigated in his experiments. One of his experiments involved administering two different diets to a group of rabbits. Rabbits are sensitive to a diet which includes cholesterol, and their bodily responses particularly that of the aorta demonstrates a change that similarly resembles the Human atherosclerosis. In the experiment one diet involved a large amount of sito-sterol, which is a type of plant sterol. The other diet included cholesterol. The observations of the experiment indicated that Schoenheimer and his associates' theories that plant sterols were not absorbable were probable. Furthur studies were conducted and the findings concluded that plant sterols were non-absorbable, and therefore animals with plant only diets must synthesise the cholesterol necessary for their tissues as they do not receive absorbable cholesterol. During this period Schoenheimer became aware that cholesterol had an intermediary metabolism and that it was chemically inconvertable with other sterols. In one of his later experiments using sterols, he did discover a small percentage of one sterol, dihydrocholesterol in animal tissue. He investigated this finding using a dog which showed dihydrocholesterol was formed in the tissues. This finding revealed to Schoenheimer that cholesterol was an active metabolite. Schoenheimer and his associates also investigated ergo-sterol, and its behaviour within the bodies of rats, mice, and rabbits. The findings of this study revealed that egro-sterol was not absorbable. This research shaped Schoenheimer's scientific career and research path.

Later work: 1933-1941
In 1933, Schoenheimer emigrated to the United States, where his scientific research took a different focus. Prior to his emigration, his work was mostly focused on the metabolism of cholesterol. In 1934 Schoenheimer began his work on intermediary metabolism, and how stable isotopes could be applied to the study. Schoenheimer worked alongside David Rittenburg and later Konrad Bloch. Schoenheimer and his colleagues began their research by conducting experiments with the use of deuterium. Deuterium, which is a stable isotope of hydrogen, was discovered by physical chemist Harold Urey in 1932. One of the methods used in the experiment involved heavy water administered into animals in order to analyse the deuterium present in the different constituents of the body. This suggested which type of substances were utilising the hydrogen present in body fluids and revealed the role water posed in metabolic processes. Their experiment also provided information regarding the breakdown process of lipid compounds containing deuterium in experimental animals. Prior to this study, it was assumed that animals utilised fats directly from foods that they had recently ingested, and that fat stores were only used amid starvation. The experiment revealed that fatty acids remained stored in body depots even during starvation.

Schoenheimer and his colleagues then began a study of protein metabolism using the isotope of nitrogen as it became available. Schoenheimer and his colleague David Rittenberg, analysed how synthesised amino acids containing nitrogen would operate within an animal's body. They used adult rats as the subject of their experiment and added amino acids synthesised from isotopic ammonia to their diet. When these diets were applied in nitrogen equilibrium it was found they were incorporated into tissue proteins at an intensive and rapid rate. There was also evidence of chemical transformation as heavy nitrogen was present in amino acids, which were isolated from protein, following ingestion. This chemical transformation was similar to that demonstrated in the fatty acids of his previous experiments on intermediary metabolism. The results of the experiment revealed that body proteins are in a continuous and dynamic state of synthesis and degradation. Schoenheimer and Rittenberg were responsible for discovering that body constituents were in a state of constant chemical renewal, as they were previously believed to be in a static state. Experiments on the metabolism of amino acids, fatty acids, and excretory products are used to support and demonstrate this concept of metabolic "regeneration". These molecules go through a process of replacement and interchange in the body tissue, as well as other transformations and fundamental chemical reactions. This method of isotope labelling molecules enabled Schoenheimer and his colleagues to investigate various issues in intermediary metabolism.

By the late 1930s, Schoenheimer's work had contributed to the rising interest in intermediary metabolism and the isotope method.

Later life and death
Schoenheimer had married Salome Glucksohn, a noted zoologist and geneticist, in 1937. They emigrated to the United States together, and they had no children. They later divorced. Schoenheimer was invited to conduct lectures detailing his scientific work and findings. In 1937, he conducted his Harvey Lecture and in 1941 his Dunham Lecture was conducted by his colleagues in his behalf. At the height of his career he committed suicide by ingesting potassium cyanide at his home in Yonkers, having struggled with depression for multiple years.

Use of Schoenheimer's scientific findings
Schoenheimer's scientific work and his development of isotope tagging techniques enabled biochemists to discover the various metabolic pathways of the body.

Schoenheimer was among the first scientists to identify that the bodies of humans and animals had processes of renewal and regeneration. The methods and techniques used by Schoenheimer also provided a means to measure quantities of substances within the body prior to the advent of the technologies and software for dynamic modeling.

Schoenheimer's 1933 metabolic balance study in animals presented early evidence of "end-product feedback inhibition of cholesterol synthesis". In later years, with greater advancements in science and technology, including the advent of radioactive isotopes, greater information on cholesterol feedback was discovered.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Rudolph Schoenheimer


text:
New Milford, Connecticut

New Milford is a town in Litchfield County, Connecticut, United States. The town, part of Greater Danbury, as well as the New York Metropolitan Area, has a population of 28,115 as of the 2020 census. New Milford lies 14 mi north of Danbury on the banks of the Housatonic River, and shares its border with the northeastern shore of Candlewood Lake. It is the largest town in the state of Connecticut in terms of land area at nearly 63.7 mi2 (164.9822 km$2$). The town center is listed as a census-designated place (CDP).

New Milford is located roughly 50 mi west of Hartford, 63 mi northeast of New York City proper, and 80 miles from Midtown Manhattan.

New Milford consists of a number of town sub-divisions (i.e. boroughs, districts, communities, or neighborhoods), including Gaylordsville, Merryall, and Northville. The town's infrastructure largely branches off of either side of the highway routes U.S. 7 and U.S. 202, which intersect and split within the town and together form its main thoroughfare.

The area constituting contemporary New Milford was originally inhabited by the indigenous Wawyachtonoc people, while the town of New Milford itself was formally established by English colonists in the early 18th century.

Native Americans
The indigenous Wawyachtonoc people were a sub-group of the Paugussett Nation, and later a Mahican-affiliated Native American tribe, that lived in the area of contemporary New Milford both before and during the colonial era. They had a farming and fishing culture, cultivating corn—mainly by the Housatonic and Still rivers —squash, beans and tobacco, and fished in freshwater areas. They spoke an Algonquian language. The Wawyachtonoc's primary village, "Weantinock", was located near present-day New Milford, along the Housatonic River.

Colonial times
In 1707, John Noble Sr., previously of Westfield, Massachusetts, and his eight-year-old daughter Sarah Noble were the first Anglo-American settlers. (A public school was later named after Sarah Noble.) They were soon joined by others who had bought land there.

On October 17, 1711, twelve families (including a total about 70 people) petitioned the Connecticut General Assembly to create the town, together with the associated privilege of levying a tax to support a minister. With the legislature's approval, the town was organized the next year. The residents soon secured Daniel Boardman to preach, and he was ordained as the minister of the Congregational Church on November 21, 1716.

In 1722, most of northwestern Connecticut (except for the town of Litchfield) was placed under the jurisdiction of New Haven County. In 1730, the eastern half of northwestern Connecticut was transferred to the jurisdiction of Hartford County. But New Milford, Salisbury and Sharon continued in New Haven County until the formation of Litchfield County in 1751.

American Revolution
Roger Sherman lived in New Milford before moving to New Haven in 1761. He later became a member of the Continental Congress and signed both the Declaration of Independence and U.S. Constitution. The lot of his former house is the site of the present Town Hall.

During the American Revolution, the 7th Connecticut Regiment (also known as the 19th Continental Regiment) was raised in town on September 16, 1776. The regiment, and the New Milford men in it, would see action in the Battle of Brandywine, Battle of Germantown and the Battle of Monmouth. In total, the town "sent 285 men to fight in the War out of a total population of 2,776."

The Boardman family

 * David Sherman Boardman (1768–1864) was the youngest child of Deacon Sherman and Sarah (Bostwick) Boardman. He became a lawyer in town and later chief judge in Litchfield County Court. He served as judge of probate for the district of New Milford in 1805, and held the place by successive annual appointments for sixteen years. He was elected Representative to the General Assembly eight times.
 * Elijah Boardman (1760–1823) was a U.S. senator representing Connecticut. Born in New Milford, he was educated by private tutors, and served in the Revolutionary War.
 * William Whiting Boardman (1794–1871), a U.S. Representative born in town, was the son of Elijah Boardman. He was a Connecticut state senator in the fourth district, 1830–32, a member of the Connecticut State House of Representatives, 1836–1839, 1845, and 1849–1851; Speaker of the Connecticut State House of Representatives, 1836, 1839, and 1845; US Representative from Connecticut's second district, 1840–1843. He died in New Haven, and is interred at Grove Street Cemetery in New Milford.

19th and 20th centuries
During the early- to mid-19th century, New Milford was home to several locations that were part of the Underground Railroad network.

In the second half of the 19th century, many new industries came to town. The Water Witch Hose Company No. 2, local telephone and electricity companies, and newspapers were all founded. Factories in town made buttons, paint and varnish, hats, furniture, pottery, lime, dairy products and pasteboard, among other goods. Tobacco became the major crop in the area, and tobacco warehouses sprang up to handle its storage and processing before sales.

In 1942 Buck's Rock Camp was founded off Bucks Rock Road, and has remained in operation ever since.

The house that inspired the 1946 novel and 1948 film, Mr. Blandings Builds His Dream House, still stands in the Merryall section of town.

21st century
The town has constructed a 1,000,000-gallon sewer plant expansion on West Street, a sewer pump station on Boardman Road, reconstruction of the Rte. 67/ Grove Street Intersection, and ambulance facility on Scovill Street.

The town has added a skate park at Young's Field (2006), reconstructed the tennis and basketball courts at Young's Field (2010), reconstructed the basketball court at Williamson Park in Gaylordsville (2010), and improved Lynn Deming Park (2017), and is working on the New Milford River Trail, which will eventually join the existing 1.5-mile Sega Meadows Park trail (2012), 3.5 miles of River Road, and the 0.25-mile Young's Field River Trail (2017) and link them to the greenways in the neighboring towns of Brookfield and Kent. Several streetscape projects were completed by the Department of Public Works (DPW) with grant money on Church Street, Whittlesey Avenue, and the west side of East Street (2009/2010). Candlewoof Dog Park is completed on Pickett District Road. A bocce ball court was constructed at the Senior Center by Boy Scout Troop 66 (2012).

New Milford is frequented on weekends between the months of April and December, when visitors attend the Elephant's Trunk Flea Market, a large outdoor flea market located near the southern end of the town which WRKI has claimed is the largest weekly flea market in New England.

The trend of town population growth has continued but slowed since the beginning of the 21st century.

National Register of Historic Places sites

 * Boardman's Bridge – Boardman Road at Housatonic River, northwest of New Milford (added June 13, 1976)
 * Carl F. Schoverling Tobacco Warehouse – 1 Wellsville Avenue (added May 12, 1982)
 * E. A. Wildman & Co. Tobacco Warehouse – 34 Bridge Street (added November 20, 1988)
 * Hine-Buckingham Farms – 44, 46, and 48 Upland Road, 78, 81 Crossman Road (added June 7, 2004)
 * Housatonic Railroad Station – Railroad Street (added April 1, 1984)
 * J. S. Halpine Tobacco Warehouse – West and Mill Streets (added 1982)
 * John Glover Noble House (added September 29, 1977)
 * Lover's Leap Bridge – south of New Milford on Pumpkin Hill Road (added June 13, 1976)
 * Merritt Beach & Son Building – 30 Bridge Street (added May 28, 1992)
 * Merryall Union Evangelical Society Chapel – Chapel Hill Road (added July 5, 1986)
 * New Milford Center Historic District – Bennitt and Elm Streets, Center Cemetery, East, South Main, Mill, and Railroad Streets (added July 13, 1986)
 * United Bank Building – 19-21 Main Street (added May 12, 1982)

Geography
New Milford is located on the northeastern shore of Candlewood Lake. The East Aspetuck River, Still River and Housatonic River flow through the town. Downtown New Milford is home to a large town green, commonly cited as the longest town green in the state of Connecticut.

According to the United States Census Bureau, the town has a total area of 165.1 km2, making it the largest town in Connecticut. Behind New Milford is Greenwich with 47.62 square miles. 159.5 km2 of New Milford is land, and 5.6 km2 of New Milford (3.40%) is water. The CDP corresponding to the town center has a total area of 3.4 sqmi, of which 3.4 sqmi  is land and 0.04 sqmi  (0.88%) is water.

Greater New Milford Area
The Greater New Milford Area, also known as Southern Litchfield County, encompasses a cluster of charming towns nestled in the scenic landscapes of Connecticut. This region includes Bridgewater, Kent, New Milford, Roxbury, Sherman, Warren, and Washington. With a combined urban and town proper population of 43,732, the area is celebrated for its rich history, rural charm, and picturesque surroundings. Residents and visitors alike are drawn to the area's historic architecture, vibrant community life, and a harmonious blend of urban and rural living.

Principal Communities

 * Gaylordsville (06755)
 * Boardman Bridge
 * Lower Merryall
 * Merwinsville
 * New Milford Center
 * Northville
 * Park Lane
 * Still River
 * Upper Merryall
 * Lanesville
 * Candlewood Hills
 * Sunny Valley
 * Pickett District
 * Squash Hollow

Climate
New Milford has a humid continental climate, with mild to warm humid summers and cold to very cold winters and precipitation being relatively uniformly distributed throughout the year. The highest recorded temperature was 103 °F (39 °C) in July 1966, while the lowest recorded temperature was −18 °F (−28 °C) in January 1968. Snowfall is generally frequent in winter.

Demographics
As of the census of 2010, there were 28,142 people, 10,618 households, and 7,503 families residing in the town. The population density was 456.9 PD/sqmi. There were 11,731 housing units at an average density of 190.4 /sqmi. The racial makeup of the town was 91.71% White, 1.72% Black or African American, 0.24% Native American, 2.77% Asian, 0.04% Pacific Islander, 1.65% from other races, and 1.87% from two or more races. Hispanic or Latino of any race was 6.02% of the population.

Of the 10,618 households, 33.4% had children under the age of 18 living with them, 58.0% were married couples living together, 8.8% had a female householder with no husband present, and 29.3% were non-families. 23.0% of all households were made up of individuals, and 7.9% had someone living alone who was 65 years of age or older. The average household size was 2.62 and the average family size was 3.13.

In the town, the population had 24.30% under the age of 18, 6.87% from 18 to 24, 24.90% from 25 to 44, 31.75% from 45 to 64, and 12.18% who were 65 years of age or older. The median age was 41.4 years. For every 100 females, there were 97.4 males. For every 100 females age 18 and over, there were 93.6 males.

As of the 2000 Census the median income for a household in the town was $65,354, and the median income for a family was $75,775. Males had a median income of $50,523 versus $34,089 for females. The per capita income for the town was $29,630. About 2.1% of families and 3.3% of the population were below the poverty line, including 2.7% of those under age 18 and 5.5% of those age 65 or over.

Religion

New Milford is known for its large church and religious school, the nondenominational Faith Church. It is also home to two Catholic churches; a Lutheran church; a Christian Science community; a longstanding Quaker community; a house of worship belonging to the United Church of Christ; a United Methodist church; and an Assemblies of God (Pentecostal) church; as well the Episcopalian (Anglican) St. John's Episcopal Church, located next to the town green. A Jewish Reform synagogue, Temple Sholom, is located near the town's border with Sherman.

The Canterbury School, a well-known Catholic boarding school, is located near downtown New Milford.

Sports
New Milford is home to the GMS Rowing Center. Founded in 2003, it manages a US Rowing Training Center Program. It has a highly successful Middle and High School (Junior) Program which competes at Youth National Championships, Junior National Team Trials, The "Royal Canadian Henley" and has sent rowers to the Junior World Rowing Championships. In 2011 GMS also had rowers representing the US at the Under 23 World Championships in Amsterdam, the Netherlands and at the World Rowing Championships at Bled, Slovenia.

Elementary schools

 * Northville Elementary School
 * Hill & Plain Elementary School

Intermediate schools

 * Sarah Noble Intermediate School
 * Schaghticoke Middle School

High schools

 * New Milford High School

Private schools

 * Canterbury School
 * New Milford is home to the Canterbury School, a well-known Roman Catholic boarding school. The school's Chapel of Our Lady features the Jose M. Ferrer Memorial Carillon.
 * Faith Preparatory
 * Education without Walls

Transportation
New Milford is served by fixed-bus routes of the Housatonic Area Regional Transit. The main highways of the town are U.S. Route 7 and U.S. Route 202.

There has been continued talk about a proposal to electrify and restore the Danbury Branch of the Metro-North Railroad north of Danbury to New Milford. These efforts have included a Rail Study in 2008, proposed state legislation in 2017, and stimulus money in 2021. The Danbury Branch provides commuter rail service between Danbury, to South Norwalk, Stamford, and Grand Central Terminal in New York City. The tracks north of Danbury are currently used by the Housatonic Railroad for freight service.

Notable people

 * Léonie Fuller Adams (1899–1988), poetry consultant to the Library of Congress (now titled poet laureate)
 * Charles A. Beard (1874–1948), historian, activist
 * Mary R. Beard (1876–1958), historian, activist
 * Elizabeth Bentley (1908–1963), spy
 * David Sherman Boardman (1768–1864), lawyer, judge and politician
 * Elijah Boardman (1760–1823), U.S. senator
 * William Whiting Boardman (1794–1871), U.S. congressman
 * Emily Sophie Brown (1881–1985), one of the first women to serve in the Connecticut House of Representatives
 * Kenny Coolbeth (born 1977), motorcycling champion
 * Fortunato Depero (1892–1960), painter, writer, sculptor and graphic designer
 * Jack Douglas (1908–1989), writer
 * Florence Eldridge (1901–1988), stage and screen actress
 * Diane von Fürstenberg (born 1946), fashion designer, who plans to be buried at her 100 acre farm in town
 * Peter Gallagher, actor
 * Ethan Hawke (born 1970), actor, writer
 * Lillian Hellman (1905–1984), playwright
 * Skitch Henderson (1918–2005), pianist, composer and conductor
 * Eric Hodgins (1899–1971), author
 * Ian Hunter (born 1939), English singer-songwriter
 * Keith Kane, guitarist and founding member of Vertical Horizon
 * Eartha Kitt (1927–2008), singer, actress, author
 * Columbia Lancaster (1803–1893), U.S. congressman
 * Jeremy Levin, businessman, physician and scientist
 * Max Lowenthal (1888–1971), lawyer and civil servant
 * Fredric March (1897–1975), film and stage actor
 * Florence Maybrick (1862–1941), accused murderer, prison reform advocate
 * Seth Meyers, American stand-up comedian, television host, actor, writer, and producer
 * Hap Moran (1901–1994), football player
 * Dhan Gopal Mukerji (1890–1936), writer, author, Newbery Medal recipient 1928
 * William H. Noble (1788–1850), U.S. congressman
 * M. Scott Peck (1936–2005), psychiatrist and self-help author
 * Natacha Rambova (1897–1966), costume and set designer, dancer, actress, academic, former wife of Rudolph Valentino
 * Thomas Riley, US ambassador to Morocco 2003–2009
 * Joan Rivers (1933–2014), comedian, actress, writer, producer
 * Roger Sherman (1721–1793), signer of Declaration of Independence and Constitution
 * Jean Simmons (1929–2010), British actress
 * Eric Sloane (1905–1985), artist
 * Walker Todd (1786–1840), lawyer, member of the New York State Senate (2nd D.) and Inspector of Mount Pleasant State Prison
 * Solmous Wakeley (1794–1867), pioneer Wisconsin legislator
 * Mary B. Weaver (1887–1978), Connecticut politician
 * Joseph J. Went (born 1930), general
 * Horace Wheaton (1803–1882), U.S. congressman
 * Theodore White (1915–1986), political author of the 1960s–1970s

Movies filmed in New Milford
The following movies with their actual or expected year of release have been filmed in New Milford:
 * The Brass Ring (1983) (TV)
 * Mr. Deeds (2002)
 * Zero Day (2003)
 * What Alice Found (2003)
 * The Ballad of Jack and Rose (2005)
 * The Six Wives of Henry LeFay (2007)
 * The Private Lives of Pippa Lee (2009)
 * 25/8 renamed to My Soul to Take (2009)
 * Candlewood (2022)

title: New Milford, Connecticut


text:
Talk:Almanac

Comments
This is again something which in my view is better handled using a definition that by attempting to turn it into an article. I vote the link should be redirected to the Wiktionary definition of almanac. --(talk to)BozMo 12:43, 21 May 2004 (UTC)

Historical Gap
There's a great gap from Ptolemy's Phaesis to the 17th c. English printed almanacs. Much needs to be filled in here. --SteveMcCluskey 02:39, 12 June 2006 (UTC)

Origin of word?
In the first section, this article specifies an origin for the word "almanac." In the very next section, it says the origin is unclear. Only one of these statements can be true. Which one is it? --  Denelson83  21:29, 2 September 2007 (UTC)

 * As far as I can tell, "unclear" is closer to the mark (with the relationship between the modern Arabic word and the medieval Arabic word being one of the question marks). I've added a link to the online etymological dictionary, and re-worded accordingly.  If people can find more sources, maybe we can make a more definitive statement. Kingdon 17:22, 6 September 2007 (UTC)

The origin of the word is very, very obscure
The 4 May 2009 version of this article's etymology section says Almanac is "from the Arabic word al-manakh[ref1] "calendar, almanac", citing the "Kitab al-Manakh," a 13th century publication by eminent Moroccan scholar, mathematician and astronomer, Ibn al-Banna al-Marrakushi.[ref2]" However, Roger Bacon used the word Almanac in a book dated 1267, when Ibn al-Banna was only 10 years old. Moreover the biography of Ibn al-Banna at MacTutor History of Mathematics archive says "he [al-Banna] is the first to use the expression almanakc (in Arabic al-manakh meaning weather) in a work containing astronomical and meteorological data."

The following is a quote from the Oxford English Dictionary about the eytmology of Almanac. I've copied this text from the website laudatortemporisacti.blogspot.com.

 * Appears in Medieval Latin as almanac(h) in end of 13thC, and soon after (though it may have been earlier) in most of the Romance langs., It. almanacco, Sp. almanaque, Fr. almanach, the immediate source of which was apparently a Spanish Arabic al-manākh. Pedro de Alcala, in his Arabic-Castilian Vocabulista (1505), has 'manākh, almanaque, calendario'; also 'manaḥ (probably meant for same word), relox del sol' [sundial]. But the word occurs nowhere else as Arabic, has no etymon in the language, and its origin is uncertain.... The earliest notices are: 1267 Roger Bacon, Opus Majus xv. (1733) 120 'Antiqui astronomi ponunt principium anni circiter principium Octobris, sicut patet in expositione tabularum, quae Almanac vocantur'; 1267 Roger Bacon, Opus Tertium xi. (1859) 36 'Hae tabulae vocantur Almanach vel Tallignum, in quibus..homo posset inspicere omnia ea quae in caelo sunt omni die, sicut nos in calendario inspicimus omnia festa sanctorum'. Circa 1345 Giovanni Villani, Cronica XI. xli, 'Secondo l'almanacco di Profazio Giudeo, e delle tavole Toletane dovea essere la detta congiunzione di Saturno e di Giove a di 20 del detto mese di Marzo' [where the 'Tables of Toledo' (constructed c 1080 by  Arzachel) again point to the Arabs in Spain].

The OED then goes on to report a few etymology candidates, and rejects them all.

The etymology book by Weekley (1921) similarly says: "First seen in Roger Bacon. Apparently from Spanish Arabic, al-manakh, but this is not an Arabic word [interpret: this is not a word found in Arabic texts].... The word remains a puzzle." The etymology book by Skeat (1888) similary concludes that the construction of an Arabic etymology "is not satisfactory".

Returning to the current Wikipedia article, the article goes on to say: "the ultimate origin of the word is unknown." The word "ultimate" there is misleading because it's insinuating that (a) an Arabic origin is known and (b) the etymology of the Arabic word is unknown. Whereas the earliest documented use of the word is by Roger Bacon, a man who couldn't speak Arabic. I propose inserting the following text from the book "Word Origins" by John Ayto (2005): "The ultimate source of the word is obscure. Its first syllable, al-, and its general relevance to medieval science and technology, strongly suggest an Arabic origin, but no convincing candidate has been found." Seanwal111111 (talk) 08:19, 4 May 2010 (UTC)

The origin of the word, "Almanac," is from Patristic Greek "almenichiata" and dates to before 339 A.D., prior to the origin of Arabic. It is found in Eusebius Caesarius, De Praep. Evang. III, 4. (Migne, Patrologia Graeca, XXI, 169c) The word almenichiata is [Ptolemaic?] Egyptian for the supernatural rulers of the celestial bodies according to Porphyry. —Preceding unsigned comment added by John N. Lupia III (talk • contribs) 03:53, 3 October 2007 (UTC)
 * This statement is problematic. First of all, Arabic did not "originate" at some time after A.D. 339, it represents a continuous development from Proto-Semitic, and has several written sources before A.D. 339. Second, the paragraph is not consistent. Even if it (for some valid reason) were correct that the origin or the word should not be sought in Arabic, the origin cannot, according to the statement above, at least, be Greek, as the next sentence goes on to claim that it is Egyptian. Third, the article as it stands is in itself problematic, as it is formed as a polemic statement ("prior to the origin of Arabic") even though the article itself does not make any reference to Arabic before that sentence. Rewriting is needed. Trondtr (talk) 06:39, 27 December 2007 (UTC).

 * Here's what the Oxford English Dictionary has to say about that item in Eusebius:
 * Eusebius, De Praep. Evangel. iii. 4, quotes Porphyrius as to the Egyptian belief in astrology, in horoscopes, and so-called lords of the ascendant, 'whose names are given in the almenichiaká (ἐν τοῖς ἀλμενιχιακοῖς), with their various powers to cure diseases, their risings and settings, and their presages of things future.' Notwithstanding the suggestive sound and use of this word (of which however the real form is very uncertain), the difficulties of connecting it historically either with the Spanish Arabic manākh, or with med.L. almanach without Arabic intermediation, seem insurmountable. Nor does the sense really point to such tables as those described by Roger Bacon, Chaucer, and Regiomontanus.
 * Similary the Etymology Dictionary by Weekley (1921) says: "Eusebius (4 cent.) has Greek almenikiaka, calendars, but there is a great gap between this and the medieval forms." Seanwal111111 (talk) 08:19, 4 May 2010 (UTC)

Resolve The article is littered with scraps of pro-Arabic jumping up and down insistently. This is unacceptable; the matter must be resolved. If a scholarly concensus in favor of an Arabic root can be found then it should be given first place, with other theories mentioned. Otherwise all origin theories should be listed, ideally in order of etymological respectability, and all such discussion weeded out when it spills elsewhere. Either way, needs attention. — Xiong 熊 talk * 09:10, 20 December 2017 (UTC)

Works and Days
Hesiod's poem, Works and Days, was a good example of a agriculturally-focused astronomical (as well as ethically and generally advising) text, after the Babylonians but before the Hellenistic period. Furthermore, I strongly object to calling this agricultural tradition of astronomy "Hellenistic" because that word implies the Hellenistic period, beginning 323 with the death of Alexander the Great (see Hellenistic Period), when in fact the texts of Democritus and Hesiod were written earlier. Hesiod's work dates from about 700 BCE (Works and Days.

Moreover, I can name other relevant ancient texts that ought to mentioned in the history of almanacs. MULAPIN, a Babylonian star catalog (Mul.Apin), comes to mind. Also, the Egyptians knew that the morning rising of Sirius marked the beginning of summer (Sirius), though I do not know of any text they had to do so. Quintus Twig (talk) 20:24, 5 December 2009 (UTC)

Primarily historical in content?
Can it be said that almanacs are primarily historical in content? And if they're not just historical, what forecasts do they make? For example, why would I want to buy an astronomical almanac when I can get a periodical that will tell me what is going to happen in the upcoming year? Concerning what an almanac 'is', I think an explanation of the advantages of an almanac, say over other relevant sources of information, would go a long way toward enhancing this definition. Regards --71.107.92.100 (talk) 17:29, 29 December 2010 (UTC) —Preceding unsigned comment added by 71.107.89.52 (talk) 16:33, 28 December 2010 (UTC)

Ladies Almanack
Ladies Almanack is listed under US Almanacs but is it really an almanac or is it a one time collection of inside jokes and stories? Thank you. Rissa, copy editor (talk) 22:35, 5 October 2014 (UTC)

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Courses aligned to HUMSS strand
Courses aligned to HUMSS strand 136.158.17.180 (talk) 11:04, 17 October 2023 (UTC)

ENGLISH
With example from English Explain six function of language 197.250.98.103 (talk) 17:29, 13 November 2023 (UTC)

title: Talk:Almanac


text:
An Evening with Kevin Smith

An Evening with Kevin Smith is a DVD featuring question and answer sessions that the comedian and filmmaker Kevin Smith held with his fans at various American colleges in 2001/2002. The colleges were: Clark University, Cornell University, Indiana University, Kent State University and University of Wyoming. During the sessions, Smith answers questions regarding his movies, as well as his life. He discusses how he got started in the movie industry, how different films came about, his friendship with Jason Mewes, and his relationship with the media, fans, and various other celebrities.

Plot
The film features numerous comedic stories from Smith's life at that point in his early 30s. Smith first unearthed stories such as his relationship with Warner Bros. and their famously unreleased “Superman Lives”. The story became the basis for a 2016 documentary. The story Smith tells involves producer Jon Peters wanting to include elements of generic blockbuster cliché in Smith's script, these include Superman fighting a large spider, a story point later included in Peters' box office bomb Wild Wild West.

Another story Smith recalls is of when he first met his future wife (Jennifer Schwalbach Smith) whilst promoting Dogma in 1999 and the birth of his daughter that same year. Smith tells of how he was physically injured the night he first slept with his wife, a fact he never told her until a full year into their marriage.

One of Smith's most popular stories from the DVD is of when he was unknowingly forced to make a near 5-hour long documentary for Prince about God and the evolution of man, both of which are two topics Smith has little to no involvement in. Smith reveals he was angry with the pop star towards the end of the week he spent with him, especially when he learns of the documentary never seeing the light of day, instead being put into Prince's vault which includes over 100 original music videos and hundreds of hours of music previously unreleased according to Smith.

Reception
On Rotten Tomatoes the film has a 100% rating with 6 positive reviews collected. Joel Cunningham, writing for Digitally Obsessed, stated that the DVD was "essential viewing for any true fan of Jay and Silent Bob" and complimented Smith's abilities as a story teller. Adam Tyner of DVD Talk ranked An Evening with Kevin Smith as "highly recommended" though he noted that "at least some familiarity with Kevin Smith and his body of work is required to get much out of this two-disc set."

title: An Evening with Kevin Smith


text:
British Film Institute

The British Film Institute (BFI) is a film and television charitable organisation which promotes and preserves film-making and television in the United Kingdom. The BFI uses funds provided by the National Lottery to encourage film production, distribution, and education. It is sponsored by the Department for Culture, Media and Sport, and partially funded under the British Film Institute Act 1949.

Purpose
The BFI was established in 1933 to encourage the development of the arts of film, television and the moving image throughout the United Kingdom, to promote their use as a record of contemporary life and manners, to promote education about film, television and the moving image generally, and their impact on society, to promote access to and appreciation of the widest possible range of British and world cinema and to establish, care for and develop collections reflecting the moving image history and heritage of the United Kingdom.

Archive
The BFI maintains the world's largest film archive, the BFI National Archive, previously called National Film Library (1935–1955), National Film Archive (1955–1992), and National Film and Television Archive (1993–2006). The archive contains more than 50,000 fiction films, over 100,000 non-fiction titles, and around 625,000 television programmes. The majority of the collection is British material but it also features internationally significant holdings from around the world. The Archive also collects films which feature key British actors and the work of British directors.

Cinemas
The BFI runs the BFI Southbank (formerly the National Film Theatre (NFT)) and the BFI IMAX cinema, both located on the south bank of the River Thames in London. The IMAX has the largest cinema screen in the UK and shows popular recent releases and short films showcasing its technology, which includes IMAX 70mm screenings, IMAX 3D screenings and 11,600 watts of digital surround sound. BFI Southbank (the National Film Theatre screens and the Studio) shows films from all over the world, particularly critically acclaimed historical and specialised films that may not otherwise get a cinema showing. The BFI also distributes archival and cultural cinema to other venues – each year to more than 800 venues all across the UK, as well as to a substantial number of overseas venues.

Education
The BFI offers a range of education initiatives, in particular to support the teaching of film and media studies in schools. In late 2012, the BFI received money from the Department for Education to create the BFI Film Academy Network for young people aged between 16 and 25. A residential scheme is held at the NFTS every year.

Festivals
The BFI runs the annual London Film Festival along with BFI Flare: London LGBT Film Festival and the youth-orientated Future Film Festival.

Other activities

 * See also Category:British Film Institute films

The BFI publishes the monthly Sight & Sound magazine, as well as films on Blu-ray, DVD and books. It runs the BFI National Library (a reference library), and maintains the BFI Film & TV Database and Summary of Information on Film and Television (SIFT), which are databases of credits, synopses and other information about film and television productions. SIFT has a collection of about 7 million still frames from film and television.

The BFI has co-produced a number of television series featuring footage from the BFI National Archive, in partnership with the BBC, including The Lost World of Mitchell & Kenyon, The Lost World of Friese-Greene and The Lost World of Tibet.

The BFI has also produced contemporary artists' moving image work, most notably through the programme of the BFI Gallery, which was located at BFI Southbank from March 2007 to March 2011. The programme of the gallery resulted in several new commissions by leading artists, including projects which engaged directly with the BFI National Archive, among which are Patrick Keiller's 'The City of the Future', Iain Forsyth and Jane Pollard's 'RadioMania: An Abandoned Work' and Deimantas Narkevicious' 'Into the Unknown'. The Gallery also initiated projects by film-makers such as Michael Snow, Apichatpong Weerasethakul, Jane and Louise Wilson and John Akomfrah.

The BFI also operates a streaming service called BFI Player. This streaming service offers a variety of niche and art films.

History

The institute was founded in 1933. Despite its foundation resulting from a recommendation in a report on Film in National Life, at that time the institute was a private company, though it has received public money throughout its history. This came from the Privy Council and Treasury until 1965, and from the various culture departments since then.

The institute was restructured following the Radcliffe Report of 1948, which recommended that it should concentrate on developing the appreciation of filmic art, rather than creating film itself. Thus control of educational film production passed to the National Committee for Visual Aids in Education and the British Film Academy assumed control for promoting production. From 1952 to 2000, the BFI provided funding for new and experimental film-makers via the BFI Production Board.

The institute received a royal charter in 1983. This was updated in 2000, and in the same year the newly established UK Film Council took responsibility for providing the BFI's annual grant-in-aid (government subsidy). As an independent registered charity, the BFI is regulated by the Charity Commission and the Privy Council.

In 1988, the BFI opened the London Museum of the Moving Image (MOMI) on the South Bank. MOMI was acclaimed internationally and set new standards for education through entertainment, but it did not receive the high levels of continuing investment that might have enabled it to keep pace with technological developments and ever-rising audience expectations. The museum was "temporarily" closed in 1999 when the BFI stated that it would be re-sited. This did not happen, and MOMI's closure became permanent in 2002 when it was decided to redevelop the South Bank site. This redevelopment was itself then further delayed.

Today
The BFI is currently managed on a day-to-day basis by its chief executive, Ben Roberts. Supreme decision-making authority rests with a chair and a board of up to 15 governors. The current chair is Jay Hunt, a television executive, who took up the post in February 2024. Governors, including the Chair, are appointed by the Secretary of State for Culture, Media and Sport.

The BFI operates with three sources of income. The largest is public money allocated by the Department for Culture, Media and Sport. For the year 2021–22, the BFI received £74.31m from the DCMS as Grant-in-Aid funding. The second largest source is commercial activity such as receipts from ticket sales at BFI Southbank or the BFI London IMAX theatre (£5m in 2007), sales of DVDs, etc. Thirdly, grants and sponsorship of around £5m are obtained from various sources, including National Lottery funding grants, private sponsors and through donations (J. Paul Getty, Jr., who died in 2003, left the BFI a legacy of around £1m in his will). The BFI is also the distributor for all Lottery funds for film (in 2011–12 this amounted to c.£25m).

As well as its work on film, the BFI also devotes a large amount of its time to the preservation and study of British television programming and its history. In 2000, it published a high-profile list of the 100 Greatest British Television Programmes, as voted for by a range of industry figures.

The delayed redevelopment of the National Film Theatre finally took place in 2007, creating in the rebranded "BFI Southbank" new education spaces, a contemporary art gallery dedicated to the moving image (the BFI Gallery), and a pioneering mediatheque which for the first time enabled the public to gain access, free of charge, to some of the otherwise inaccessible treasures in the National Film & Television Archive. The mediatheque has proved to be the most successful element of this redevelopment, and there are plans to roll out a network of them across the UK.

An announcement of a £25 million capital investment in the Strategy for UK Screen Heritage was made by Secretary of State for Culture, Media and Sport at the opening night of the 2007 London Film Festival. The bulk of this money paid for long overdue development of the BFI National Archive facilities in Hertfordshire and Warwickshire.

During 2009, the UK Film Council persuaded the government that there should only be one main public-funded body for film, and that body should be the UKFC, while the BFI should be abolished. In 2010, the government announced that there would be a single body for film. Despite intensive lobbying (including, controversially, using public funding to pay public relations agencies to put its case forward), the UKFC failed to persuade the government that it should have that role and, instead, the BFI took over most of the UKFC's functions and funding from 1 April 2011, with the UKFC being subsequently abolished. Since then, the BFI has been responsible for all Lottery funding for film—originally in excess of £25m p.a., and currently in excess of £40m p.a.

The BFI Film Academy forms part of the BFI's overall 5–19 Education Scheme. The programme is being supported by the Department for Education in England who have committed £1m per annum funding from April 2012 and 31 March 2015. It is also funded through the National Lottery, Creative Scotland and Northern Ireland Screen.

On 29 November 2016, the BFI announced that over 100,000 television programmes are to be digitised before the video tapes, which currently have an estimated five-to-six-year shelf life, become unusable. The BFI aims to make sure that the television archive is still there in 200 years' time.

The BFI announced in February 2021 that it is teaming up with American diversity and inclusion program #StartWith8Hollywood founded by Thuc Doan Nguyen to make it global.

Leadership
The BFI is currently chaired by Jay Hunt and run by CEO Ben Roberts.

BFI Chair

 * George Sutherland-Leveson-Gower, 5th Duke of Sutherland (1933–1936)
 * Sir Charles Cleland (1936–1937)
 * Sir George Clerk (1938–1939)
 * William Brass, 1st Baron Chattisham (1939–1945)
 * Patrick Gordon Walker (1946–1948)
 * Cecil Harmsworth King (1948–1952)
 * S. C. Roberts (1952–1956)
 * Sylvester Gates (1956–1964)
 * Sir William Coldstream (1964–1971)
 * Sir Denis Forman (1971–1973)
 * Lord Lloyd of Hampstead (1973–1976)
 * John Freeman (1976–1977)
 * Enid Wistrich (Acting) (1977–1978)
 * Sir Basil Engholm (1978–1981)
 * Lord Attenborough (1982–1992)
 * Jeremy Thomas (1993–1997)
 * Sir Alan Parker (1998–1999)
 * Joan Bakewell (1999–2002)
 * Anthony Minghella (2003–2007)
 * Roger Laughton (Acting) (2008)
 * Greg Dyke (2008–2016)
 * Josh Berger (2016–2021)
 * Tim Richards (2021–2024)
 * Jay Hunt (2024–)

BFI directors

 * J. W. Brown (1933–1936)
 * Oliver Bell (1936–1949)
 * Denis Forman (1949–1955)
 * James Quinn (1955–1964)
 * Stanley Reed (1964–1972)
 * Keith Lucas (1972–1978)
 * Anthony Smith (1979–1987)
 * Wilf Stevenson (1988–1997)
 * Jane Clarke (acting, 1997)
 * John Woodward (1998–1999)
 * Jon Teckman (1999–2002)
 * Adrian Wootton (acting, 2002–2003)
 * Amanda Nevill (2003–2020)
 * Ben Roberts (2020–present)

title: British Film Institute