Mapping text document into LDA-based topic-space is a classical way to extract high level representation of text documents. Unfortunatly, LDA is higly sensitive to hyperparameters related to class number or word and topic distribution, and there is not any systematic way to prior estimate optimal configurations. Morover, various hyperparameter configurations offer complementary views on the document.

In this paper, we propose a method based on a two-step process that, first, expands representation space by using a set of topic spaces and, second, compacts representation space by removing poorly relevant dimensions. These two steps are based respectivelly on multi-view LDA-based representation spaces and factor-analysis models. This model provides a view-independant representation of documents while extracting complementary information from a massive multi-view representation.

Experiments are conducted on the DECODA conversation corpus and Reuters-21578 textual dataset. Results show the effectiveness of the proposed multi-view compact representation paradigm. The proposed categorization system reaches an accuracy of 86.9% and 86.5% respectively with manual and automatic transcriptions of conversations, and a macro-F1 of 80% during a classification task of the well-known studied Reuters-21578 corpus, with a significant gain compared to the baseline (best single topic space configuration), as well as methods and document representations previously studied.

Index Terms-Latent Dirichlet Allocation, Factor analysis, Cvector, Classification

I. INTRODUCTION

One of the most efficicent way to process noisy text documents consists in mapping word-level surface forms into semantic spaces, where documents are represented by meaningfull abstract features.

Numerous unsupervised methods for topic-space estimation were proposed in the past, mostly based on the extaction of interesting regularities in huge text corpus. The Latent Dirichlet Allocation (LDA) [START_REF] Blei | Latent dirichlet allocation[END_REF] was largely used for text mining, speech analytics or information retrieval tasks; one of its main drawbacks is the tuning of the model, that involves various meta-parameters such as the number of classes (that determines the model granularity), word distribution methods, Manuscript received December 1, 2012; revised December 27, 2012. Corresponding author: M. Morchid (email: mohamed.morchid@univ-avignon.fr). temporal spans. . . Performance of systems that use topic models can then be quite unstable if the decision process is highly dependent on these meta-parameters.

Classically, this abstract representation involves the selection of a number of classes composing the topic space (n) as well as the LDA hyper-parameters (α and β). The hyperparameters α and β control both the topic distribution for each document and the word distribution into each class of the topic space itself. The number of classes n contained into the topic space control the "granularity" of the model from a general topic-based representation (few number of classes into the model) to a relatively precise representation (large number of classes). Finding the optimal parameters is crucial since topic model perplexity, that expresses its quality, is highly dependent to these features. Moreover, the multitheme context of the proposed study implies a more complex dialogue representation [START_REF] Morchid | Improving dialogue classification using a topic space representation and a gaussian classifier based on the decision rule[END_REF].

In this paper, we tackle these two drawbacks by using multiple topic spaces obtained by varying the LDA hyperparameters α, β and the topic number n. Each of these space offers a specific view on the documents and our goal, at this point, is to extract relevant and complementary information for the large set of diferent views. A potential issue with such a massive multi-view approach is due to the diversity of views, wich introduces both a relevant variability needed to represent different contexts of the document, and a noisy variability related to topic spaces processing. Thus, a topicbased representation of a document is built from the document content itself and the mapping process of a document into several topic spaces generates a noisy variability related to the difference of the document and each class content. In the same way, the relevant variability is from the common content between the document and the classes composing the topic space.

We propose to reduce this noisy variability by compacting multiple views of documents using factor analysis technique. Factor analysis is a very old data-analysis method that was successfully applied fisrt to speaker identification and, latter, generalized to various speech and audio categorization tasks.

In this field, the factor analysis paradigm is used as a decomposition model that enables to separate the representation space into two subspaces containing respectively useful and useless information. The general Joint Factor Analysis (JFA) paradigm [START_REF] Kenny | A study of interspeaker variability in speaker verification[END_REF] considers multiple variabilities that may be crossdependent. Thereby, JFA representation allows to compen-sate the variability within sessions of a same speaker. This representation is an extension of the GMM-UBM (Gaussian Mixture Model-Universal Background Model) models [START_REF] Reynolds | Robust text-independent speaker identification using gaussian mixture speaker models[END_REF]. The authors in [START_REF] Dehak | Frontend factor analysis for speaker verification[END_REF] extract, from the GMM super-vector, a compact super-vector called an i-vector. The aim of the compression process (i.e. i-vector extraction) is to represent the supervector variability in a low dimensional space. Although this compact representation is widely used in speaker recognition systems, this method has been little used in the field of text classification.

In this paper, we propose to apply factor analysis to compensate noisy variabilities due to the multiplication of LDA models when varying all LDA hyper-parameters. We also propose to evaluate this approach on two different classification tasks using respectively automatic transcriptions, obtained from an Automatic Speech Recognition (ASR) system, and usual textual documents. Two classification tasks are then considered: the theme identification of RATP call centre (Paris Public Transportation Authority) dialogues [START_REF] Bechet | Decoda: a call-centre human-human spoken conversation corpus[END_REF] and the Reuters-21578 (ModApte split) classification task [START_REF] Asuncion | Uci machine learning repository[END_REF].

The intuition behind this study is that varying LDA hyperparameters α and β should allow us to obtain an optimal topic-based representation of the document, while the multiple views of a given document are obtained by varying the number of classes into the topic space. Indeed, when one varies LDA hyper-parameters, the topic space structure is not deeply modified, which is the case when the number of classes is changed.

Furthermore, a normalization approach to condition document representations (multi-model and i-vector) is proposed. The two methods showed improvements for speaker verification: within Class Covariance Normalization (WCCN) [START_REF] Dehak | Frontend factor analysis for speaker verification[END_REF] and Eigen Factor Radial (EFR) [START_REF] Bousquet | Intersession compensation and scoring methods in the i-vectors space for speaker recognition[END_REF]. The last one includes length normalization [START_REF] Garcia-Romero | Analysis of i-vector length normalization in speaker recognition systems[END_REF]. Both of these methods dilate the total variability space as the mean to reduce the within class variability. In our multi-model representation, the within class variability is redefined according to both document content (vocabulary) and topic space characteristics (words distribution among the topics). Thus, the speaker is represented by a theme, and the speaker session is a set of topic-based representations (frames) of a document (session).

The paper is organized as follows. Section II presents previous related works. The document representation is described in Section III. Section IV introduces the i-vector compact representation and presents its application to text documents. Sections V and VI report experiments and results. The last section concludes and proposes some perspectives.

II. RELATED WORK

Considerable research have been proposed to combine topic related information with n-gram models [START_REF] Bellegarda | Exploiting both local and global constraints for multi-span statistical language modeling[END_REF], [START_REF] Clarkson | Statistical language modeling using the cmu-cambridge toolkit[END_REF], [START_REF] Iyer | Relevance weighting for combining multidomain data for¡ i¿ n¡/i¿-gram language modeling[END_REF], [START_REF] Kneser | Language model adaptation using dynamic marginals[END_REF]. The basic idea of these approaches is to exploit the differences of word n-gram distributions across topics. That is, first the whole training data is separated into several topic-specific clusters, and then topic-specific LM are built using the topicspecific data. One problem of this approach is data fragmentation, which results in the data sparseness problem. In order to remedy the data sparseness problem, linear interpolation (or LM mixture) has been applied.

Several methods have been proposed considering that word n-grams have different word probability distributions in different topics and represent a document with a mixture of topic language models. These methods demonstrated their performance on various tasks, such as sentence [START_REF] Bellegarda | Exploiting latent semantic information in statistical language modeling[END_REF] or keyword [START_REF] Suzuki | Keyword extraction using term-domain interdependence for dictation of radio news[END_REF] extraction.

Considering documents as bags-of-words [START_REF] Salton | Automatic text processing: the transformation[END_REF], Latent Dirichlet Allocation (LDA) [START_REF] Blei | Latent dirichlet allocation[END_REF] was proposed as a new method for obtaining word probabilities as mixtures of word distributions in hidden topics. PLSA and LDA models have been shown to generally outperform LSA on IR tasks [START_REF] Hofmann | Unsupervised learning by probabilistic latent semantic analysis[END_REF]. Furthermore, probabilities of a hidden topic given a document can be computed with LDA providing topic classification features that capture word dependencies related to the semantic contents of a given conversation.

Supervised LDA [START_REF] Rubin | Statistical topic models for multi-label document classification[END_REF] has been proposed in the context of multi-label topic classification to estimate word and topic label probabilities given a training corpus annotated with-label data. In all the approaches considered above, the choice of the number of topics is empirical. Many studies have proposed suggestions for solving this problem. Authors in [START_REF] Arun | On finding the natural number of topics with latent dirichlet allocation: Some observations[END_REF] proposed to use a Singular Value Decomposition (SVD) to represent the words of the vocabulary. This method has to be evaluated with the Kullback-Liebler divergence metric for each topic space. It is not rigorous and time consuming.

Authors in [START_REF] Teh | Sharing clusters among related groups: Hierarchical dirichlet processes[END_REF] proposed to use a Hierarchical Dirichlet Process (HDP) method to find the "right" number of topics by assuming that the data have a hierarchical structure. In [START_REF] Zavitsanos | Determining automatically the size of learned ontologies[END_REF], authors presented a method to learn the right depth of an ontology depending of the number of topics of LDA models. The study presented by [START_REF] Cao | A density-based method for adaptive lda model selection[END_REF] is quite similar to [START_REF] Teh | Sharing clusters among related groups: Hierarchical dirichlet processes[END_REF]. The authors consider as the right number of topics, the average correlation between pairs of topics at each stage of the process. All these methods assume that a document can have representations in only one hidden space which is limited by the fact that classes of a LDA hidden space are correlated [START_REF] Blei | Correlated topic models[END_REF]. Moreover, authors in [START_REF] Li | Pachinko allocation: Dag-structured mixture models of topic correlations[END_REF] consider a class as a node of an acyclic graph and as a distribution over other classes contained in the same topic space.

We proposed some studies to show the contribution of a compact dialogue representation from multiple views, based on the i-vector framework [START_REF] Morchid | I-vector based approach to compact multi-granularity topic spaces representation of textual documents[END_REF], [START_REF]I-vector based representation of highly imperfect automatic transcriptions[END_REF]. In [START_REF] Morchid | I-vector based approach to compact multi-granularity topic spaces representation of textual documents[END_REF], we proposed to represent a dialogue in a set of topic spaces learned from a LDA algorithm, by varying the number of classes contained into the LDA topic space. Then, this multiple representation of the dialogue is compacted with the use of the i-vector framework. We proposed in [START_REF]I-vector based representation of highly imperfect automatic transcriptions[END_REF] to learn a set of LDA topic spaces by varying the α hyper-parameter, which controls topic distribution for each document contained into the training corpus as well as the documents contained into the validation set. This last distribution is obtained during the inference process with the use of the Gibbs Sampling algorithm [START_REF] Griffiths | Finding scientific topics[END_REF]. These studies evaluate the impact of LDA hyper-parameters separately and use only noisy transcriptions (dialogues) obtained from an automatic speech recognition system (ASR).

III. MULTI-VIEW REPRESENTATION OF DOCUMENTS IN A HOMOGENEOUS SPACE

The approach considered in this paper focuses on modeling the variability between different documents expressing the same theme t 1 . For this purpose, it is important to select relevant features that represent semantic contents for the theme of a document. An attractive set of features for capturing possible semantically relevant word dependencies is obtained with LDA [START_REF] Blei | Latent dirichlet allocation[END_REF], as described in Section II.

Given a training set of conversations D, a hidden topic space is derived and a conversation d is represented by its probability in each topic of the hidden space. Estimation of these probabilities is affected by a variability inherent to the estimation of the model parameters. If many hidden spaces are considered and features are computed for each hidden space, it is possible to model the estimation variability together with the variability of the linguistic expression of a theme by different speakers in different real-life situations. Even if the purpose of the application is theme identification and a training corpus annotated with themes is available, supervised LDA [START_REF] Griffiths | Finding scientific topics[END_REF] is not suitable for the proposed approach. LDA is used only for producing different feature sets involved in statistical variability models.

In order to estimate the parameters of different hidden spaces, a set of discriminative words V is constructed as described in [START_REF] Morchid | Improving dialogue classification using a topic space representation and a gaussian classifier based on the decision rule[END_REF]. Each theme t contains a set of specific words. Note that the same word may appear in several discriminative word sets. All the selected words are then merged without repetition to form V . The entire application vocabulary is used for estimating the hidden spaces while only the words of the discriminative vocabulary are used for integrating the features obtained in the hidden spaces.

Several techniques, such as Variational Methods [START_REF] Blei | Latent dirichlet allocation[END_REF], Expectation-propagation [START_REF] Minka | Expectation-propagation for the generative aspect model[END_REF] or Gibbs Sampling [START_REF] Griffiths | Finding scientific topics[END_REF], have been proposed for estimating the parameters describing a LDA hidden space. Gibbs Sampling is a special case of Markovchain Monte Carlo (MCMC) [START_REF] Geman | Stochastic relaxation, gibbs distributions, and the bayesian restoration of images[END_REF] and gives a simple algorithm for approximate inference in high-dimensional models such as LDA [START_REF] Heinrich | Parameter estimation for text analysis[END_REF]. This overcomes the difficulty to directly and exactly estimate parameters that maximize the likelihood of the whole data collection defined as:

p(W | - → α , - → β ) = w∈W p( - → w | - → α , - → β ) (1)
for the whole data collection W knowing the Dirichlet parameters -→ α and -→ β . Gibbs Sampling makes it possible to estimate the LDA parameters in order to represent a new document d with the r th topic space of size n, and to obtain a feature vector V z r d of the topic representation of d. The j th feature V z r j d = P (z r j |d) (where 1 ≤ j ≤ n) is the probability of topic z r j to be generated by the unseen document d in the r th topic space of size n (see Figure 1) and V w z r j = P (w|z r j ) is the vector representation of a word into r.

1 For comparaison, a set of textual documents from the well-known Reuters-21578 dataset is used during the experiments as well. A. Variation of LDA model parameters for a document multiview Thus, a set of p topic spaces are learned using LDA, presented in its plate notation in Figure 2, by varying the hyper-parameters of the p (here, p = 500) topic spaces:

• the number of classes n into the topic space (Section III-A1), • the α parameter (Section III-A2),

• and the β parameter (Section III-A3).

1) Varying n:

The number of topics is varied to obtain p topic spaces of size n. The number of topics n varies from 5 to 505. Thus, a set of 500 topic spaces is estimated. This is high enough to generate, for each document, many feature sets for estimating the parameters of a variability model.

2) Varying α: In the LDA technique, the topic z is drawn from a multinomial over θ which is drawn from a Dirichlet distribution over -→ α . Thus, a set of p topic spaces of size q is learned using LDA by varying the topic distribution parameter

- → α = [α 1 , . . . , α q ] t .
The standard heuristic is α 0 = 50 q [27], which for the setup of the n th topic space

(1 ≤ n ≤ p) would be -→ α n [α n , . . . , α n q times
] t with:

α n = n p × α 0 = n p × 50 q . (2)
The larger α n (α n ≥ 1) is, the more uniform P (z|d) will be (see Figure 3). Nonetheless, this is not what we want: different transcriptions have to be associated with different topic distributions. In the meantime, the higher the α is, the more the draws from the Dirichlet will be concentrated around the mean (see Figure 3 with α = 20), which, for a symmetric alpha vector, will be the uniform distribution over q. The number of topics q is fixed to 50, and 500 topic spaces are built (p = 500) in our experiments. Thus, α n varies between a low value (sparse topic distribution α 1 = 0.002) to 1 (uniform Dirichlet α p = 1). α = 0.002 q q q q q q q q q q Item 2 4 6 8 10 0.0 0.4 0.8 α = 0.02 q q q q q q q q q q Item 2 4 6 8 10 0.0 0.4 0.8 α = 0.2 q q q q q q q q q q Item 2 4 6 8 10 0.0 0.4 0.8 α = 1 q q q q q q q q q q Item 2 4 6 8 10 0.0 0.4 0.8 α = 2 q q q q q q q q q q Item 2 4 6 8 10 0.0 0.4 0.8 α = 20 q q q q q q q q q q Item Fig. 3. Dirichlet distribution with a varied αn.

3) Varying β: In the same way, the hyper-parameter β controls the sparsity of words distribution in each class in the topic space. Thus, the larger β is, the more uniform P (w|z) will be. This means that the probability of each word contained into a class will be roughly the same, and therefore, the classes themselves will be thematically close. During the inference process which allows us to represent the document in the topic space, the distribution of topics for a given document have to be different, mostly if the documents are not labeled with the same theme. The φ matrix is drawn from a Dirichlet with β parameter. The results obtained with different values of α shown in Figure 3, could be considered for different values of β.

The standard heuristic is β 0 = 0.1 [START_REF] Griffiths | Finding scientific topics[END_REF], which for the setup of the n th topic space

(1 ≤ n ≤ p) would be -→ β n [β n , . . . , β n |V |times ] t
with:

β n = n p × β 0 = n p × 0.1 . (3)
The number of topics q is fixed to 50, and 500 topic spaces are built (p = 500) in our experiments. Thus, β n varies between a low value (sparse topic distribution α 1 = 0.0002) to 1 (uniform Dirichlet β p = 0.1).

The next process allows us to obtain a homogeneous representation of document d for the r th topic space r. Section III-B presents the mapping of each thematic representation of a document into a homogenous space composed with a set of discriminant words.

B. Multiple representations in a homogenous space of discriminant words

The feature vector V z m d of d is mapped to the common vocabulary space V composed with a set of |V | discriminative words [START_REF] Morchid | Improving dialogue classification using a topic space representation and a gaussian classifier based on the decision rule[END_REF] of size 166, to obtain a new feature vector V w d,r = {P (w|d) r } w∈V of size |V | for the r th topic space r of size n where the i th (0 ≤ i ≤ |V |) feature is:

V wi d,r = P (w i |d) = n j=1 P (w i |z r j )P (z r j |d) = n j=1 V wi z r j × V z r j d = --→ V wi z r , --→ V z r d
where •, • is the inner product, δ being the frequency of the term w i in d, V wi z r j = P (w i |z j ) and V z r j d = P (z j |d) evaluated using Gibbs Sampling in the topic space r.

IV. COMPACT MULTI-VIEW REPRESENTATION

The multi-view representations of each theme in a large number of hidden spaces may cause large discrepancies in the theme identification accuracy when different hidden space sizes are used. In this section, an i-vector-based method to represent automatic transcriptions is presented. Initially introduced for speaker recognition, i-vectors [START_REF] Kenny | A study of interspeaker variability in speaker verification[END_REF] have become very popular in the field of speech processing and recent publications show that they are also reliable for language recognition [START_REF] Martınez | Language recognition in ivectors space[END_REF] and speaker diarization [START_REF] Franco-Pedroso | Atvs-uam system description for the audio segmentation and speaker diarization albayzin 2010 evaluation[END_REF]. I-vectors are an elegant way of reducing the input space dimensionality while retaining most of the relevant information. The technique was originally inspired by the Joint Factor Analysis framework [START_REF] Kenny | Joint factor analysis versus eigenchannels in speaker recognition[END_REF]. Hence, i-vectors convey the speaker characteristics among other information such as transmission channel, acoustic environment or phonetic content of speech segments. The next sections describe the i-vector extraction process, the application of this compact representation to textual documents (called c-vector), and the vector transformation with the EFR method and the Mahalanobis metric.

A. Total variability space definition I-vector extraction could be seen as a probabilistic compression process that reduces the dimensionality of speech supervectors according to a linear-Gaussian model. I-vectors is also an elegant way of mapping a high dimensional representation of an entity into a feature vector of reduced dimensions while retaining while preserving most if not all the relevant information content of the initial representation.

The speech (of a given speech recording) super-vector m s of concatenated GMM means is projected in a low dimensionality space, named Total Variability space, with:

m (h,s) = m + Tx (h,s) , ( 4
)
where m is the mean super-vector of the UBM 2 and is constructed by concatenation the means of all the Gaussians in the UBM. T is a low rank matrix (M D × R), where M is the number of Gaussians in the UBM and D is the cepstral feature size, which represents a basis of the reduced total variability space. T is named Total Variability matrix; the components of x (h,s) are the total factors which represent the coordinates of the speech recording in the reduced total variability space called i-vector (i for identification).

B. From i-vector speaker identification to c-vector textual document classification

The proposed approach uses i-vectors to model transcription representation through each topic space in a homogeneous vocabulary space. These short segments are considered as basic semantic-based representation units. Indeed, vector V w d represents a segment or a session of a transcription d. In the following, (d, r) will indicate the document representation d in the topic space r. In our model, the segment super-vector m (d,r) of a transcription d knowing a topic space r is modeled:

m (d,r) = m + Tx (d,r) (5)
where x (d,r) contains the coordinates of the topic-based representation of the document in the reduced total variability space called c-vector (c for classification).

where T is a low rank matrix of dimensions (J × C), where J (M × |V |, |V | is the number of words contained into the discriminative words list V ) is the number of elements of the super-vector and C is the number of elements in a reduced total variability space where the vector representing d is called cvector (for classification vector). The c-vector is obtained as described below by adapting to theme identification of textual data an algorithm for computing I-vectors used for speaker verification.

T is named total variability matrix; the components of are the elements of the C-vector. The T matrix is estimated, as described below, using training data and an estimation x (d,r) of is obtained with maximum posterior probability (MAP) estimation as described in the following. Let N (d,r) and X (d,r) be two vectors containing the zero order and first order document 2 The UBM is a GMM that represents all the possible observations. Algorithm 1: Estimation of matrix T and latent variable x (d,r) .

For each document d mapped into the topic space r: x (d,r) ← 0, T ← random ; Estimate statistics: N (d,r) , X (d,r) (eq.6); for i = 1 to nb iterations do for all d and r do Center statistics: X (d,r) (eq.7); Estimate L (d,r) and B (d,r) (eq.8); Estimate x (d,r) (eq.9); end Estimate matrix T (eq. 10 and 11) ; end statistics respectively. The statistics are estimated against the UBM:

N r [g] = t∈r γ g (t); {X (d,r) } [g] = t∈(d,r) γ g (t) • t (6)
where γ g (t) is the a posteriori probability of Gaussian g for the observation t. In the equation, t∈(d,r) represents the sum over all the frames belonging to the document d. Let X (d,r) be the state dependent statistics defined as follows:

{X (d,r) } [g] ={X (d,r) } [g] -m [g] • (d,r) N (d,r) [g] (7)
Let L (d,r) be a R×R matrix, and B (d,r) a vector of dimension R, both defined as:

L (d,r) = I + g∈UBM N (d,r) [g] • {T} t [g] • Σ -1 [g] • {T} [g] B (d,r) = g∈UBM {T} t [g] • Σ -1 g • {X (d,r) } [g] , (8)
By using L (d,r) and B (d,r) , x (d,r) can be obtained using the following equation:

x (d,r) = L -1 (d,r) • B (d,r) (9)
The matrix T can be estimated line by line, with {T} i

[g]
being the i th line of {T} [g] then:

T i [g] = LU -1 g • RU i g , (10)
where RU i g and LU g are given by:

LU g = (d,r) L -1 (d,r) + x (d,r) x t (d,r) • N (d,r) [g] RU i g = (d,r) {X (d,r) } [i] [g] • x (d,r) (11)
Algorithm 1 shows the pseudo-code for the method adopted to estimate the conversation multi-view variability matrix. A standard likelihood function can be used to assess the convergence as shown with more details in [START_REF] Matrouf | A straightforward and efficient implementation of the factor analysis model for speaker verification[END_REF].

C-vector representation suffers from 3 raised issues. In the following, the application of these important constraints is discussed:

• In theory c-vectors (Equation 5) should have normal distribution N (0, I). • The so called radial effect should be removed.

• The full rank total factor space should be used to apply discriminant transformations. The next section presents a solution to these 3 problems.

C. C-vector standardization

A solution to standardize c-vectors has been developed in [START_REF] Bousquet | Intersession compensation and scoring methods in the i-vectors space for speaker recognition[END_REF]. The authors proposed to apply transformations for training and test transcription representations. The first step is to evaluate the empirical mean x and covariance matrix V of the training c-vector. Covariance matrix V is decomposed by diagonalization into:

PDP T ( 12
)
where P is the eigenvector matrix of V and D is the diagonal version of V. A training i-vector x (d,r) is transformed in x (d,r) as follows:

x (d,r) = D -1 2 P T (x (d,r) -x) (x (d,r) -x) T V -1 (x (d,r) -x) (13)
The numerator is equivalent by rotation to V -1 2 (x (d,r) -x) and the Euclidean norm of x (d,r) is equal to 1. The same transformation is applied to the test c-vectors, using the training set parameters x and mean covariance Vas estimations of the test set of parameters.

Figure 4 shows the transformation steps: Figure 4-(a) is the original training set; Figure 4-(b) shows the rotation applied to the initial training set around the principal axes of the total variability when P T is applied; Figure 4-(c) shows the standardization of c-vectors when D -1 2 is applied; and finally, Figure 4-(d) shows the c-vector x (d,r) on the surface area of the unit hypersphere after a length normalization by a division of (x (d,r) -x) T V -1 (x (d,r) -x).

V. EXPERIMENTAL PROTOCOL

The proposed c-vector representation is evaluated in the context of the theme identification of automatic human-human telephone conversation transcriptions and of the categorization of textual newswire collection. This representation is built from a set of feature vectors. Each one is composed with scores of discriminative words. Then, the metric used to associate a document to a class is the Mahalanobis metric.

A LDA model allowed us to elaborate 500 topic spaces by varying LDA hyper-parameters (see Section III-A). A topic space having less than 5 topics is not suitable for large corpus such as those used during our experiments (see Section V-B). For each theme or category, a set of |V | specific words is identified as explained in Section V-D. All the selected words are then merged without repetition to compose V . The topic spaces are made with the LDA Mallet Java implementation 3 .

Next sections describe the datasets used for the experiments, the Mahalanobis distance between two vectors, the metrics to 3 http://mallet.cs.umass.edu/ evaluate the system performance, and finally a study is given to find out the best number of discriminative words for each configuration.

A. Mahalanobis distance

Given a new observation x, the goal of the task is to identify the theme (or category) belonging to x. Probabilistic approaches ignore the process by which c-vectors were extracted and they pretend instead they were generated by a prescribed generative model. Once a c-vector is obtained from a document, its representation mechanism is ignored and it is regarded as an observation from a probabilistic generative model. The Mahalanobis scoring metric assigns a document d with the most likely theme C. Given a training dataset of documents, let W denote the within document covariance matrix defined by:

W = K k=1 n t n W k = 1 n K k=1 nt i=0 x k i -x k x k i -x k t ( 14
)
where W k is the covariance matrix of the k th theme C k , n t is the number of utterances for the theme C k , n is the total number of documents, and x k is the centroid (mean) of all documents x k i of C k . Each document does not contribute to the covariance in an equivalent way. For this reason, the term nt n is introduced in equation 14. If homoscedasticity (equality of the class covariances) and Gaussian conditional density models are assumed, a new observation x from the test dataset can be assigned to the most likely theme C kBayes using the classifier based on the Bayes decision rule:

C kBayes = arg max k {N (x | x k , W)} = arg max k - 1 2 (x -x k ) t W -1 (x -x k ) + a k
where W is the within theme covariance matrix defined in equation 14; N denotes the normal distribution and a k = log (P (C k )). It is noted that, with these assumptions, the Bayesian approach is similar to Fisher's geometric approach:

x is assigned to the class of the nearest centroid, according to the Mahalanobis metric [START_REF] Xing | Distance metric learning with application to clustering with side-information[END_REF] of W -1 :

C kBayes = arg max k - 1 2 ||x -x k || 2 W -1 + a k

B. Datasets

To evaluate the effectiveness of the proposed compact version of a multi-granularity representation of a document, the experiments are conduced by using both documents from automatic transcriptions (DECODA corpus presented in Section V-B1) and classical textual documents (Reuters-21578 corpus presented in Section V-B2).

q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q -3 -2

-1 0 1 2 3 -2 -1 0 1 2
a.Inital: M q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q -3 -2

-1 0 1 2 3 -2 -1 0 1 2
b.Rotation: P t q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q -3 -2

-1 0 1 2 3 -2 -1 0 1 2
c.Standardization: D -1 2 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q -3 -2

-1 0 1 2 3 -2 -1 0 1 2 d.Norm: (x -x) t V -1 (x -x)
Fig. 4. Effect of the standardization with the EFR algorithm.

1) DECODA corpus:

The first corpus is a set of humanhuman telephone conversations in the customer care service (CCS) of the RATP Paris transportation system. This corpus comes from the DECODA project [START_REF] Bechet | Decoda: a call-centre human-human spoken conversation corpus[END_REF] and is used to perform experiments on the conversation theme identification. It is composed of 1,242 telephone conversations, corresponding to about 74 hours of signal, split as described in Table I. To extract textual content of dialogues from DECODA corpus, an Automatic Speech Recognition (ASR) system is needed. The LIA-Speeral ASR system [START_REF] Linarès | The lia speech recognition system: from 10xrt to 1xrt[END_REF] is used for the experiments. Acoustic model parameters were estimated from 150 hours of speech in telephone conditions. The vocabulary contains 5,782 words. A 3-gram language model (LM) was obtained by adapting a basic LM with the training set transcriptions. A "stop list" of 126 words 4 was used to remove unnecessary words (mainly function words) which results in a Word Error Rate (WER) of 33.8% on the training, 45.2% on the development, and 49.5% on the test. These high WER are mainly due to speech disfluencies and to adverse acoustic environments (for example, calls from noisy streets with mobile phones)

2) Reuters-21578 dataset: To evaluate the relevance of the proposed compact representation of a document, the categorization task of top-10 classes of the Reuters-21578 ModApte splitcorpora [START_REF] Asuncion | Uci machine learning repository[END_REF] is used. Table II presents the number of documents of both training, testing and development sets for each of the 10 classes of Reuters corpus [START_REF]Hybrid feature selection for text classification[END_REF], [START_REF] Zhu | Using gini-index for feature weighting in text categorization[END_REF]. 4 http://code.google.com/p/stop-words/

C. Metrics

The Mahalanobis distance allows us to evaluate the similarity between two vectors (here, the document representation and the centroid of each class) and to label a document (or a dialogue in the DECODA corpus) with a certain class. At the end of this process, an efficient metric have to be chosen to evaluate the performance of the categorization system proposed in this paper. This section presents two metrics: the accuracy, for DECODA theme identification task, and the Macro-F1, for automatic labeling process of Reuters-21578 documents. The accuracy is the metric chosen during the previous studies concerning the DECODA theme identification task. In the same way, to compare the results obtained with automatic transcription (DECODA) and textual documents (Reuters), the accuracy is also used as an evaluation metric for the Reuters corpus. This last one is usually evaluated with the Macro-F1 in previous studies. For this reason, this metric is employed to evaluate the proposed compact representation of textual documents (Reuters) in comparison to previous studies. Next sections describe these two metrics.

1) Macro-F1 metric: This well-known dataset categorization task is usually evaluated using the macro-F1 metric. F1measure is computed for each class within the dataset and then, the average over all of the classes is obtained. Hence, equal weight is assigned to each class regardless of the class frequency [START_REF] Larson | Introduction to information retrieval[END_REF]. Computation of Macro-F1 can be formulated as:

Macro-F1 = K k=1 F k K , F k = 2 × p k × r k p k + r k , (15)
where p k and r k are respectively the precision and the recall of the class k among the K classes, determined as follow :

p k = T P k T P k + F P k and r k = T P k T P k + F N k . ( 16
)
F P k represents the number of documents that do not belong to the class k but are classified to this class incorrectly (i.e. false positives); T P k is the number of documents correctly classified as class k (i.e. true positives); F N k represents the number of documents that belong to class k but which are not classified to this class (i.e. false negatives).

2) Accuracy metric: Theme identification task in the DE-CODA project consists in associating the most likely theme to a dialogue between an agent and a customer. To evaluate the effectiveness of the proposed method, the authors in [START_REF] Morchid | Theme identification in telephone service conversations using quaternions of speech features[END_REF], [START_REF] Morchid | A lda-based topic classification approach from highly imperfect automatic transcriptions[END_REF], [START_REF] Bouallegue | Factor analysis based semantic variability compensation for automatic conversation representation[END_REF], [START_REF]Subspace gaussian mixture models for dialogues classification[END_REF], [START_REF] Morchid | Theme identification in human-human conversations with features from specific speaker type hidden spaces[END_REF] used only the accuracy defined as:

accuracy(d) = 1 K K k=1 r k = 1 K K k=1 T P k T P k + F N k (17)
One can find more about evaluation metrics including macro-and micro-metrics in [START_REF] Van Asch | Macro-and micro-averaged evaluation measures[END_REF].

D. Size of discriminative words set

The method proposes to build a compact representation of a given document from a set of feature vectors V w r i d . This vector is composed with the score of each word contained into a discriminative set of words. The mapping step of the thematic representation V z r j d is needed to obtain a homogenous and with equal size representation of the document.

Figure 5 shows theme identification accuracies obtained with different configurations (Train./Dev./Test) and different discriminative words set size |V | for DECODA corpus and macro-F1 for Reuters dataset. Note that, for the DECODA corpus, ASR corresponds to automatic transcriptions of dialogues. The number of classes contained into the topic space is fixed to 50. The main remark is that the best accuracy or macro-F1 is roughly achieve with a set of 20 discriminant words for each configuration of training and development sets. We can also point out that the larger the size of discriminative words set is, the lower the accuracy is. Thus, a set size of 20 discriminative words seems to be the most effective for theme identification task. Other experiments (not presented here due to space considerations) with topic spaces having different numbers of classes (not only 50), show that the best number of discriminative words is around 20 words. Thus, the following experiments are performed with a vocabulary V of size 20.

Parameters configuration

n α β n 5 ≤ n ≤ 505 α = 50 50 = 1 β = 0.1 α n = 50 0.002 ≤ α ≤ 1 β = 0.1 β n = 50 α = 50 50 = 1 0.0002 ≤ β ≤ 0.1

VI. EXPERIMENTS AND RESULTS

The proposed c-vector approach is applied to the same classification task and corpus proposed in [START_REF] Morchid | Improving dialogue classification using a topic space representation and a gaussian classifier based on the decision rule[END_REF] (state-of-the-art in text classification). Experiments are conducted using the multiple topic spaces estimated with a LDA approach. From these multiple topic spaces, a classical way is to find the one that reaches the best performance [START_REF] Morchid | Improving dialogue classification using a topic space representation and a gaussian classifier based on the decision rule[END_REF]. The first experiments presented in Section VI-A are conduced with the DECODA dataset composed with dialogues between an agent and a customer presented in Section V-B1. The compact vector of a textual document is then used to represent documents from Reuters-21578 corpus [START_REF] Asuncion | Uci machine learning repository[END_REF] (see Section V-B2) in a categorization task.

For both tasks, the multiple topic spaces are built by varying one parameter among α, β, and the number of classes into the topic space itself as shown in Table III. First of all, we can see that this baseline approach reached best classification accuracies with multi-view representation of highly imperfect transcription when varying the parameter α, that controls sparsity of topics distribution in documents of training set, for ASR DECODA datasets. These results achieve 86.9% and 80.1% respectively on the development and the test sets.

A. Compact representation of highly imperfect automatic transcriptions

Then, the variation of the hyper-parameter β obtains the second best accuracy in terms of theme identification with 82.9% and 74.0% on the development and test sets.

We can point out that these results are close to those obtained with a multiple representation by varying the number of classes n into the topic space (81.7% and 76.4% for development and test sets). Since difference on the development set is not negligible (82.9 -81.7 = 1.2 points), the result achieved with the test set is quit similar for both β and n multiple representations (74.0% and 76.4%).

Nonetheless, we note that the classification performance is rather unstable, and may completely change from a topic space configuration to another. The gap between the lower and the higher classification results is also important, with a difference of 32.5 points on the development set (same tendency is observed on the test set) when the parameter n is varying. As a result, finding the best topic space size seems crucial for this classification task, particularly in the context of highly imperfect automatic dialogue transcriptions containing more than one theme.

Then, the main remark regarding the accuracies obtained by varying the LDA hyper-parameters, is that the best results are clearly achieved by varying the parameter α, while the two others parameters (β and n) obtain roughly the same accuracies. This is non-intuitive: we expected that the number of topics n would have a higher impact on the topic space statistical structure than the hyper-parameter α. Nonetheless, this remark is effective and relevant when the goal is to map a document in a single topic space. Thus, the inference process is sensitive to the topic distribution of an unseen document into the topic space which is controlled by the parameter α. The purpose here is to build different views of the same document to avoid the complex choice of LDA model hyper-parameters, and to consider different "views" of the same document. Thus, the number of topics, which controls the granularity of topic spaces, allows us to better represent the multiple views of a document and compact this multiple representation by compensating the noise variability.

Tables ?? and IV present accuracies obtained with the proposed c-vector approach coupled with the EFR algorithm with different c-vector sizes and a different number of Gaussians into the GMM-UBM for DECODA ASR datasets. The results presented in Table V show the theme identification accuracies The configuration is whether TRS or ASR, for both training and test sets. We can firstly note that this compact representation allows it to outperform results obtained with the best topic space configuration (baseline), with a gain of 7.9 points5 on the development data and of 7.7 points6 on the test data. Some results obtained with different document representations as well as different classification methods, are presented in Table VI. Indeed, throughout these previous studies, several approaches were proposed to puzzle out this categorization task of such noisy documents. The most classical one is a term frequency representation coupled with a support vector machines [START_REF] Morchid | Improving dialogue classification using a topic space representation and a gaussian classifier based on the decision rule[END_REF] (SVM) classification approach (TF-IDF-Gini+SVM). This method is applied for ASR dataset configurations and obtain good results (73.5% for ASR).

This basic representation of a document with the termfrequency reveals little in way of intra-or inter-documents statistical structure. For this reason, a set of more abstract features from a topic space (LDA) are used to represent the document. This representation is coupled with a SVM classification approach and a Gaussian classifier (Mahalanobis) in [START_REF] Morchid | Improving dialogue classification using a topic space representation and a gaussian classifier based on the decision rule[END_REF] which allows us to improve the results obtained (LDA+Maha.). This classifier, based on a decision rule, was also used with different representations of the same document, depending on the speaker [START_REF] Morchid | Theme identification in human-human conversations with features from specific speaker type hidden spaces[END_REF] with an accuracy of 87.2% and 84.1% for development and test sets respectively.

Another issue related to document structure (words distribution into the document), is the position of each occurrence of a word in a document. Indeed, in the conversation context, the agent have to decide the theme of the dialogue during the first sentences and have to follow a strict protocol. Thus, the position of words impact the document labeling task. Moreover, a same dialogue may contain more than one theme. For these reasons, a theme in a dialogue may change from segment to another. Thus, a document representation which considers the word occurrence positions in the document is proposed as well. This representation takes the form of a hyper-complexe named quaternion [START_REF] Morchid | Theme identification in telephone service conversations using quaternions of speech features[END_REF], and contains 4 elements. In each element, authors in [START_REF] Morchid | Theme identification in telephone service conversations using quaternions of speech features[END_REF] insert the term frequency of the word in a particular segment of the dialogue. This representation is extremely dependent to the document transcription quality.

The proposed c-vector compact representation obtains the best results. This method is from the Joint Factor Analysis framework (JFA). Table VI presents some interesting results obtained with other methods from JFA such as the semantic variability compensation (filter) [START_REF] Bouallegue | Factor analysis based semantic variability compensation for automatic conversation representation[END_REF] or the Subspace Gaussian Mixture Models (SGMM) [START_REF]Subspace gaussian mixture models for dialogues classification[END_REF]. These methods are applied with the ASR configuration to compensate noise variability (automatic transcription process + semantic variability due to multiple document mapping in several topic spaces). The SGMM method is evaluated with different adaptation algorithms (EM, MAP and JFA). One can notice that the method, which achieves the best results in terms of theme identification and noise variability compensation, is the compact representation c-vector.

B. Compact representation of textual documents

Figure 7 shows macro-F1 obtained on the classification task of Reuters-21578 dataset with different compact representations obtained by varying LDA parameters (n, α and β). The first remark, is that the best results are obtained when the parameter is α varies (91.1% for the development set and 76.8% for the test set), then, when the parameter β varies (87.6% for development set and 74.1% for test set), and finally when the number of classes into a topic space varies (82.9% for development set and 72.6% for test set). Even if the difference ∆ of macro-F1 is significative for the development set from a parameter to another (3.5 ≤ ∆ ≤ 8.2), this difference is reduced when the test set is considered (1.5 ≤ ∆ ≤ 4.2).

Table VII presents accuracies obtained with the proposed c-vector approach coupled with the EFR algorithm with different c-vector sizes and a different number of Gaussians into the GMM-UBM for the Reuters-21578 dataset. The results presented in Table VIII show the categorization macro-F1 scores obtained with different LDA parameter variations (α, β and n). The three last columns present best accuracies obtained with both the development and test sets, and the last column presents results obtained when the best configuration found with the development set is applied to the test set (real configuration since, in a real case of dialogue categorization, the test label is unknown). by varying parameter α) with a gain of 4.8 and 9.1 points on the test set in the best and real conditions respectively.

One can point out that the best results are obtained by varying α parameter for the baseline, while the best macro-F1 score is obtained by varying the granularity of the topic space (n) with the compact representation c-vector proposed in this paper. These results confirm the initial intuition that the α parameter control the inference process of an unseen document and the multi-view representation requires a set of topic spaces with different granularities (n). Nonetheless, Table VIII shows that the macro-F1 obtained with the best test (penultimate column), are not as distant for both TbT or c-vector representation as in the "real" conditions (best configuration of the development set applied for the test set). Moreover, the ∆ difference of the macro-F1 of the TbT representation when parameters α and β vary for the test set is small (∆ = 2.5 and ∆ = 1.8 points for best and real conditions respectively). This difference is more visible with the compact representation (c-vector) with ∆ = 4.1 points for test set in "real"condition between representations when α and β vary.

Table IX presents macro-F1 obtained with different document representations and different classification methods. Outcomes obtained with the TbT baseline approach when the number of classes n varies are the less performant (63.62%).

The baseline TbT, with varying parameter β or α, obtains good results (69.13% and 70.87% respectively) compared to those obtained with an Hybrid Feature Selection (HFS) coupled with either a SVM (63.66%) or a decision tree classification (66.19%) method [START_REF]Hybrid feature selection for text classification[END_REF]. HFS consists on two successive selections of relevant features: filter and wrapper selection stages. The filter select features (words) by using the document frequency (DF number of document containing this term [START_REF] Manning | Introduction to information retrieval[END_REF], [START_REF] Yang | A comparative study on feature selection in text categorization[END_REF], [START_REF] Forman | An extensive empirical study of feature selection metrics for text classification[END_REF]), the mutual information [START_REF] Yang | A comparative study on feature selection in text categorization[END_REF], the Chisquare which examine the independence of 2 terms [START_REF] Manning | Introduction to information retrieval[END_REF] and the information gain [START_REF] Yang | A comparative study on feature selection in text categorization[END_REF], [START_REF] Forman | An extensive empirical study of feature selection metrics for text classification[END_REF] which performs the importance of a term for a given class. The wrapper method is a genetic algorithm-based selection [START_REF] Gunal | The search for optimal feature set in power quality event classification[END_REF].

A more classical approach based on term frequency (TF-IDF) with or without the Gini criteria (TF-Gini) coupled with a kNN [START_REF] Yongmin | Improvement of the decision rule in knn text categorization[END_REF] classification algorithm obtains better results (67.15% and 67.93 for TF-IDF and TF-Gini respectively) compared to HFS methods, but less good than those obtained with TbT β or α.

All these approaches are based on a single representation of the document (TF-IDF, TF-Gini, TbT, HFS) and do not take into account different views of this document. The best outcomes in terms of macro-F1 is obtained with the compact representation of the document (cvector) with a gain of 9.5 points. We can conclude that this original c-vector approach allows to better handle variabilities contained in document: in a classification context, a better accuracy can be obtained and the results can be more consistent when varying the c-vector size and the number of Gaussians.

VII. CONCLUSIONS

This paper presents an original multi-view representation of textual documents or automatic speech dialogue transcriptions, and a fusion process with the use of a factor analysis method called i-vector. The first step of the proposed method is to represent a document in multiple topic spaces of different sizes (i.e. number of topics), α or β. Then, a compact representation of the document from the multiple views is processed to compensate the vocabulary and the variability of the topic-based representations. The effectiveness of the proposed approach is evaluated in a classification task of theme dialogue identification and document clustering from Reuters-21578.

Thus, the of the system identifies document class using the i-vector approach. This compact representation was initially developed for speaker recognition and we showed that it can be successfully applied to a text classification task. Indeed, this solution allowed the system to obtain better classification accuracy than with the use of the classical best topic space configuration or others well-known methods. In fact, we highlighted that this original compact version of all topic-based representations of documents, called c-vector in this work, coupled with the EFR normalization algorithm, is a better solution to deal with document variabilities (high word error rates or bad acoustic conditions for transcriptions, unusual word vocabulary, etc). This promising compact representation allows us to effectively solve both the difficult choice of the right number of topics and the multi-theme representation issue of particular textual documents. Finally, the classification accuracy reached 86.5% with a gain of 2.4 points compared to the best previous accuracies observed (LDA Speaker). In the case of textual document from Reuters, the gain of 9.5 points is more promising in terms of macro-F1.

In a future work, we plan to evaluate this new representation of textual documents in other information retrieval tasks, such as keyword extraction or automatic summarization systems.

PLACE PHOTO HERE

Richard Dufour Biography text here.

PLACE PHOTO HERE

Georges Linarès Biography text here.

PLACE PHOTO HERE

Renato De Mori Biography text here.

Fig. 1 .

 1 Fig. 1. Example of a document d mapped into a topic space of size q.

Fig. 2 .

 2 Fig. 2. Generative model for documents in plate notation for Latent Dirichlet Allocation (LDA).

Fig. 5 .

 5 Fig. 5. Theme classification accuracies (%) of development set from DE-CODA data set and macro-F1 for Reuters-21578 (b) development set using various discriminative words sets size |V | (1 ≤ |V | ≤ 100) (x-axis).

Figures 6

 6 Figures 6 present the theme classification performance obtained on the development and test sets using various topicbased representation configurations with the EFR normalization algorithm (baseline) for ASR datasets from DECODA project.First of all, we can see that this baseline approach reached best classification accuracies with multi-view representation of highly imperfect transcription when varying the parameter α, that controls sparsity of topics distribution in documents of training set, for ASR DECODA datasets. These results achieve 86.9% and 80.1% respectively on the development and the test sets.Then, the variation of the hyper-parameter β obtains the second best accuracy in terms of theme identification with 82.9% and 74.0% on the development and test sets.We can point out that these results are close to those obtained with a multiple representation by varying the number

Fig. 6 .

 6 Fig. 6. Theme classification accuracies (%) using various topic-based representations with EFR normalization (baseline) on the development and test sets from Decoda corpus with different experimental configurations with both Training and Validation datasets from ASR. X-axis represents represents the varying parameter: the number n of classes contained into the topic space (a) and (b); α (c) and (d) and β (e) and (f).

  Total Variability Space for LDA-based multi-view text categorization Mohamed Morchid * , Mohamed Bouallegue * , Richard Dufour * , Georges Linarès * and Renato De Mori * , Fellow, IEEE * Laboratoire d'Informatique d'Avignon (LIA), University of Avignon, France † McGill University, School of Computer Science, Montreal, Quebec, Canada

TABLE I DECODA

 I DATASET.

	Class		Number of samples
	label	training development testing
	problems of itinerary	145	44	67
	lost and found	143	33	63
	time schedules	47	7	18
	transportation cards	106	24	47
	state of the traffic	202	45	90
	fares	19	9	11
	infractions	47	4	18
	special offers	31	9	13
	Total	740	175	327

TABLE II TOP

 II -10 CLASSES OF REUTERS-21578 DATASET.

	Class		Number of samples
	label	training development testing
	earn	2,590	287	1,087
	acq	1,485	165	719
	money-fx	484	54	179
	grain	390	43	149
	crude	350	39	189
	trade	332	37	117
	interest	312	35	131
	ship	177	20	89
	wheat	191	21	71
	corn	163	18	56
	Total	6,474	719	2,787

TABLE IV THEME

 IV CLASSIFICATION ACCURACIES (%) WITH DIFFERENT c-VECTORS AND GMM-UBM SIZES FOR TRAINING SET FROM ASR → TEST FROM ASR BY VARYING THE NUMBER OF TOPICS n.The three last columns present best accuracies obtained with both the development and test sets, and the last column presents results obtained when the best configuration found with the development set is applied to the test set (real configuration since, in a real case of dialogue categorization, the test label is unknown).

			(c) Variation of the number of classes n
	size			DEV					TEST
	of			Number of Gaussians in GMM-UBM
	c-vector	32	64	128	256	512	32	64	128	256	512
	60	82.9 82.9	88.0	84.0	86.3	85.0	83.2	83.2	83.8	84.7
	80	85.1 81.7	84.6	82.9	86.3	82.9	79.5	83.2	84.7	82.0
	100	82.4 82.9	85.1	89.7	88.0	84.1	81.0	84.7	86.5	83.5
	120	83.4 84.0	81.7	87.4	85.1	82.9	83.2	85.0	84.4	81.6
	140	81.1 84.6	87.4	84.6	83.4	85.3	82.9	84.1	82.9	82.9
	160	78.9 82.3	82.9	83.4	82.9	86.5	84.7	80.7	82.9	81.7
	180	81.1 81.7	80.6	83.4	82.3	85.0	80.7	79.8	78.6	79.2
	200	82.3 82.9	84.6	81.1	81.7	83.5	81.3	79.8	79.8	76.1
				(a) Variation of parameter α
	size			DEV					TEST
	of			Number of Gaussians in GMM-UBM
	c-vector	32	64	128	256	512	32	64	128	256	512
	60	81.1 82.9	78.9	78.9	77.1	82.9	78.6	72.8	80.1	71.0
	80	82.9 84.6	75.4	80.6	76.0	81.3	79.2	73.4	78.3	69.1
	100	85.7 86.9	79.4	80.0	72.6	78.9	80.4	80.1	75.5	63.9
	120	80.0 82.9	75.5	74.3	73.7	83.2	80.4	71.0	70.6	60.2
	140	79.4 80.0	79.4	76.0	68.6	74.3	73.1	75.0	69.4	59.6
	160	74.3 80.6	73.1	78.3	68.0	77.7	75.2	70.3	68.2	61.2
	180	76.6 83.4	72.0	73.7	66.3	72.2	71.9	61.2	66.1	57.5
	200	72.0 74.3	68.0	66.9	67.4	70.3	70.3	68.8	66.4	55.4
				(b) Variation of parameter β
	size			DEV					TEST
	of			Number of Gaussians in GMM-UBM
	c-vector	32	64	128	256	512	32	64	128	256	512
	60	84.0 84.0	74.9	76.0	73.7	73.0	77.3	70.8	75.1	67.5
	80	76.6 83.4	79.4	74.3	76.0	73.6	75.1	72.4	72.7	69.9
	100	71.4 85.7	74.3	76.0	76.6	77.8	75.4	68.7	68.5	69.9
	120	74.3 77.7	71.4	76.6	65.7	80.4	70.5	68.7	75.7	66.6
	140	66.6 78.3	63.4	64.6	65.1	73.7	69.0	67.8	67.2	62.6
	160	69.4 76.0	68.6	61.1	65.1	70.3	74.5	70.2	63.2	69.3
	180	70.9 77.1	68.6	65.7	62.9	70.9	72.4	68.3	61.4	66.0
	200	68.6 73.7	60.6	66.3	56.0	69.7	63.9	65.0	63.8	68.0
	obtained with ASR DECODA dataset and LDA parameter
	variations (α, β and n).

TABLE IX COMPARISON

 IX BETWEEN THE PROPOSED COMPACT c-VECTOR REPRESENTATION AND DIFFERENT DOCUMENT REPRESENTATIONS AND CATEGORIZATION ALGORITHMS IN TERMS OF CLASSIFICATION MACRO-F1 (%) OF REUTERS DATASET.

	representation	algorithm	TEST
	Document	categorization	Acc. (%)
	TbT (n)	Maha.	63.62
	[37] HFS	SVM	63.66
	[37] HFS	Decision Tree	66.19
	[38] TF-IDF	kNN	67.15
	[38] TF-Gini	kNN	67.93
	TbT (β)	Maha.	69.13
	TbT (α)	Maha.	70.87
	c-vector (n)	Maha.	80.04

Lower difference when the baseline system is applied with the development set (83.8%) and the c-vector representation with the development set by varying the parameter n (91.7%).

[START_REF] Bechet | Decoda: a call-centre human-human spoken conversation corpus[END_REF] Lower difference when the baseline system is applied with the test set (83.2%) and the c-vector representation with the test set by varying respectively the parameter α and n (89.3%).

ACKNOWLEDGMENT

This work was funded by the SUMACC and DECODA projects supported by the French National Research Agency (ANR) under contracts ANR-10-CORD-007 and ANR-09-CORD-005.

The first remark is that results obtained with the proposed compact version of a multi-view representation of a document (81.6% and 80.0% for test in the best and real conditions respectively by varying parameter n), outperform those obtained with the best configuration of LDA parameters (76.8% and 70.9% for test in the best and real conditions respectively