ieeetrans2009

SUBMITTED TO IEEE AUDIO, SPEECH AND LANGUAGE PROCESSING 1

An Information Theoretic Approach to SpeakerDiarization of Meeting Data

Deepu Vijayasenan,Student Member, IEEE,Fabio Valente,Member, IEEE,and Herve Bourlard,Fellow, IEEE

Abstract—A speaker diarization system based on an informa-tion theoretic framework is described. The problem is formulatedaccording to the Information Bottleneck (IB) principle. Unlikeother approaches where the distance between speaker segmentsis arbitrarily introduced, the IB method seeks the partition thatmaximizes the mutual information between observations andvariables relevant for the problem while minimizing the distortionbetween observations. This solves the problem of choosing thedistance between speech segments, which becomes the Jensen-Shannon divergence as it arises from the IB objective functionoptimization. We discuss issues related to speaker diarizationusing this information theoretic framework such as the criteriafor inferring the number of speakers, the trade-off betweenquality and compression achieved by the diarization system, andthe algorithms for optimizing the objective function. Furthermorewe benchmark the proposed system against a state-of-the-artsystem on the NIST RT06 (Rich Transcription) data set forspeaker diarization of meetings. The IB based system achieves aDiarization Error Rate of 23.2% compared to 23.6% for thebaseline system. This approach being mainly based on non-parametric clustering, it runs significantly faster than the baselineHMM/GMM based system, resulting in faster-than-real-timediarization. 1

Index Terms—Speaker Diarization, Meetings data, InformationBottleneck.

I. I NTRODUCTION

Speaker Diarization is the task of decidingwho spokewhen in an audio stream and is an essential step for severalapplications such as speaker adaptation in Large VocabularyAutomatic Speech Recognition (LVCSR) systems, speakerbased indexing and retrieval. This task involves determiningthe number of speakers and identifying the speech segmentsassociated with each speaker.

The number of speakers is not a priori known and mustbe estimated from data in an unsupervised manner. The mostcommon approach to speaker diarization remains the oneproposed in [1] which consists of agglomerative bottom-upclustering of acoustic segments. Speech segments are clusteredtogether according to some similarity measure until a stoppingcriterion is met. Given that the final number of clusters isunknown and must be estimated from data, the stoppingcriterion is generally related to the complexity of the estimatedmodel. The use ofBayesian Information Criterion[2] as amodel complexity metric has been proposed in [1] and iscurrently used in several state-of-the-art diarization systems.

1Initial Submission July 04, 2008. First revision, submitted October 15,2008.

Agglomerative clustering is based on similarity measuresbetween segments. Several similarity measures have been con-sidered in the literature based on BIC [1], modified versionsofBIC [3], [4], Generalized Log-Likelihood Ratio [5], Kullback-Leibler divergence [6] or cross-likelihood distance [7]. Thechoice of this distance measure is somewhat arbitrary.

In this paper we investigate the use of a clustering techniquemotivated from an information theoretic framework knownas theInformation Bottleneck(IB) [8]. The IB method hasbeen applied to clustering of different types of data likedocuments [9], [10] and images [11]. IB clustering [8], [12]is a distributional clustering inspired from Rate-Distortiontheory [13]. In contrast to many other clustering techniques,it is based on preserving the relevant information specific toa given problem instead of arbitrarily assuming a distancefunction between elements. Furthermore, given a data set tobe clustered, IB tries to find the trade-off between the mostcompact representation and the most informative representa-tion of the data. The first contribution of this paper is theinvestigation of IB based clustering for speaker diarization andits comparison with state-of-the-art systems based on a Hid-den Markov Model/Gaussian Mixture Model (HMM/GMM)framework. We discuss differences and similarities of the twoapproaches and benchmark them in a speaker diarization taskfor meeting recordings.

Speaker diarization has been applied to several types ofdata e.g. broadcast news recordings, conversational telephonespeech recordings and meeting recordings. The most recentefforts in the NIST Rich Transcription campaigns focus onmeeting data acquired in several rooms with different acousticproperties and with a variable number of speakers. The audiodata is recorded in a non-intrusive manner using MultipleDistant Microphones (MDM) or a microphone array. Giventhe variety of acoustic environments, the conversational na-ture of recordings and the use of distant microphones, thoserecordings represent a very challenging data set. Progressinthe diarization task for meeting data can be found in [14] andin [15].

Recently, attention has shifted onto faster-than-real-timediarization systems with low computational complexity (seee.g. [16], [17], [18], [19]). In fact in the meeting case scenario,faster than realtime diarization would enable several appli-cations (meeting browsing, meeting summarization, speakerretrieval) on a common desktop machine while the meeting istaking place.

Conventional systems model the audio stream using a fullyconnected HMM in which each state corresponds to a speaker


cluster with emission probabilities represented by GMM prob-ability density functions [3], [20]. Merging two segmentsimplies estimating a new GMM model that represents datacoming from both segments as well as the similarity measurebetween the new GMM and the remaining speaker clusters.This procedure can be computationally demanding.

As second contribution, this paper also investigates the IBclustering for a fast speaker diarization system. IB is a non-parametric framework that does not use any explicit modelingof speaker clusters. Thus, the algorithm does not need toestimate a GMM for each cluster, resulting in a considerablyreduced computational complexity with similar performanceto conventional systems.

The remainder of the paper is organized as follows. InSection II, we describe the Information Bottleneck principle.Sections II-A and II-B, respectively, summarize agglomerativeand sequential optimization of the IB objective functions.Section III discusses methods for inferring the number ofclusters. Section IV describes the full diarization system, whileSections V and VI present experiments and benchmark tests.Finally, Section VII discusses results and conclusions.

II. I NFORMATION BOTTLENECK PRINCIPLE

The Information Bottleneck (IB) [8], [12] is a distributionalclustering framework based on information theoretic princi-ples. It is inspired from the Rate-Distortion theory [13] inwhich a set of elementsX is organized into a set of clustersC minimizing the distortion betweenX and C. Unlike theRate-Distortion theory, the IB principle does not make anyassumption about the distance between elements ofX . Onthe other hand, it introduces the use of a set ofrelevancevariables, Y , which provides meaningful information aboutthe problem. For instance, in a document clustering problem,the relevance variables could be represented by the vocabularyof words. Similarly, in a speech recognition problem, therelevance variables could be represented as the target sounds.IB tries to find the clustering representationC that conveysas much information as possible aboutY . In this way the IBclustering attempts to keep the meaningful information withrespect to a given problem.

Let Y be the set of variables of interest associated withXsuch that∀x ∈ X and ∀y ∈ Y the conditional distributionp(y|x) is available. Let clustersC be a compressed represen-tation of input dataX . Thus, the information thatX containsabout Y is passed through the compressed representation(bottleneck) C. The Information Bottleneck (IB) principlestates that this clustering representation should preserve asmuch information as possible about the relevance variablesY (i.e., maximizeI(Y, C)) under a constraint on the mu-tual information betweenX and C i.e. I(C, X). Dually,the clusteringC should minimize the coding length (or thecompression) ofX usingC i.e. I(C, X) under the constraintof preserving the mutual informationI(Y, C). In other words,IB tries to find a trade-off between the most compact and mostinformative representation w.r.t. variablesY . This correspondsto maximization of the following criterion:

F = I(Y, C)−1

βI(C, X) (1)

whereβ (notation consistent with [8]) is the Lagrange multi-plier representing the trade off between amount of informationpreservedI(Y, C) and the compression of the initial represen-tation I(C, X).

Let us develop mathematical expressions forI(C, X) andI(Y, C). The compression of the representationC is charac-terized by the mutual informationI(C, X):

I(C, X) =∑

x∈X,c∈C

p(x)p(c|x)logp(c|x)

p(c)(2)

The amount of information preserved aboutY in the repre-sentation is given byI(Y, C) :

I(Y, C) =∑

y∈Y,c∈C

p(c)p(y|c)logp(y|c)

p(y)(3)

The objective functionF must be optimized w.r.t thestochastic mappingp(C|X) that maps each element of thedatasetX into the new cluster representationC.

This minimization yields the following set of self -consistentequations that defines the conditional distributions required tocompute mutual informations (2) and (3) (see [8] for details):

p(c|x) = p(c)Z(β,x) exp(−βDKL[p(y|x)||p(y|c)])

p(y|c) =∑

x p(y|x)p(c|x)p(x)p(c)

p(c) =∑

x p(c|x)p(x)

(4)

where Z(β, x) is a normalization function andDKL[., .]represents the Kullback-Liebler divergence given by:

DKL[p(y|x)||p(y|c)] =∑

y∈Y

p(y|x) logp(y|x)

p(y|c)(5)

We can see from the system of equations (4) that asβ →∞the stochastic mappingp(c|x) becomes a hard partition ofX ,i.e. p(c|x) can take values0 and1 only.

Various methods to construct solutions of the IB objectivefunction include iterative optimization, deterministic anneal-ing, agglomerative and sequential clustering (for exhaustive re-view see [12]). Here we focus only on two techniques referredto as agglomerative and sequential information bottleneck,which will be briefly presented in the next sections.

A. Agglomerative Information Bottleneck

Agglomerative Information Bottleneck (aIB) [9] is a greedyapproach to maximize the objective function (1). The aIBalgorithm creates hard partitions of the data. The algorithm isinitialized with the trivial clustering of|X | clusters i.e, eachdata point is considered as a cluster. Subsequently, elementsare iteratively merged such that the decrease in the objectivefunction (1) at each step is minimum.

The decrease in the objective function∆F obtained bymerging clustersci andcj is given by:

∆F(ci, cj) = (p(ci) + p(cj)) · dij (6)

where dij is given as a combination of two Jensen-Shannondivergences:

dij = JS[p(y|ci), p(y|cj)]−1

βJS[p(x|ci), p(x|cj)] (7)


Input:Joint Distributionp(x, y)Trade-off parameterβ

Output:Cm: m-partition of X , 1 ≤ m ≤ |X |

Initialization:C ≡ XFor i = 1 . . .N

ci = {xi}p(ci) = p(xi)p(y|ci) = p(y|xi)∀y ∈ Yp(ci|xj) = 1 if j = i, 0 otherwise

For i, j = 1 . . .N, i < jFind ∆F(ci, cj)

Main Loop:While |C| > 1

{i, j} = arg mini′,j′ ∆F(ci, cj)Merge{ci, cj} ⇒ cr in C

p(cr) = p(ci) + p(cj)

p(y|cr) =[p(y|ci)p(ci)+p(y|cj)p(cj)]

p(cr)

p(cr|x) = 1, ∀x ∈ ci, cj

Calculate∆F(cr, c), ∀c ∈ C

Fig. 1. Agglomerative IB algorithm [12]

where JS denotes the Jensen-Shannon (JS) divergence be-tween two distributions and is defined as:

JS(p(y|ci), p(y|cj)) = πi DKL[p(y|ci)||qY (y)] +

+πj DKL[p(y|cj)||qY (y)] (8)

JS(p(x|ci), p(x|cj)) = πi DKL[p(x|ci)||qX(x)] +

+πj DKL[p(x|cj)||qX(x)] (9)

with:

qY (y) = πi p(y|ci) + πj p(y|cj) (10)

qX(x) = πi p(x|ci) + πj p(x|cj) (11)

πi = p(ci)/(p(ci) + p(cj))

πj = p(cj)/(p(ci) + p(cj))

The objective function (1) decreases monotonically with thenumber of clusters. The algorithm merges cluster pairs untilthe desired number of clusters is attained. The new clustercr obtained by merging the individual clustersci and cj ischaracterized by:

p(cr) = p(ci) + p(cj) (12)

p(y|cr) =p(y|ci)p(ci) + p(y|cj)p(cj)

p(cr)(13)

It is interesting to notice that the JS divergence is notan arbitrarily introduced similarity measure between elementsbut a measure that naturally arises from the maximization ofthe objective function. For completeness we report the fullprocedure described in [12] in Fig 1.

However, at each agglomeration step, the algorithm takesthe merge decision based only on a local criterion. Thus aIBis a greedy algorithm and produces only an approximation tothe optimal solution which may not be the global solution tothe objective function.

B. Sequential Information Bottleneck

Sequential Information Bottleneck (sIB) [10] tries to im-prove the objective function (1) in a given partition. Unlikeagglomerative clustering, it works with a fixed number ofclustersM . The algorithm starts with an initial partition ofthe space intoM clusters{c1, ..., cM}. Then some elementxis drawn out of its clustercold and represents a new singletoncluster. x is then merged into the clustercnew such thatcnew = argmin

c∈C∆F(x, c) where∆F(., .) is as defined in (6).

It can be verified that ifcnew 6= cold thenF(Cnew) < F(Cold)i.e., at each step the objective function (1) either improves orstays unchanged. This is performed for eachx ∈ X . Thisprocess is repeated several times until there is no change inthe clustering assignment for any input element. To avoidlocal maxima, this procedure can be repeated with severalrandom initializations. The sIB algorithm is summarized forcompleteness in Fig 2.

III. M ODEL SELECTION

In typical diarization tasks, the number of speakers in agiven audio stream is not a priori known and must be estimatedfrom data. This means that the diarization system has to solvesimultaneously two problems: finding the actual number ofspeakers and clustering together speech from the same speaker.This problem is often cast into a model selection problem. Thenumber of speakers determines the complexity of the model interms of number of parameters. The model selection criterionchooses the model with the right complexity and thus thenumber of speakers. Let us consider the theoretical foundationof model selection.

Consider a datasetX , and a set of parametric models{m1, · · · , mM} where mj is a parametric model withnj

parameters trained on the dataX . Model selection aims atfinding the modelm such that:

m = arg maxj{p(mj |X)} = argmax

j

[

p(X |mj)p(mj)

p(X)

]

(14)

Given that p(X) is constant and assuming uniform priorprobabilitiesp(mj) on modelsmj , maximization of (14) onlydepends onp(X |mj). In case of parametric modeling withparameter setθj , e.g. HMM/GMM, it is possible to write:

p(X |mj) =

∫

p(X, θj|mj)dθj (15)

This integral cannot be computed in closed form in the caseof complex parametric models with hidden variables (e.g.HMM/GMM). However several approximations for (15) arepossible, the most popular one being theBayesian InformationCriterion (BIC) [2]:

BIC(mj) = log(p(X |θj, mj))−pj

2log N (16)


Input:Joint Distributionp(x, y)Trade-off parameterβCardinality valueM

Output:PartitionC of X into M clusters

Initialization:C ← random partition ofX into M clustersFor everyci ∈ C:

p(ci) =∑

xj∈cip(xj)

p(y|ci) = 1p(ci)

∑

xj∈cip(y|xj)p(xj)

p(ci|xj) = 1 if xj ∈ ci, 0 otherwise

Main Loop:While not Done

Done← TRUEFor everyx ∈ X :

cold ← clusterx belongsSplit cold ⇒ {c′old, {x}}

p(c′old) = p(cold)− p(x)

p(y|c′old) = p(y|cold)p(cold)−p(y,x)p(c′

old)

p(c′old|xi) = 1; ∀xi ∈ cold, xi 6= x

cnew = arg minc∈C ∆F({x}, c)Merge{cnew, {x}} ⇒ c′new

p(c′new) = p(cnew) + p(x)

p(y|c′new) = p(y|cnew)p(cnew)+p(y,x)p(c′new)

p(c′new |xi) = 1; ∀xi ∈ cnew, xi = x

If cnew 6= cold

Done← FALSE

Fig. 2. Sequential IB algorithm [12]

where pj is the number of free parameters in the modelmj , θj is the MAP estimate of the model computed fromdataX , andN is the number of data samples. The rationalebehind (16) is straightforward: models with larger numbersofparameters will produce higher values oflog(p(X |θj, mj)) butwill be more penalized by the termpj

2 log N . Thus the optimalmodel is the one that achieves the best trade-off between dataexplanation and complexity in terms of number of parameters.However, BIC is exact only in the asymptotic limitN →∞.It has been shown [1] that in the finite sample case, like inspeaker clustering problems, the penalty term must be tunedaccording to a heuristic threshold. In [3], [4], [21], a modifiedBIC criterion that needs no heuristic tuning has been proposedand will be discussed in more details in Section VI-A.

In the case of IB clustering, there is no parametric modelthat represents the data and model selection criteria basedona Bayesian framework like BIC cannot be applied. Severalalternative solutions have been considered in the literature.

Because of the information theoretic basis, it is straightfor-ward to apply theMinimum Description Length(MDL) prin-ciple [22]. The MDL principle is a formulation of the modelselection problem from an information theory perspective.The

optimal model minimizes the following criterion.

FMDL(m) = L(m) + L(X |m) (17)

whereL(m) is the code length to encode the model with afixed length code andL(X |m) is the code length requiredto encode the data given the model. As model complexityincreases, the model explains the data better, resulting inadecrease in number of bits to encode the data given the model(lower L(X |m)). However, the number of bits required toencode the model increases (highL(m)). Thus, MDL selects amodel that has the right balance between the model complexityand data description.

In case of IB clustering, letN = |X | be the number of inputsamples, andM = |C| the number of clusters. The number ofbits required to code the modelm and the dataX given themodel is :

L(m) = N logN

M(18)

L(X |m) = N [H(Y |C) + H(C)] (19)

Since H(Y |C) = H(Y ) − I(Y, C) the MDL criterion be-comes:

FMDL = N [H(Y )− I(Y, C) + H(C)] + N logN

M(20)

Similar to the BIC criterion,N log NM

acts like a penalty termthat penalizes codes that uses too many clusters.

When aIB clustering is applied, expression (20) is evalu-ated for each stage of the agglomeration that produces|X |different clustering solutions. Then the number of clusters thatminimizes (20) is selected as the actual number of speakers.

Another way of inferring the right number of clusters can bebased on theNormalized Mutual Information (NMI)I(Y,C)

I(X,Y ) .

The Normalized Mutual InformationI(Y,C)I(X,Y ) represents the

fraction of original mutual information that is captured bythe current clustering representation. This quantity decreasesmonotonically with the number of clusters (see Figure 3). Itcan also be expected that this quantity will decrease morewhen dissimilar clusters are merged. Hence, we investigatea simple thresholding ofI(Y,C)

I(X,Y ) as a possible choice todetermine the number of clusters. The threshold is heuristicallydetermined on a separate development data set.

IV. A PPLYING IB TO DIARIZATION

To apply the Information Bottleneck principle to the di-arization problem, we need to define input variablesX tobe clustered and the relevance variablesY representing themeaningful information about the input.

In the initial case of document clustering, documents repre-sent the input variableX . The vocabulary of words is selectedas the relevance variable. Associated conditional distributions{p(yi|xj)} are the probability of each wordyi in documentxj . Documents can be clustered together with IB using thefact that similar documents will have similar probabilities ofcontaining the same words.

In this paper, we investigate the use of IB for clusteringof speech segments according to cluster similarity. We definein the following the input variablesX = {xj}, the relevancevariablesY = {yi} and the conditional probabilitiesp(yi|xj).


100 200 300 400 5000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

|C|

I(C

;Y)/

I(X

;Y)

Fig. 3. Normalized mutual information decreases monotonically with thenumber of clusters.

A. Input Variables X

The Short Time Fourier Transform (STFT) of the inputaudio signal is computed using30ms windows shifted by astep of10ms.19 Mel Frequency Cepstral Coefficients (MFCC)are extracted from each windowed frame. Let{s1, s2, · · · sT }be the extracted MFCC features. Subsequently, a uniformlinear segmentation is performed on the feature sequence toobtain segments of a fixed lengthD (typically 2.5 seconds).The input variablesX are defined as the set of these seg-ments{x1, x2, · · · , xM}. Thus each segmentxj consists of asequence of MFCC features{sj

k}k=1,···,D.If the length of the segment is small enough,X may be

considered as generated by a single speaker. This hypothesis isgenerally true in case of Broadcast News audio data. Howeverin case of conversational speech with fast speaker change rateand overlapping speech (like in meeting data), initial segmentsmay contain speech from several speakers.

B. Relevance Variables Y

Motivated by the fact that GMMs are widely used in speakerrecognition and verification systems (see e.g. [23]), we choosethe relevant variablesY = {yj} as components of a GMMestimated from the meeting data. A shared covariance matrixGMM is estimated from the entire audio file. The number ofcomponents of the GMM is fixed proportional to the lengthof the meeting i.e. the GMM hasP

Dcomponents whereP is

the length of the audio stream (in seconds) andD is lengthof segments (in seconds) defined in section IV-A.

The computation of conditional probabilitiesp(Y = yi|X =xj) is straightforward. Consider a Gaussian Mixture Modelf(s) =

∑L

j=1 wjN (s, µj , Σj) where L is the number ofcomponents,wj are weights,µj means andΣj covariancematrices. It is possible to project each speech framesk ontothe space of Gaussian components of the GMM. Adopting thenotation used in previous sections, the space induced by GMMcomponents would represent the relevance variableY .

Computation ofp(yi|sk) is then simply given by:

p(yi|sk) =wiN (sk, µi, Σi)

∑L

j=1 wjN (sk, µj, Σj); i = 1, . . . , L (21)

The probabilityp(yi|sk) estimates the relevance that theith component in the GMM has for speech framesk. Sincesegmentxj is composed of several speech frames{sj

k},distributions{p(yi|s

jk)} can be averaged over the length of

the segment to get the conditional distributionp(Y |X).In other words, a speech segmentX is projected into the

space of relevance variablesY estimating a set of conditionalprobabilitiesp(Y |X).

C. Clustering

Given the variablesX andY , the conditional probabilitiesp(Y |X), and trade-off parameterβ, Information Bottleneckclustering can be performed. The diarization system involvestwo tasks: finding the number of clusters (i.e. speakers) andan assignment for each speech segment to a given cluster.

The procedure we use is based on the agglomerative IBdescribed in Section II-A. The algorithm is initialized withM clusters withM = |X | and agglomerative clustering isperformed, generating a set of possible solutions in betweenM and 1 clusters.

Out of theM = |X | possible clustering solutions of aIB, wechoose one according to the model selection criteria describedin Section III i.e.Minimum Description Lengthor NormalizedMutual Information.

However, agglomerative clustering does not seek the globaloptimum of the objective function and can converge to localminima. For this reason, the sIB algorithm described inSection II-B can be applied to improve the partition. Giventhat sIB works only on fixed cardinality clustering, we proposeto use it to improve the greedy solution obtained with the aIB.

To summarize, we study the following four different typesof clustering/model selection algorithms:

1 agglomerative IB + MDL model selection.2 agglomerative IB + NMI model selection.3 agglomerative IB + MDL model selection + sequential

IB.4 agglomerative IB + NMI model selection + sequential IB.

D. Diarization algorithm

We can summarize the complete diarization algorithm asfollows:

1 Extract acoustic features{s1, s2, · · · , sT } from the audiofile.

2 Speech/non-speech segmentation and reject non-speechframes.

3 Uniform segmentation of speech in chunks of fixed sizeD, i.e. definition of setX = {x1, x2, · · · , xM}.

4 Estimation of GMM with shared diagonal covariancematrix i.e. definition of setY .

5 Estimation of conditional probabilityp(Y |X).6 Clustering based on one of the methods described in

Section IV-C.


7 Viterbi realignment using conventional GMM systemestimated from previous segmentation.

Steps 1 and 2 are common to all diarization systems. Speechis segmented into fixed length segments in step 3. This steptries to obtain speech segments that contain speech from onlyone speaker. We use a uniform segmentation in this workthough other solutions like speaker change detection or K-means algorithm could be employed.

Step 4 trains a background GMM model with shared covari-ance matrix from the entire audio stream. Though we use datafrom the same meeting, it is possible to train the GMM on alarge independent dataset i.e. a Universal Background Model(UBM) can be used.

Step 5 involves conditional probabilityp(y|x) estimation.In step 6 clustering and model selection are performed on thebasis of the Information Bottleneck principle.

Step 7 refines initial uniform segmentation by performinga set of Viterbi realignments. this step modifies the speakerboundaries and is discussed in the following section.

E. Viterbi Realignment

As described in IV-A, the algorithm clusters speech seg-ments of a fixed length D. Hence, the cluster boundariesobtained from the IB are aligned with the endpoints ofthese segments. Those endpoints are clearly arbitrary and canbe improved re-aligning the whole meeting using a Viterbialgorithm.

The Viterbi realignment is performed using an ergodicHMM. Each state of the HMM represents a speaker cluster.The state emission probabilities are modeled with GaussianMixture Models, with a minimum duration constraint. EachGMM is initialized with a fixed number of components.

The IB clustering algorithm infers the number of clustersand the assignment fromX segments toC clusters. A sepa-rate GMM for each cluster is trained using data assignmentproduced by the IB clustering. The whole meeting data is thenre-aligned using the ergodic HMM/GMM models. During there-alignment a minimum duration constraint of 2.5 seconds isused as well.

V. EFFECT OFSYSTEM PARAMETERS

In this section we study the impact of the trade-off pa-rameterβ (SectionV-B), the performance of the agglomerativeand sequential clustering (Section V-C), the model selectioncriterion (Section V-D) and the effect of the Viterbi re-alignment (Section V-E) on development data.

A. Data description

The data used for the experiments consist of meetingrecordings obtained using an array of far-field microphonesalso referred as Multiple Distant Microphones (MDM). Thosedata contain mainly conversational speech with high speakerchange rate and represent a very challenging data set.

We study the impact of different system parameters on thedevelopment dataset which contains meetings from previousyears’ NIST evaluations for “Meeting Recognition Diariza-tion” task [14]. This development dataset contains12 meeting

recordings each one around10 minutes. The best set ofparameters is then used for benchmarking the proposed systemagainst a state-of-the-art diarization system. Comparison isperformed on the NIST RT06 evaluation data for “MeetingRecognition Diarization” task . The dataset contains ninemeeting recordings of approximately30 minutes each. Afterevaluation, the TNO20041103-1130 was found noisy andwas not included in the official evaluation. However, resultsare reported with/without this meeting in the literature [24],[25]. We present results with and without this meeting for thepurpose of comparison.

Preprocessing consists of the following steps: signalsrecorded with Multiple Distant Microphones are filtered usinga Wiener filter denoising for individual channels followed bya delay-and-sum beamforming [26], [15]. This was performedusing theBeamformIttoolkit [27]. Such pre-processing pro-duces a single enhanced audio signal from individual far-fieldmicrophone channels. 19 MFCC features are then extractedfrom the beam-formed signal.

The system performance is evaluated in terms of DiarizationError Rates (DER). DER is the sum of missed speech errors(speech classified as non-speech), false alarm speech error(non-speech classified as speech) and speaker error [28].Speech/non-speech (spnsp) error is the sum of missed speechand false alarm speech. For all experiments reported in thispaper, we include the overlapped speech in the evaluation.

Speech/non-speech segmentation is obtained using a forcedalignment of the reference transcripts on close talking micro-phone data using the AMI RT06 first pass ASR models [29].Results are scored against manual references force alignedbyan ASR system. Being interested in comparing the clusteringalgorithms, the same speech/non-speech segmentation willbeused across all experiments.

B. Trade-offβ

The parameterβ represents the trade-off between theamount of information preserved and the level of compression.To determine its value, we studied the diarization error of theIB algorithm in the development dataset. The performance ofthe algorithm is studied by varyingβ on a log-linear scaleand applying aIB clustering. The optimal number of clustersis chosen according to an oracle. Thus, the influence of theparameter can be studied independently of model selectionmethods or thresholds. The Diarization Error Rate (DER)of the development dataset for different values of beta ispresented in Fig 4. These results do not include Viterbi re-alignment. The value ofβ = 10 produce the lowest DER.In order to understand how the optimal value ofβ changesacross different meetings, we report in Table I optimalβ foreach meeting, DER for the optimalβ and forβ = 10. In eightmeetings out the twelve, theβ that produces the lowest DERis equal to 10. In four meetings the optimalβ is different from10, but only in one (CMU20050228) the DER is significantlydifferent from the one obtained usingβ = 10. To summarizethe optimal value ofβ seems to be consistent across differentmeetings.

Figure 5 shows the DER curve w.r.t. number of clustersfor two meetings (LDC20011116-1400 and CMU20050301-


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−−|C|→

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DE

R→

LDC_20011116−1400

β=1β=10β=100β=∞

1 2 3 4 5 6 7 8 9 105

10

15

20

25

30

35

40

45

50

−−|C|→

−−

DE

R→

CMU_20050301−1415

β=1β=10β=100β=∞

Fig. 5. DER as a function of number of clusters (|C|) for different values of parameterβ

TABLE IOPTIMAL VALUE FOR β FOR EACH MEETING IN THE DEVELOPMENT

DATASET. DER FOR THE OPTIMALβ AS WELL AS β = 10 ARE REPORTED.

DER at DER atMeeting optimal β optimal β β = 10

AMI 20041210-1052 10 4.6 4.6AMI 20050204-1206 10 10.0 10.0

CMU 20050228-1615 50 20.4 25.3CMU 20050301-1415 10 9.4 9.4ICSI 20000807-1000 100 11.9 12.3ICSI 20010208-1430 10 12.9 12.9LDC 20011116-1400 1000 6.2 8.7LDC 20011116-1500 10 18.7 18.7NIST 20030623-1409 10 6.0 6.0NIST 20030925-1517 10 24.3 24.3

VT 20050304-1300 10 7.3 7.3VT 20050318-1430 100 28.5 29.7

100

101

102

103

104

10

15

20

25

30

35

40

45

50

55

− β →

− D

ER

→

Fig. 4. Effect of varying parameterβ on the diarization error for thedevelopment dataset. The optimalβ is chosen asβ = 10

1415). It can be seen that the DER is flat forβ = 1 anddoes not decrease with the increase in number of clusters.This low value ofβ implies more weighting to the regular-ization term 1

βI(C, X) of the objective function in Equation

(1). Thus the optimization tries to minimizeI(C, X). Thealgorithm uses hard partitions i.e.p(c|x) ∈ {0, 1}, this leadsto H(C|X) = −

∑

x∈X p(x)∑

c∈C p(c|x) log p(c|x) = 0 andas a resultI(C, X) = H(C) − H(C|X) = H(C). Henceminimizing I(C, X) is equivalent to minimizingH(C) in

this case. ThusH(C) is minimized while clustering with lowvalues ofβ which in turn leads to a highly unbalanced distri-bution where most of the elements are assigned to one singlecluster(H(C) ≈ 0). Thus the algorithm always convergestowards one large cluster followed by several spurious clustersand the DER stays almost constant. Conversely, whenβ is high(eg: β = ∞), effect of this regularization term vanishes. Theoptimization criterion focuses only on the relevance variablesetI(Y, C) regardless of the data compression. The DER curvethus becomes less smooth.

For intermediate values ofβ, the clustering seeks the mostinformativeandcompact representation. For the value ofβ =10, the region of low DER is almost constant for comparativelymore values of|C|. In this case, the algorithm forms largespeaker clusters initially. Most of the remaining clustersaresmall and merging these clusters does not change the DERconsiderably. This results in a regularized DER curve as afunction of number of clusters (see Figure 5).

C. Agglomerative and Sequential clustering

In this section, we compare the agglomerative and se-quential clustering described in Sections II-A, II-B on thedevelopment data. As before model selection is performedusing an oracle and the value ofβ is fixed at 10 as foundin the previous section. Agglomerative clustering achieves aDER of 13.3% while sequential clustering achieves a DERof 12.4%, i.e. 1% absolute better. Results are presented inTable II. Improvements are obtained on 8 of the 12 meetingsincluded in the development data.

Also the additional computation introduced by the sequen-tial clustering is small when initialized with aIB output. ThesIB algorithm converges faster in this case than using randominitial partitions. In the development data it was observedthatthe sequential clustering converged in4 iterations through themeeting as compared to6 while using sIB alone (averagenumber of iterations across all development data).

D. Model selection

In this section, we discuss experimental results with themodel selection algorithms presented in Section III. Two


TABLE IIDIARIZATION ERROR RATE OF DEVELOPMENT DATA FOR INDIVIDUAL

MEETINGS FOR AIB AND A IB+SIB USING ORACLE MODEL SELECTIONAND WITHOUT V ITERBI RE-ALIGNMENT.

aIBMeeting aIB + sIB

AMI 20041210-1052 4.6 3.7AMI 20050204-1206 10.0 8.3

CMU 20050228-1615 25.3 25.2CMU 20050301-1415 9.4 10.1ICSI 20000807-1000 12.3 13.2ICSI 20010208-1430 12.9 13.0LDC 20011116-1400 8.7 7.0LDC 20011116-1500 18.7 17.5NIST 20030623-1409 6.0 5.7NIST 20030925-1517 24.3 23.9

VT 20050304-1300 7.3 5.2VT 20050318-1430 29.7 25.6

ALL 13.3 12.4

different model selection criteria – Normalized Mutual Infor-mation (NMI) and Minimum Description Length (MDL) –are investigated to select the number of clusters. They arecompared with an oracle model selection which manuallychooses the clustering with the lowest DER. The Normalized

TABLE IIIOPTIMAL VALUE FOR NMI THRESHOLD FOR EACH MEETING IN THE

DEVELOPMENT DATASET. THE DER IS REPORTED FOR THE OPTIMAL

VALUE AS WELL AS FOR 0.3. THE CLUSTERING IS PERFORMED WITHβ = 10

optimal NMI DER at DER atMeeting threshold opt th. thres 0.3

AMI 20041210-1052 0.3 9.6 9.6AMI 20050204-1206 0.3 14.9 14.9

CMU 20050228-1615 0.3 26.5 26.5CMU 20050301-1415 0.3 9.6 9.6ICSI 20000807-1000 0.4 13.5 20.0ICSI 20010208-1430 0.3 14.4 14.4LDC 20011116-1400 0.3 9.2 9.2LDC 20011116-1500 0.2 20.6 21.9NIST 20030623-1409 0.4 7.8 11.9NIST 20030925-1517 0.4 25.2 30.6

VT 20050304-1300 0.3 5.9 5.9VT 20050318-1430 0.3 34.9 34.9

Mutual Information is a monotonically increasing functionwith the number of clusters. The value is compared againsta threshold to determine the optimal number of clusters in themodel. Figure 6 illustrates the change of overall DER overthe whole development dataset for changing the value of thisthreshold. The lowest DER is obtained for the value of0.3.In order to understand how the optimal value of the thresholdchanges across different meetings, we report in in Table IIIoptimal threshold for each meeting, DER for the optimalthreshold and for threshold equal to0.3. In eight meetings outthe twelve contained in the development data set, the thresholdthat produces the lowest DER is equal to0.3. Only in twomeetings (ICSI20000807-1000 and NIST20030925-1517)results obtained with the optimal threshold are significantlydifferent from those obtained with the value0.3.To summarizethe optimal value of the threshold seems to be consistent acrossdifferent meetings.

The MDL criterion described in equation (20) is also

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.915

20

25

30

35

40

45

−− NMI Threshold →

−−

DE

R →

(a) (b)

Fig. 6. Effect of varying NMI threshold on the diarization error for thedevelopment dataset. The optimal threshold is fixed as0.3

explored for performing model selection. Speaker error ratescorresponding to both the methods are reported in Table IV.The NMI criterion outperforms the MDL model selection by∼ 2%. The NMI criterion is2.5% worse than the oracle modelselection.

TABLE IVDIARIZATION ERRORRATES FOR DEV DATASET WITHNMI, MDL AND

ORACLE MODEL SELECTION.

aIB aIB+sIBModel without with without with

selection Viterbi Viterbi Viterbi ViterbiOracle 13.3 10.3 12.4 10.0MDL 17.3 14.3 16.2 13.8NMI 15.4 12.6 14.3 12.5

E. Viterbi realignment

The Viterbi realignment is carried out using an ergodicHMM as discussed in Section IV-E. The number of com-ponents of each GMM is fixed at30 based on experimentson the development dataset. The performance after Viterbirealignment is presented in Table IV. The DER is reduced byroughly3% absolute for all the different methods. The lowestDER is obtained using sequential clustering with NMI modelselection.

VI. RT06 MEETING DIARIZATION

In this section we compare the IB system with a state-of-the-art diarization system based on HMM/GMM. Results areprovided for the NIST RT06 evaluation data. Section VI-Adescribes the baseline system while Section VI-B describesthe results of the IB based system. Section VI-C compares thecomputational complexity of the two systems.

A. Baseline System

The baseline system is an ergodic HMM as describedin [3], [15]. Each HMM state represents a cluster. Thestate emission probabilities are modeled by Gaussian MixtureModels (GMM) with a minimum duration constrain of2.5s.


19 MFCC coefficients extracted from the beam-formed signalare used as the input features. The algorithm follows anagglomerative framework, i.e, it starts with a large numberofclusters (hypothesized speakers) and then iteratively mergessimilar clusters until it reaches the best model. After eachmerge, data are re-aligned using a Viterbi algorithm to refinespeaker boundaries.

The initial HMM model is built using uniform linear seg-mentation and each cluster is modeled with a 5 componentGMM. The algorithm then proceeds with bottom-up agglom-erative clustering of the initial cluster models [1]. At eachstep, all possible cluster merges are compared using a modifiedversion of the BIC criterion [2], [3] which is described below.

Consider a pair of clustersci and cj with associated dataDi andDj respectively. Also let the number of parameters formodeling each cluster respectively bepi andpj parameterizedby the GMM modelsmi and mj. Assume the new clusterchaving dataD obtained by mergingDi and Dj is modeledwith a GMM modelm parameterized byp Gaussians. Thepair of clusters that results in the maximum increase in theBIC criterion (given by equation 16) are merged.

(i′, j′) = argmaxi,j

BIC(m)− [BIC(mj) + BIC(mi)] (22)

In [3], the model complexity (i.e. the number of parameters)before and after the merge is made the same. This is achievedby keeping the number of Gaussians in the new modelm thesame, i.e, as the sum of number of Gaussians inmj andmi.i.e., p = pi + pj . Under this condition equation (22) reducesto

(i′, j′) = argmaxi,j

logp(D|m)

p(Di|mi)p(Dj |mj)(23)

This eliminates the need of the penalty term from the BIC.Following the merge, all cluster models are updated usingan EM algorithm. The merge/re-estimation continues until nomerge results in any further increase in the BIC criterion.This determines the number of clusters in the final model.This approach yields state-of-the art results [15] in several di-arization evaluations. The performance of the baseline systemis presented in Table V. The table lists missed speech, falsealarm, speaker error and diarization error.2

TABLE VRESULTS OF THE BASELINE SYSTEM

File Miss FA spnsp spkr err DERAll meetings 6.5 0.1 6.6 17.0 23.6Without TNO meeting 6.8 0.1 6.9 15.7 22.7

B. Results

In this section we benchmark the IB based diarization sys-tem on RT06 data. The same speech/non-speech segmentationis used for all methods. According to results of previoussections the value ofβ is fixed at 10. The NMI threshold value

2We found that one channel of the meeting in RT06 denoted withVT 20051027-1400 is considerably degraded. This channel was removedbefore beamforming. This produces better results for both baseline and IBsystems compared to those presented in [16].

is fixed at0.3. Viterbi re-alignment of the data is performedafter the clustering with a minimum duration constrain of2.5sto refine cluster boundaries.

Table VI reports results for aIB and aIB+sIB clusteringboth with/without TNO meeting. Conclusions are drawn onthe original data set. Results for both NMI and MDL criteriaare reported. NMI is more effective than MDL by0.7%.

TABLE VIDIARIZATION ERRORRATE FOR RT06EVALUATION DATA .

Model aIB+ sIB+selection Viterbi Viterbi

All meetingsMDL 24.4 23.8NMI 23.7 23.2

Without TNO meetingMDL 23.9 23.5NMI 23.0 22.8

Sequential clustering (aIB+sIB) outperforms agglomerativeclustering by 0.5%. As in the development data, the bestresults are obtained by aIB+sIB clustering with NMI modelselection. This system achieves a DER of23.2% as comparedto 23.6% for the baseline system.

Table VII reports diarization error for individual meetingsof the RT06 evaluation data set. We can observe that overallperformances are very close to those of the baseline systembut results per meeting are quite different.

TABLE VIIDIARIZATION ERROR RATE FOR INDIVIDUAL MEETINGS USINGNMI

MODEL SELECTION.

Viterbi realignMeeting Baseline aIB aIB + sIB

CMU 20050912-0900 17.8 20.1 18.7CMU 20050914-0900 15.3 21.9 20.8

EDI 20050216-1051 46.0 48.5 50.5EDI 20050218-0900 23.8 33.3 33.1

NIST 20051024-0930 12.0 16.2 17.3NIST 20051102-1323 23.7 15.7 15.0TNO 20041103-1130 31.5 28.7 26.1

VT 20050623-1400 24.4 9.6 9.4VT 20051027-1400 21.7 20.0 18.4

TABLE VIIIESTIMATED NUMBER OF SPEAKERS BY DIFFERENT MODEL SELECTION

CRITERIA.

aIB + sIBMeeting #speakers NMI MDL

CMU 20050912-0900 4 5 5CMU 20050914-0900 4 6 6

EDI 20050216-1051 4 7 7EDI 20050218-0900 4 7 7

NIST 20051024-0930 9 7 7NIST 20051102-1323 8 7 7TNO 20041103-1130 4 7 6

VT 20050623-1400 5 8 8VT 20051027-1400 4 6 4

Table VIII shows the number of speakers estimated bydifferent algorithms for the RT06 eval data. The number ofspeakers is mostly higher than the actual. This is due to thepresence of small spurious clusters with very short duration(typically less than 5 seconds). However those small clustersdoes not significantly affect the final DER.


C. Algorithm Complexity

Both the The IB bottleneck algorithm and the baselineHMM/GMM system use the agglomerative clustering frame-work. Let the number of clusters at a given step in theagglomeration be K. At each step, the agglomeration algorithmneeds to calculate the distance measure between each pair ofclusters. i.e.,12K(K−1) distance calculations. Let us considerthe difference in the two methods:

• In the HMM/GMM model, each distance calculationinvolves computing the BIC criterion as given by equa-tion (23). Thus a new parametric modelm has to beestimated for every possible merge. This requires traininga GMM model for every pair of clusters. The training isdone using the EM algorithm which is computationallydemanding. In other words, this method involves the useof EM parameter estimation for every possible clustermerge.

• In the IB framework, the distance measure is the sum oftwo Jenson-Shannon divergences as described by equa-tion (7). The JS divergence calculation is straightforwardand computationally very efficient. Thus the distancecalculation in the IB frame work is much faster ascompared to the HMM/GMM approach. The distributionobtained merging two clusters is given by equations (12-13) which simply consists in averaging distributions ofindividual clusters.

In summary while the HMM/GMM systems make intensiveuse of the EM algorithm, the IB based system performs theclustering in the space of discrete distributions using closeform equations for distance calculation and cluster distributionupdate. Thus the proposed approach require less computationthan the baseline.

We perform benchmark experiments on a desktop machinewith AMD AthlonTM 2.4GHz 64 X2 Dual Core Processorand 2GB RAM. Table IX lists the real time factors for thebaseline and IB based diarization systems for the RT06 meet-ing diarization task. It can be seen that the IB based systemsare significantly faster than HMM/GMM based system. Notethat most of the algorithm time for IB systems is consumedfor estimating the posterior features. The clustering is veryfast and takes only around30% of the total algorithm time.Also, introducing the sequential clustering contributes verylittle to the total algorithm time (≈ 8%). Overall the proposeddiarization system is considerably faster than-real time.

TABLE IXREAL TIME FACTORS FOR DIFFERENT ALGORITHMS ONRT06EVAL DATA

posterior Viterbimethod calculation clustering realign TotalaIB 0.09 0.06 0.07 0.22aIB +sIB 0.09 0.08 0.07 0.24Baseline – – – 3.5

VII. D ISCUSSIONS ANDCONCLUSIONS

We have presented speaker diarization systems based onthe information theoretic framework known as the Informa-tion Bottleneck. This system can achieve Diarization Error

rates close to those obtained with conventional HMM/GMMagglomerative clustering. In the following we discuss maindif-ferences between this framework and traditional approaches.

• Distance measure: in the literature, several distance mea-sures have already been proposed for clustering speakerse.g. BIC, generalized log-likelihood ratio, KL divergenceand cross-likelihood distances. The IB principle statesthat when the clustering seeks the solution that preservesas much information as possible w.r.t a set of relevancevariables, the optimal distance between clusters is repre-sented by theJensen-Shannondivergence (see equation8). JS divergence can be written as the sum of two KLdivergences and has many appealing properties related toBayesian error (see [30] for detailed discussion). Thissimilarity measure between clusters is not arbitrarilyintroduced but is naturally derived from the IB objectivefunction (see [9]).

• Regularization: The trade-off parameterβ betweenamount of mutual information and compression regular-izes the clustering solution as shown in Section V-B. Weverified that this term can reduce the DER and make theDER curve more smooth against the number of clusters.

• Parametric Speaker Model: HMM/GMM based systemsbuild an explicit parametric model for each cluster andfor each possible merge. This assumes that each speakerprovides enough data for estimating such a model. Onthe other hand, the system presented here is based on thedistance between clusters in a space of relevance variableswithout any explicit speaker model. The set of relevancevariables is defined through a GMM estimated on theentire audio stream. Furthermore the resulting clusteringtechniques are significantly faster than conventional sys-tems given that merges are estimated in a space of discreteprobabilities.

• Sequential clustering: Conventional systems based onagglomerative clustering (aIB) can produce sub-optimalsolutions due to their greedy nature. Conversely, se-quential clustering (sIB) seeks a global optimum ofthe objective function. In Sections V-C and VI-B, it isshown that sequential clustering outperforms agglomer-ative clustering by∼ 1% on development and∼ 0.5%evaluation data sets. The sequential clustering can be seenas a “purification” algorithm. In the literature, methodsaiming at obtaining clusters that contain speech froma single speaker are referred to as “purification” meth-ods. They refine the agglomerative solution accordingto smoothed log-likelihood [31] or cross Expectation-Maximization between models [32] for finding framesthat were wrongly assigned. In case of sIB, the purifica-tion is done according to the same objective function, andthe correct assignment of each speech segment is basedon the amount of mutual information it conveys on therelevance variables. Furthermore, as reported in Table IX,its computational complexity is only marginally higherthan the one obtained using agglomerative clustering.

In conclusion the proposed system based on the IB principlecan achieve on RT06 evaluation data a DER of23.2% as


compared to23.6% of HMM/GMM baseline while running0.3xRT i.e. significantly faster than the baseline system.

ACKNOWLEDGEMENTS

This work was supported by the European Union under the integrated projectsAMIDA, Augmented Multi-party Interaction with Distance Access, contract numberIST-033812, as well as KERSEQ project under the Indo Swiss Joint Research Program(ISJRP) financed by the Swiss National Science Foundation. This project is pursued incollaboration with EPFL under contract number IT02. The authors gratefully thank theEU and Switzerland for their financial support, and all project partners for a fruitfulcollaboration.

Authors would like to thank Dr. Chuck Wooters and Dr. Xavier Anguera for theirhelp with baseline system and beam-forming toolkit. Authors also would like to thankDr. John Dines for his help with the speech/non-speech segmentation and Dr. Phil Garnerfor his suggestions for improving the paper.

The Authors thank all the reviewers for their valuable comments and suggestionswhich improved the paper considerably.

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