Rémi Gaudin
email: rgaudin@eric.univ-lyon2.fr

Sylvaine Barnier

Nicolas Nicoloyannis

Maks Banens

Clustering of Bi-Dimensional and Heterogeneous Times Series: Application to Social Sciences Data

We present an application of bi-dimensional and heterogeneous time series clustering in order to resolve a Social Sciences study issue. The dataset is the result of a survey involving more than eight thousand handicapped persons. Sociologists need to know if there are in this dataset some homogeneous classes of people according to two attributes: the idea that handicapped people have about the quality of their life and their couple status (i.e. if they have a partner or not). These two attributes are time series so we had to adapt the k-Means clustering algorithm in order to be efficient with this kind of data. For this purpose, we use the Longest Common Subsequence time series distance for its efficiency to manage time stretching and we extend it to the bidimensional and heterogeneous case. The results of our unsupervised process give some pertinent and surprising clusters that can be easily analyzed by sociologists.

Introduction

In data mining research, time series represent an actual challenge due to the unique structure of this kind of data. Most classic data mining algorithms, which were initially conceived for classic (i.e. non temporal) data, do not work well for time series. The need to adapt data mining methods to time series has created a new field of research called temporal data mining [START_REF] Antunes | Temporal data mining: an overview[END_REF][START_REF] Lin | An overview of temporal data mining[END_REF].

Temporal data mining includes association rules [START_REF] Das | Finding similar time series[END_REF][START_REF] Das | Rule discovery from time series[END_REF], indexing (query by content) [START_REF] Keogh | Exact indexing of dynamic time warping[END_REF][START_REF] Yi | Efficient retrieval of similar time sequences under time warping[END_REF], feature mining [START_REF] Kudenko | Feature generation for sequence categorization[END_REF][START_REF] Lesh | Scalable feature mining for sequential data[END_REF], the discovery of recurrent or surprising motifs [START_REF] Buhler | Finding motifs using random projections[END_REF][START_REF] Chiu | Probabilistic discovery of time series motifs[END_REF][START_REF] Keogh | Finding surprising patterns in a time series database in linear time and space[END_REF][START_REF] Lin | Finding motifs in time series[END_REF], classification [START_REF] Chappelier | Time in connexionist models[END_REF][START_REF] James | A self-organizing feature map for sequences[END_REF][START_REF] Keogh | An enhanced representation of time series which allows fast and accurate classification, clustering and relevance feedback[END_REF][START_REF] Somervuo | Self-organizing maps and learning vector quantization for feature sequences[END_REF] and clustering [START_REF] Gaudin | Apprentissage non supervisé de séries temporelles à l'aide des k-means et d'une nouvelle méthode d'agrégation de séries[END_REF][START_REF] Lin | Learning clinical pathway patterns by hidden markov model[END_REF][START_REF] Lin | Iterative incremental clustering of time series[END_REF][START_REF] Oates | Clustering time series with hidden markov models and dynamic time warping[END_REF][START_REF] Vlachos | A Wavelet-Based Anytime Algorithm for K-Means Clustering of Time-Series[END_REF].

Time series clustering is a difficult field where numerous papers propose algorithms that work well with artificial data but they are not efficient in real-world dataset problems [START_REF] Keogh | On the need for time series data mining benchmarks: A survey and empirical demonstration[END_REF]. Time series clustering using Hidden Markov Models is proposed in [START_REF] Lin | Learning clinical pathway patterns by hidden markov model[END_REF][START_REF] Oates | Clustering time series with hidden markov models and dynamic time warping[END_REF]. Some approaches perform clustering using k-Means algorithm with Euclidean distance measure [START_REF] Lin | Iterative incremental clustering of time series[END_REF][START_REF] Vlachos | A Wavelet-Based Anytime Algorithm for K-Means Clustering of Time-Series[END_REF]. A time series clustering algorithm that uses k-Means with Dynamic Time Warping distance measure is proposed in [START_REF] Gaudin | Apprentissage non supervisé de séries temporelles à l'aide des k-means et d'une nouvelle méthode d'agrégation de séries[END_REF]. Although it is efficient with several artificial datasets, it does not work with real heterogeneous dataset like the one we have deal with.

Multivariate time series clustering is a more difficult issue where few methods and distances are already proposed. Traditional distances like Weighted Sum SVD [START_REF] Shahabi | Real-time pattern isolation and recognition over immersive sensor data streams[END_REF], Principal Component Analysis similarity factor (S PCA ) [START_REF] Krzanowski | Between-groups comparison of principal components[END_REF][START_REF] Singhal | Clustering of multivariate time-series data[END_REF] or Eros [START_REF] Yang | A PCA-based similarity measure for multivariate time series[END_REF] are only for numerical data with the same size. Moreover they are often too complex for large dataset and they are basically used for indexing process in databases (e.g. with k-Nearest Neighbors method). In another work, Lee et al propose a method to index sequences of multidimensional points [START_REF] Lee | Similarity Search for Multidimensional Data Sequences[END_REF]. They extend the ideas presented by Faloutsos et al. in [START_REF] Faloutsos | Fast Subsequence Matching in Time Series Databases[END_REF] and they use the Euclidean distance. Some works on indexing moving objects (i.e. bidimensional time series) are proposed in order to answer spatial proximity query [START_REF] Agarwal | Indexing moving points[END_REF][START_REF] Kollios | On Indexing Mobile Objects[END_REF][START_REF] Pfoser | Novel Approaches in Query Processing for Moving Objects[END_REF][START_REF] Qu | Supporting Fast Search in Time Series for Movement Patterns in Multiple Scales[END_REF][START_REF] Saltenis | Indexing the Positions of Continuously Moving Objects[END_REF]. Also in [START_REF] Vlachos | Robust similarity measures for mobile object trajectories[END_REF][START_REF] Vlachos | Discovering similar multidimensional trajectories[END_REF], an efficient indexing of trajectories is performed by Vlachos et al. using Longest Common Subsequence (LCSS) distance. For reasons that we explain in the next section, this method is relatively suitable for our issue. But Vlachos et al. are dealing with numerical data, so we have to make this distance work with heterogeneous data as well. Moreover this technique, and also all the others described above, has not been used for unsupervised clustering with algorithm such k-Means yet.

Our work is based on a study carried out by the French National Institute for Statistics and Economic Studies (INSEE). This study is trying to show how living in couples affects the view that handicapped people have on their lives. The dataset owns the result of a survey involving 8403 handicapped persons. For each year all along their life, they had to give a numeric estimation of the quality of their life, and at the same time they also noted down if they had a partner or not (Fig. 1). Sociologists need to know if it exists in this dataset some homogeneous classes of people according to its "couple status / life-quality estimation" behaviors. So we have a set of 8403 bi-dimensional and heterogeneous time series that we try to classify in an unsupervised way. The aim is that sociologists can work with our partitioning in order to bring out relevant categories of handicapped people. We can sum up the difficulties of our issue as follows:

-Bi-dimensional and heterogeneous data: Each handicapped person is represented by two time series; one numeric (the life quality estimation) and one symbolic (to have a partner or not). -Temporal gap: Different persons may have the same bi-dimensional pattern that occurs at different moments in time axis. The process has to match two same patterns despite the potential time axis gap. -Time series with very different size: Lengths of time series may vary between 2 and 80. The distance measure that we use must be able to manage these differences. -Unsupervised clustering: All the process must be automatic. This is more a data exploratory analysis than a machine learning problem. So firstly we have to choose an efficient distance measure, and then we have to develop an algorithm that uses the distance measure and performs the clustering in a satisfying way. In section 2, we present the LCSS distance and explain why it is efficient and how we adapt it for our bi-dimensional and heterogeneous issue. In section 3, we describe how we adapt the k-Means clustering algorithm with LCSS and get a complete clustering process. In section 4 we experiment our process on the dataset and present the results. We conclude in section 5.

Longest Common Subsequence Distance

Euclidean distance is the most widely used distance measure, even for calculating distances between data such as time series, because it is easy to compute and very fast. The operation consists in matching a given point from a time series with the point from another one that occurs at the same time. The main drawback of Euclidean distance is its inability to manage time axis gap. Two time series with the same shapes that do not occur concurrently on time axis may have a high Euclidean distance. This result is very illogical and it can significantly perturb the clustering [START_REF] Keogh | Scaling Up Dynamic Time Warping for Data Mining Applications[END_REF].

For the particular case of our dataset, we need a distance measure that is able to match some shapes that not occur at the same time. Indeed, some handicapped persons may have similar "couple status / life-quality estimation" patterns at different periods of their life. Among all the measures able to perform time series distance in this way, the Dynamic Time Warping (DTW) distance is the most popular. The particularity of DTW is that it compare two time series together by allowing a given point from one time series to be matched with one or several points from the other [START_REF] Berndt | Using Dynamic Time Warping to Find Patterns in Time Series[END_REF][START_REF] Sakoe | Dynamic programming algorithm optimisation for spoken word recognition[END_REF]. We choose not to use this distance for two reasons: Firstly, DTW manages only numeric time series. Its adaptation to symbolic data is not obvious and it includes some additional parameters that are difficult to fix. Secondly, DTW forces all elements of each time series to be matched, even if these elements do not have any relevant meaning. Typically for our dataset we have a lot of non relevant periods (e.g. when neither the life-quality appreciation nor the couple status changes for a handicapped person). The Longest Common Subsequence (LCSS) distance, like DTW, is a time stretching distance. It matches two time series together by allowing them to stretch, without rearranging the sequence of the elements [START_REF] Agrawal | Fast Similarity Search in the Presence of Noise, Scaling and Translation in Time-Series Databases[END_REF][START_REF] Bollobas | Time-Series Similarity Problems and Well-Separated Geometric Sets[END_REF][START_REF] Bozkaya | Matching and Indexing Sequences of Different Lengths[END_REF][START_REF] Das | Finding similar time series[END_REF]. Whereas in Euclidean and DTW distance all elements must be matched, LCSS can keep some elements unmatched by allowing one point of a time series to be matched with one or zero point of the other (Fig. 2).

In order to force time stretching not to match too distant elements, we may add to LCSS a warping window (i.e. a constant δ) that controls how far in time we can go in order to match two points from two different time series. For example, if we set δ = 3, a point that occurs at instant t must only be matched with points from the other time series that occurs at instants t-3, t-2, t-1, t, t+1, t+2 and t+3. In fact, δ is not inevitably a constant and may vary according to time [START_REF] Ratanamahatana | Making Timeseries Classification More Accurate Using Learned Constraints[END_REF], but for simplicity we consider δ to be a constant in this paper. Moreover, we have to set a spatial window (i.e. a constant ε) as a matching threshold that defines if two point from two different time series can be matched or not. LCSS distance gives in result a value between 0 (the two time series are perfectly similar) and 1 (no common points between the two time series).

Originally, LCSS is a one-dimensional distance for numeric data. So we have extended its definition to be able to manage time series with two heterogeneous dimensions (one numeric and one symbolic) as follow:

Let Let Equal(i, j) be the matching function between the i th point of A and the j th point of B, where:

     = ε ≤ - = else b a and b a if j i Equal yj yi xj xi False True ) , ( (1)
Given the recursive function Sim(i, j) that compute the similarity between the subsequence A i = {(a x1 , a y1 ), …, (a xi , a yi )} and the subsequence

B j = {(b x1 , b y1 ), …, (b xj , b yj )} as follows: { }          - - = δ ≤ - - - + = = = otherwise j i Sim j i Sim j i Equal and j i if j i Sim j or i if j i Sim ) 1 , ( ), , 1 ( max True ) , ( ) 1 , 1 ( 1 0 0 0 ) , ( (2)
We can now define our LCSS distance as follow:

{ } n m n m Sim B A LCSS , min ) , ( 1 ) , ( - = (3)
It's important to notice that LCSS is not a metric distance. Therefore it does not necessary respect the triangular inequality LCSS(A ,B) ≤ LCSS (A, C) + LCSS(C, B).

The recursive definition of our LCSS distance has a non computational complexity and needs a dynamic programming approach [START_REF] Bellman | Dynamic Programming[END_REF][START_REF] Berndt | Finding Patterns in Time Series: A Dynamic Programming Approach[END_REF]. Dynamic programming consists in creating a m×n matrix. Inside the cell (i, j) of the matrix we store 1 if Equal(i, j) = True, 0 otherwise. Once all the cells are filled we search for the best warping path. It is the path beginning in cell (1, 1), finishing in cell (m, n) that maximise the sum of the cells it goes through (Fig. 3). The sequence of cells crossing by the best warping path is (1, 1), [START_REF] Agrawal | Fast Similarity Search in the Presence of Noise, Scaling and Translation in Time-Series Databases[END_REF][START_REF] Bellman | Dynamic Programming[END_REF], [START_REF] Antunes | Temporal data mining: an overview[END_REF][START_REF] Bellman | Dynamic Programming[END_REF], [START_REF] Bellman | Dynamic Programming[END_REF][START_REF] Berndt | Using Dynamic Time Warping to Find Patterns in Time Series[END_REF], [START_REF] Berndt | Using Dynamic Time Warping to Find Patterns in Time Series[END_REF][START_REF] Bollobas | Time-Series Similarity Problems and Well-Separated Geometric Sets[END_REF], [START_REF] Bozkaya | Matching and Indexing Sequences of Different Lengths[END_REF][START_REF] Bozkaya | Matching and Indexing Sequences of Different Lengths[END_REF].

Actually, the non recursive algorithm we use to compute the LCSS distance in an optimal and efficient way does not search directly for the best warping path. It simply obtains the LCSS distance value thanks to a cumulative similarity matrix π built as shown in Table 1 (here, for simplicity there is no warping window, but the addition it is trivial to add it).

for i = 1 to m, do:

for j = 1 to n, do: if ( (i = 1 or j = 1) and Equal(i, j) = True ) then π ij = 1 if ( (i = 1 or j = 1) and Equal(i, j) = False ) then π ij = 0 if ( i > 1 and j > 1 and Equal(i, j) = True ) then π ij = π i-1,,j-1 + 1 if ( i > 1 and j > 1 and Equal(i, j) = False ) then

π ij = max{π i-1,,j , π i,,j-1 } { } n m B A LCSS mn , min 1 ) , ( π - =
Table 1. The non recursive algorithm that computes the LCSS distance between two bi-dimensional and heterogeneous time series A and B.

So the longer step of this algorithm is the completion of the cumulative similarity matrix. This step has a complexity of O(m×n) (O(m²) if the two time series have the same length). If we add a warping window with size δ, this algorithm allows to compute LCSS in O(m×δ) time (with δ << n).

The clustering process

The k-Means algorithm

A classic way to perform clustering is the use of the k-Means algorithm [START_REF] Mcqueen | Some Methods for Classification and Analysis of Multivariate Observation[END_REF]. This approach is very interesting for us because it generates "spherical" clusters (i.e. each cluster can be considered as a hypersphere inside the multidimensional data space. The center of the hypersphere is the fictive mean between all the objects owned by this cluster. The radius is the distance between the fictive mean and the furthest object in the cluster. Because of admitting relocation after each iteration, using k-means clustering allows poor initial partitions to be corrected at a later stage. So when the fictive mean moves, the sphere-shaped structure of the cluster is conserved and it keeps its homogeneity. This characteristic is empirically observed for non metric distances like LCSS. It permits the creation of homogeneous and proportional clusters that are, for our study, less sensitive to outliers than Hierarchical Clustering clusters. The intuition behind k-Means approach is shown in Table 2.

1 Decide on a value for k. 2 Initialize the k cluster centres (randomly, if necessary).

3

Decide the class memberships of the N objects by assigning them to the nearest cluster centre.

4

Re-estimate the k cluster centres, by assuming the memberships found above are correct.

5

If none of the N objects changed membership in the last iteration, exit. Otherwise return to step 3.

Table 2. K-Means algorithm

To resolve our catalysis clustering problem, the k-Means approach has one major drawback: At step 4, the algorithm has to re-estimate the k cluster centers. This means computing the average of all the time series for each cluster in the multidimensional data space. This is straightforward with non temporal data (we just have to compute the Euclidean average) but illogical for temporal data like time series. We will resolve this difficulty with by using a variant of this algorithm proposed by Didey [START_REF] Diday | The dynamic clusters method in non hierarchical clustering[END_REF].

Using k-Means with LCSS distance

K-Means algorithm is a variant of the Forgy algorithm [START_REF] Forgy | Cluster analysis of multivariate data: efficiency versus interpretability of classification[END_REF]. The Forgy algorithm resumes the basic intuition behind all partitional clustering algorithms like k-Means. It creates clusters with only two parameters: the number of clusters noted k and the size of seeds noted c. For the reasons explained in the previous section, the distance measure used by our method is LCSS, so we have adapted this algorithm to make time series clustering work with this distance (Table 3).

Each cluster is characterized by a seed of c time series. Seeds are used to compute distances between time series and clusters as well as distances between each cluster. The c times series of a cluster are those that minimize the Inertia function. This function is also used to compute the intra-class variance between all clusters that evaluates the quality of the clustering.

The exact complexity of this algorithm ca not be determined because it depends on the relative size of each cluster during the iterations. However, for a dataset of N time series, it has a complexity inferior or equal to O( kPL.(N² + N) ), where k is the number of clusters specified by the user, P is the number of iterations until convergence, and L is the duration of one LCSS calculation (i.e. O(m×δ)).

It is obvious that the final time series clustering depends on the seeds initialization. Ideally, each seed should be initialized only with the time series that belong to the same cluster, but if we do not have any a priori knowledge about the dataset (as it is usually the case in unsupervised knowledge data discovery), we have to initialize the seeds at random. For a dataset with k time series clusters (with the same number of time series for each cluster), the probability to have a perfect initialization at random is approximately equal to k k ! k (for example if k = 6 then the probability is equal to 0.015, i.e. 1 in 65 to have a perfect initialization). Here we use intraclass variance to evaluate the quality of the seeds initialization: if a seed initialization does not give an intraclass variance inferior to a threshold, then another initialization is tried. 1 Let X be a set of N time series that we aim to split in k clusters, where X = {x 1 ,…,x n ).

2

Let S be a set of k seeds, where S = {S 1 , …, S k }. Each seed S j is composed of c time series chosen among the initial set X (randomly if necessary). One time series ca not belong to more than one seed.

3

Given L(c, S j ), the distance between the time series x i and the seed S j as follows:

∑ ∈ = j S y i j i y x LCSS c S x L ) , ( 1 )
, ( 4For i = 1,…, N do:

For j = 1,…, k do: Compute L(x i , S j ) 5

Assign to each time series x i its nearest seed (i.e. the seed S j that minimize L(x i , S j )). Because of the nature of our data, we do not use a temporal window because similar patterns that we search in two handicapped person can occur anywhere in time axis. So it leaves us only with three parameters: the number of clusters k, the size of seeds c and the spatial window ε for LCSS.

Only the numeric variable of our bi-dimensional time series needs the ε parameter. This parameter must be fixed by user according to the maximum difference that he considers that two persons have the same life estimation.

We notice that the value of c does not influence the intra-class variance defined in our algorithm (contrary to δ and k). So we can consider that the optimal value of c minimizes this variance.

We ca not use the same method to find the optimal value of k because this parameter influences the intra-class variance final value (the more k increases, the more the intra-class variance decreases). This limitation can be minimized by attempting all values of k within a large range.

Application to handicapped people dataset

We apply our algorithm on our handicapped people dataset. We split the data in two parts according to sex (i.e. one part with 4617 women and one part with 3786 men). Sociologists need to know if the "direct link" hypothesis (i.e. to have a partner implies an increase of life-quality estimation for handicapped people) is valid or not. Results of our process give, for each sex, surprising clusters that contradict this expectation. In spite of the very large multiplicity of patterns, we are able to bring out some homogeneous classes, in particular if we cluster the dataset with k = 4 (Table . 4).

The first surprising fact that we notice is the quasiperfect symmetry between the two sexes. The difference between the proportional cluster sizes for the two sexes is always inferior or equal to 1 %. That logically means that living in couples affects in the same way the view that handicapped men and women have on their lives.

The other surprising fact is the frequency of handicapped people that have no variation of their lifequality estimation in spite of their couple-status change (72 % for men and 73 % for women). The second largest cluster is composed of people without a couple-status change. People that directly relate life quality with couple status (i.e. to find a partner implies a life quality increase) are in the third cluster. With a frequency of 6 % for the two sexes, this cluster is surprisingly small. In the same way, the cluster with people that have an opposite relation between the two variables is relatively insignificant (3 % for each sex).

As a conclusion, contrary to what sociologists expect, we can consider that living in couples (or not) is not a determinant variable to explain the increase (or the decrease) in the life quality estimation of handicapped people. This conclusion may be an important decision factor for future assistance programs towards handicapped people.

M W

General tendency 72% 73% 19% 18% 6% 6% 3% 3% Table 4. The clustering result of the handicapped people dataset (with k = 4). The first and the second columns give the proportional size of each cluster for handicapped men (M) and women (W) respectively. Because of the very large multiplicity of patterns, we only show here for each cluster the main pattern that is the most representative of the general tendency of the cluster.

Conclusion

In this paper we present an exploratory analysis on a survey with 8403 handicapped persons. This dataset needs a methodology that is able to manage bi-dimensional, heterogeneous, with different size and temporal gap data. The approach we propose is based on the k-Means algorithm and the Longest Common Subsequence distance. We adapt the LCSS distance to bi-dimensional and heterogeneous data, and adapt the k-Means algorithm to be able to support this distance measure. The results obtained by our process are pertinent and surprising. They can be easily analyzed by sociologists in order to assist them in their work.

Figure 1 .

 1 Figure 1. Example of a bi-dimensional time series representing a handicapped person.

Figure 2 .

 2 Figure 2. Computation of the distance between two time series with Euclidean distance (fig. A) and LCSS distance (fig. B).

  A and B be two bi-dimensional time series with size m and n respectively, where A = {(a x1 , a y1 ), …, (a xm , a ym )} and B = {(b x1 , b y1 ), …, (b xn , b yn )}. a xi and b xi are the i th value of the numeric time series of A and B respectively. a yi and b yi are the i th value of the symbolic time series of A and B respectively.

Figure 3 .

 3 Figure 3. Example of best warping path between two time series A = {1, 2, 4, 3, 1, 1, 2, 1} and B = {1, 1, 1, 2, 4, 3, 1, 1}.The sequence of cells crossing by the best warping path is (1, 1),[START_REF] Agrawal | Fast Similarity Search in the Presence of Noise, Scaling and Translation in Time-Series Databases[END_REF][START_REF] Bellman | Dynamic Programming[END_REF],[START_REF] Antunes | Temporal data mining: an overview[END_REF][START_REF] Bellman | Dynamic Programming[END_REF],[START_REF] Bellman | Dynamic Programming[END_REF][START_REF] Berndt | Using Dynamic Time Warping to Find Patterns in Time Series[END_REF],[START_REF] Berndt | Using Dynamic Time Warping to Find Patterns in Time Series[END_REF][START_REF] Bollobas | Time-Series Similarity Problems and Well-Separated Geometric Sets[END_REF],[START_REF] Bozkaya | Matching and Indexing Sequences of Different Lengths[END_REF][START_REF] Bozkaya | Matching and Indexing Sequences of Different Lengths[END_REF].

6 LetC 7

 67 be a set of k clusters, where C = {C 1 , …, C k }. Each cluster C j is made of all time series that have S j as nearest seed.Redefine a new set of seeds S' = {S' 1 , …, S' k }. Each new seed S' j is made of the c time series x i from C j that minimize: clustering quality, calculate the intra-class variance Var(C) as follows: of Var(C) does not decrease between the iteration p and the iteration p+1 (or decrease less than an arbitrary threshold), then stop the process. Else restart a new iteration at step 4 with S = S'.

Table 3 .

 3 Didey's k-Means generalization with LCSS distance


Sexual Identities, What Are They Made Of? Constructionism, Essentialism, Materialism

Keywords:

The question I would like to discuss today is: what are the elements in Foucault's work that may help us to understand the historical and current transformations of sexual identities? I will discuss this question as a social scientist. The political question would be: should we try to understand the transformation of sexual identities? Should we transform sexual identities? My point today is not political but scientific.

To handle this question, I will start with Didier Eribon's important study: "Réflexions sur la Question Gay" 1 , that opened our eyes on the multiplicity of Foucaults. Eribon distinguishes three Foucaults: the one of Madness and Civilization, the one of The History of Sexuality Vol.

I, and the one of The History of Sexuality Vol. II and III.

Let me briefly describe these three Foucaults.

In Madness and Civilization (1962) 2 , Foucault adopts a rather traditional periodization of sexual transformation. For him the main break took place during the 17 th century, when speech got controlled, some speech inhibited, and the speechless confined. This periodization is in line with the Weberian tradition. I may just remind you of the writings of Norbert Elias 3 1 Eribon D.

and Philippe Ariès4 who, a few years before Foucault, developed similar theories on subjects including sexuality. They adopted the same periodization and, moreover, laid emphasis on the same speech control process.

The specific contribution of Foucault is his concept of speech restriction coming from above whereas the Weberian tradition considered it to be a bottom up movement; some kind of a surviving strategy under new political and social conditions. Foucault opposed a type of speech restriction that is closely related to confinement, both being directed top down.

Foucault replaces the dialectical model of opposing forces by a structuralist mono-directional model. This brings us to the second Foucault.

In The History of Sexuality Vol. I5 , Foucault maintains the top-down controlled model of sexual construction, but he changes the mechanism: he no longer considers speech to have been restricted, on the contrary, he thinks it has been encouraged and urged on. Restriction becomes production. Consequently, the notion of sexual repression is replaced by the notion of sexual incitation, including the "implementation of perversions". The top-down model of sexual construction gets exclusively discursive: repression and enclosure are no longer determinant, changing discourses become the main force behind the emergence of new sexualities. And of all discourses, the medical one is predominant. This also changes the periodization. The main break no longer occurred in the 17 th but in the 19 th century. Speaking out, and coming out, become part of the top-down model of discursive control.

On the third Foucault I will be brief. Volumes II and III of The History of Sexuality 6 move away from the question of how sexual transformation occurs in society. These volumes explore moral issues and describe how ancient and early Christian societies considered sexuality, not how this sexuality was constructed. Eribon understands this turn to ethics as the consequence of a totally different concept of sexual history. Foucault would have moved to an essentialist point of view: sexual construction would have been more or less constant in history; only the way people think of it, its moral organization would have changed.

Eribon may be right, but I think we should understand Foucault's third attitude more cautiously as the scrupulous application of Boswell's agnostic hypothesis 7 on the biological, psychological or social determinants of sexual orientation. An agnosticism that includes the possible historicity of sexuality. Indeed, if we don't know how sexuality is constructed, how much is biological, psychological or social, then we are equally ignorant on the question of how much is historical and even if there is any history in it at all. I will come back to this later. Let us just conclude on the third Foucault that his ethical turn may be consistent with an essentialist view of unhistorical sexuality.

Let us come back to the question: how can Foucault help us to understand the historical and current transformations of sexual identities? To deal with this very broad issue, I would like to highlight five aspects.

-Consciousness.

Sexuality is made up of many different elements: physical attraction, fantasies, preferences, practices, self-identification. One of the aspects that differentiate these elements is their 6 Foucault M. (1984), Histoire de la sexualité, II, L'Usage des plaisirs, Paris, Gallimard Foucault M. (1984), Histoire de la sexualité, III, Le souci de soi, Paris, Gallimard 7 Boswell J. (1990), « Categories, Experience and Sexuality », in E. Stein (1990), Forms of Desire, Sexual Orientation and the Social Constructionist Controversy, NY & London, Garland Publishing, pp. 133-173 degree of consciousness. Physical attraction is generally admitted to be beyond conscious control. It seems to come to us from the outside, sometimes against our will. We don't control physical attraction. On the other extreme, self-identification always is a conscious act. It looks like it is coming from the inside. Yet, we are not free to choose whatever self-identification we would like to adopt.

In reality, all the elements making up sexuality are produced by ourselves, come "from the inside". And yet, none of them is a conscious, free decision. Sexuality is made up by ourselves, but predominantly as an unconscious construction.

The concept of a predominantly unconscious sexuality, of course, goes back to Freud.

Foucault took it in its Lacanian, i.e. linguistic form. According to Lacan, the unconscious is a language. As a result, sexuality, as far as it is unconscious, is a linguistic construction. That is how Foucault may bring back sexual changes to discursive changes.

On the other hand, Foucault also taught us that language is not only powerful but at the same time an object of power. We saw before that the second Foucault modified the first one on the mechanisms through which power organizes the symbolic sphere (exhortation of speech instead of prohibition of speech). Both though, hold on the idea of power relationships organizing the symbolic sphere, and thereby the range of possibilities available for construing one's sexuality. By analyzing the role of power relationships, Foucault showed us the political character of the construction of unconscious sexual identities. The essentialist-constructionist debate sometimes forgot this unconscious dimension of the sexual construction. Too often, it focused on the conscious part of the construction: the way we have, individually and socially, built up gay and straight identities, lifestyles and cultures. As if sexual construction started after sexual attraction, desire, fantasies already having been constructed. The construction Foucault wrote about was exactly the construction of this sexual desire. I think it is important to come back to this concept of sexual construction as an unconscious, nonetheless political process. Even if the third Foucault seems to have moved away from it.

-Permanence.

Remember: homosexuality does not exist, only homosexual acts exist. It was one of the slogans of the Sexual Liberation Movement. The point really was: are sexual attractions, preferences, practices, etc. isolated events in someone's life, or are they all somehow related? Without it being perfectly constant, is there some permanence in someone's sexuality?

As many others at that time, Foucault may say: "Why every day life, every one's life, couldn't become a piece of art?" 8 . This is the "moral" Foucault, the one who thinks of what the future could look like. Not the one who analyses the History of Sexuality, the "implementation of perversions" that he thought of as a real "incorporation", a real construction of the sexual identity. An identity that is with us from day to day, that changes with new experiences, but only slowly and within limits that we are not as free to trace as we would like to.

There have been permanent efforts to intervene deliberately in people's sexual identity. The last reported is Robert Spitzer's "reparative therapy". 9 He claims results where many others failed. All of these therapies are based on voluntary intervention. But even with the subject's cooperation most efforts fail. This does not mean that sexual orientation/identity does not change. It means that as a rule permanence is stronger than change. It also means that possible change is a process that offers very little grip for conscious intervention. Foucault's injunction did not mean to support these therapeutic interventions. It means to stress the variety of sexual orientations/identities against too rigid categorization. Variety yes, but not fugitivity. 10 8 Foucault M., Dits et écrits, t. 4, Paris, Gallimard, p. 392. 9 Spitzer R. L. ( 2003), « Can Some Gay Men and Lesbians Change Their Sexual Orientation ? 200 Subjects Reporting a Change from Homosexual to Heterosexual Orientation », Archives of Sexual Behaviour, vol. 31, n° 5. 10 Even radical constructionists like Judith Butler agree there is permanence and unconsciousness in sexual identities: "For sexuality cannot be summarily made or unmade, and it would be a mistake to associate 3 -Exclusiveness.

Do

sexual attractions/preferences/practices exclude other sexual attractions/preferences/practices? In other words, do some preferences exclude others? In its literal form, the answer is tautologically affirmative. Preferential choice means something has been declassified as not preferential. The exclusiveness may be better formulated as follows:

can one be preferenceless? Can one be something like total pervert?

Sometimes bisexuality is supposed to be some kind of lack of preference. It may be admitted

for young children, it may be showed off as the ultimate goal of sexual liberation, but it is not considered as a "real" sexual orientation/identity, because we think it lacks exclusiveness. In reality, there is no reason to suppose bisexuals are attracted to all men and women as there is no reason to suppose homosexual men/women are attracted to all men/women. Gender choice is just one of the many features making up someone's sexual identity. 11 Here again, the moral Foucault may have claimed the multiplicity of sexual relations as part of tomorrow's liberty.

Yet, the analytical Foucault will certainly agree with Eribon, when he states that today's gays and straights will not all be bisexuals tomorrow.

Undoubtedly, exclusiveness is part of our sexual identity. Yet, exclusiveness may be more or less powerful and, most of all, it may fix on features that are not the same for everyone. The more exclusive a feature, the more any possible sexual partner that does not correspond to this feature is excluded.

The exclusive force is not just lack of interest. It is physical aversion, that is hard to overcome. As physical aversion it is part of someone's sexual orientation. It is the negative "constructivism" with "the freedom of a subject to form her/his sexuality as s/he pleases."" Butler J. (1993), Bodies that matter, New York, Routledge, p. 94.

11 Stein (1990), op. cit., distinguishes sexual orientation and sexual preferences, the former being reserved to gender choice, the latter to all other features that make up the sexual identity. Gender certainly is a particular feature. Especially in a society where gender roles are defined in a mutual contrast. Nevertheless, bisexuals are there to remind that remind that gender choice is only one of the features making up sexual identities. There is no reason to separate fundamentally sexual orientation and sexual preference.

side of it. If we take the example of gender choice, then we can say that homo-aversion is part of the exclusive heterosexual orientation as hetero-aversion is part of the exclusive homosexual orientation. But we must recall immediately that gender choice is only one of the possible exclusive features, along with age, size, corpulence, and innumerable other physical and psychological features, that we will never get to know in all details, not even for our own sexuality. The point I want to make here is that these features are as various and forceful in aversion as in attraction.

The world would have been a better one if we were able to develop preferences and remain neutral towards everything and everyone else. Unfortunately, the same process that creates attraction creates aversion. Sexual preferences tend to be exclusive in the way that they are made of practices and people we feel attracted to and others that repel us, that we exclude of our sexuality. Exclusiveness is the dimension that goes from attraction to aversion, passing through all thinkable intermediate feelings.

-Historicity.

Historicity certainly is one of the main topics in Foucault's work. It is also a topic Foucault has repeatedly changed his point of view on.

When he starts developing his thesis on the emergence of the homosexual in the 17 th century, he is close to Philippe Ariès. Foucault's emergence of homosexuality is not very different from Ariès's emergence of childhood. The central point in either concept of emerging new historical figures is the historicity, from a social perspective, of something that the individual experiences as unhistorical and essentialist.

Indeed, historicity is what is really at stake in the essentialist-constructionist debate. And all debaters try to combine the essentialist evidence at the individual level with the constructionist evidence at the historical level. For most of them, the solution is to introduce a dichotomy in the concept of sexuality itself. Robert Padgug: " "Homosexual" and "heterosexual" behavior may be universal; homosexual and heterosexual identity and consciousness are modern realities." 12 John Boswell: "Does the historical record in fact suggest that premodern patterns of sexuality are fundamentally different from modern ones?

[...] Yes and no. [Yes for] public discourse [that is] markedly different from its modern descendants." 13 No for sexuality itself that may well have been constant in history.

Anthropologists like James Weinrich make the same distinction between "real" sexuality and its social construction 14 . From the resemblances between berdaches, hijras and drag queens, three different "social constructions", he concludes there must be some unhistorical, biological reality of human sexuality behind these historical manifestations.

The examples are numerous. They all start from the concept of sexuality as a two-storey building: a social first floor on a biological basement. There is nothing wrong with this Formulated as a methodological stance, it starts as a supposition but will never be refuted. In Boswell's words: "supposition that there have been in all Western societies "gay people" and The debate on sexual identities that has been going on over the last decades and to which Foucault has contributed more than any other philosopher, has clarified some aspects, at least to me.

Sexuality cannot be conceived as a mere question of lifestyle based on self-identification. We have to recognize its unconscious and involuntary basement made of multiple desires but also of multiple aversions. Moreover, desire and aversion form some kind of coherent entity that we may call identity. This definition of identity, far from being simple and unshakable, nevertheless includes a part of permanence, of continuity. It is radically different from selfidentification, because it is unconscious and involuntary.

I agree with Butler that this identity must be considered as individually constructed in a historical environment. But unlike Butler, I think we must consider it as material. Individually constructed, but not produced, not generated out of nothing. Desire and aversion have some kind of materiality. Unshaped, amorphous, perhaps, but not optional. The construction of desire and aversion is to be seen as a shaping, a modeling more than a creation. And this construction is historical because it uses a historical context. In other times, I would have concluded by saying that sexual constructionism surely is a form of historical materialism.

  distinction. The question is: what do we put in the unhistorical basement and what on the historical first floor? Padgug, Boswell and Weinrich put the sexual orientation in the unhistorical basement.

  Sexual Landscapes : Why We Are What We Are, Why We Love Who We Love, NY, Charles Scribner's Sons 15 Boswell J. op. cit. P; 137, 172 dichotomy allows to hold on an essentialist concept of sexual attractions and aversions together with a historical concept of sexual lifestyles and self-identification. Surprisingly, "constructionist" debaters may end up with the same kind of dichotomy. Didier Eribon: "One of the definitions that I give of homosexuality ...: a gay or a lesbian is someone who ... has been or knows he/she may be insulted."16 According to this rather uncommon definition, the homosexual identity has no relation at all to physical attraction, preference, orientation or activity. It is reduced to consciousness. It starts with the stigma.Eribon may have good arguments to reduce sexuality to consciousness, but as a logical consequence he must think of a new term for all that is left over: physical attraction, orientation and/or activity. Eribon calls this "gay infancy". It includes all attraction to one's own sex that seems to come to us, whether we like it or not. Eribon's distinction between gay sexuality and gay infancy, does it repeat Padgug's distinction between behavior and identity? She would refute the dichotomy because, to her, as to Lacan, sexual desire itself is constructed. By entering the intelligible world, through a series of identifications and foreclosures, every child constructs its sexual identity together with its social and psychological identity. In this view, there is no place left for universal behavior or naturally structured desire. All sexuality becomes socially constructed, not in the public sphere of lifestyles and stigmatization, but first of all in the private sphere of family-life. And since this private sphere of family-life is itself obviously historical, sexuality cannot be but historical.Paris, Fayard, p. 66 Evidently, Butler's reading of Foucault is right for the first and second Foucault. We are not sure about the third Foucault. Boswell's work on ancient homosexuality seems to have convinced Foucault. In an interview in 1982, he states: "Homosexual conscience definitely goes beyond the individual experience, it includes the feeling to be part of a particular social group. This is an irrefutable fact that goes back to very ancient times." 17 Conclusion: about sexual materialism.

	non-gay people" … [supposition] that the rough proportions of Kinsey … were the same in most populations" 15 . If sexual attraction, preferences, and orientation are unhistorical, what is left over to be historical? For "essentialist" historians like Boswell historicity is limited to the way sexuality is appreciated, positively or negatively, and the way it is organized in lifestyles. The 12 Padgug R. (1979), « Sexual Matters : On Conceptualizing Sexuality in History », Radical History Review, 20, pp 3-23. 13 Boswel J. op. cit. historical? Other constructionists, like Judith Butler, would definitely consider gay infancy as historically 14 Weinrich J. (1987), Or Weinrich's reality and social construction? Gay infancy, is it not constructed, not constructed.

16 Eribon D. (2000)

, Papiers d'identité. Interventions sur la question gay,

Ariès Ph. (1960), L'enfant et la vie familiale sous l'ancien Régime, Paris, Plon. He writes : « Attitudes towards sexuality, and sexuality itself, vary with the environment and consequently with the periods and the mentalities." (p. 145)

Foucault M. (1976), Histoire de la sexualité, I, La Volonté de savoir, Paris, Gallimard