A Small Footprint i-vector Extractor

Transcription

1 A Small Footprint i-vetor Extrator Patrik Kenny Centre de reherhe informatique de Montréal (CRIM) Abstrat Both the memory and omputational requirements of algorithms traditionally used to extrat i-vetors at run time and to train i-vetor extrators off-line sale quadratially in the i- vetor dimensionality. We desribe a variational Bayes algorithm for alulating i-vetors exatly whih onverges in a few iterations and whose omputational and memory requirements sale linearly rather than quadratially. For typial i-vetor dimensionalities, the omputational requirements are slightly greater than those of the traditional algorithm. The run time memory requirement is sarely greater than that needed to store the eigenvoie basis. Beause it is an exat method, the variational Bayes algorithm enables the onstrution of i-vetor extrators of muh higher dimensionality than has previously been envisaged. We show that modest gains in speaker verifiation auray (as measured by the 200 NIST detetion ost funtion) an be ahieved using high dimensional i-vetors.. Introdution An important reent advane in speaker reognition is the disovery that speeh signals of arbitrary duration an be effetively represented by i-vetors of relatively low dimension (with this dimension being independent of the utterane duration) []. I-vetors have worked equally well in language reognition [2, 3] and both i-vetors and speaker fators extrated from segments of very short duration (on the order of seond) have been suessfully used in diarizing telephone onversations [4, 5, 6]. (Speaker fators are extrated in the same way as i-vetors. They differ in the way the data used to estimate the eigenvoie basis is organized.) I-vetors are so easy to work with that they are now the primary representation used in many state of the art speaker reognition systems. By banishing the time dimension altogether, the i-vetor representation enables the speaker reognition problem to be ast as a traditional biometri pattern reognition problem like fae reognition. This allows well established tehniques suh as osine distane soring, Linear Disriminant Analysis and Probabilisti Linear Disriminant Analysis (PLDA) to be applied. The advantage of a low, fixed dimensional feature representation is partiularly apparent in the ase of PLDA as this an be regarded as a simplified version of Joint Fator Analysis (JFA) whih results when eah utterane is represented by single feature vetor (rather than by a sequene of epstral vetors of random duration, as is traditional in speeh proessing). The i-vetor representation of speeh utteranes an be viewed as a type of prinipal omponents analysis of utteranes of arbitrary duration, based on the assumption that eah utterane an be modeled by a Gaussian Mixture Model (GMM) and applying probabilisti prinipal omponents analysis to the GMM supervetors. Thus the basi assumption is that all utterane supervetors are onfined to a low dimensional subspae of the GMM supervetor spae so that eah supervetor is speified by a small number of oordinates. These oordinates an be thought of as representing physial quantities whih are onstant for a given utterane (suh as voal trat length, room impulse response et.) but whih differ from one utterane to another. The i-vetor representation of the utterane is defined by these oordinates. The standard algorithm for extrating i- vetors is eigenvoie maximum a posteriori (MAP) estimation (Proposition of [7]) and the primary training algorithm used in building an i-vetor extrator is the eigenvoie estimation algorithm given in Proposition 3 of [7] (applied in suh a way that eah utterane is treated as oming from a different speaker). Both the omputational and memory requirements of these algorithms sale quadratially in the i-vetor dimensionality. This aounts for the fat that, although prinipal omponents analyzers of several thousand dimensions are ommonly used in other fields, there are to our knowledge no instanes in the urrent speaker reognition literature of i-vetor extrators of dimension greater than 800. For example an i-vetor extrator of dimension 000 (with a standard onfiguration of 2048 Gaussians and 60 dimensional aousti features) requires 8.8 Gb of storage (in double preision) at run time and twie that amount of memory is needed to train it. In this paper, we will show how to minimize the memory requirements of i-vetor extration (both at run time and during training) using an iterative variational Bayes algorithm to perform the eigenvoie MAP omputation. The algorithm onverges very quikly (3 variational Bayes iterations are typial) and no ost in speaker reognition auray is inurred. A 000 dimensional i-vetor extrator an be aommodated in less than Gb at run time and the omputational overhead is quite modest: the CPU time required to extrat a 000 dimensional i-vetor from an utterane is on the order of seond, assuming that the Baum-Welh statistis for the utterane are given. A key aspet of the variational Bayes algorithm is that both the omputational and memory requirements sale linearly rather than quadratially in the i-vetor dimensionality. This makes it possible to explore the question of whether improvements in speaker reognition auray an be obtained using very high dimensional i-vetor representations. (It is well known that approximate methods an be used to extrat i-vetors at run time without seriously ompromising speaker reognition auray but exat omputations appear to be needed for training i-vetor extrators [8]. This was our prinipal motivation for developing the variational Bayes method.) We have experimented with i-vetors of dimension as high as 600 and we will show that minor improvements in the value of the normalized 200 NIST detetion ost funtion an be obtained using very high dimensional i-vetors.

2 2.. Notation 2. Review of i-vetors The probabilisti model underlying eigenvoie MAP is an extension of probabilisti prinipal omponents analysis [9]. We assume that we are given a universal bakground model (UBM) with C mixture omponents indexed by =,..., C. For eah mixture omponent we denote by w, m and Σ the orresponding mixture weight, mean vetor and ovariane matrix. We denote by F the dimension of the aousti feature vetors. To aount for inter-utterane variability, we assoiate with eah utterane an R vetor y (the i-vetor) and with eah mixture omponent an F R matrix V. For the given utterane, the aousti feature vetors assoiated with the mixture omponent are supposed to be distributed with mean µ and ovariane matrix Σ where µ = m + V y. Thus, if we are given an utterane represented as a sequene of frames,..., T and the aliment of frames with mixture omponents is given, the likelihood of the utterane is N ln (2π) F/2 Σ /2 ( t V y m ) Σ ( t V y m ) 2 t where the sum over extends over all mixture omponents; the sum over t extends over all frames aligned with the mixture omponent ; and N is the number of suh frames. This expression an be evaluated in terms of the first and seond order statistis for eah mixture omponent, namely F = t S = t t t t. Sine the alignment of frames with mixture omponents is not in fat given, we use the Baum-Welh statistis instead. These are defined by N = t F = t S = t γ t() γ t() t γ t() t t where, for eah time t, γ t() is the posterior probability that t is generated by the mixture omponent, alulated with the UBM. (This hoie is intuitively natural and it an be motivated by variational Bayes [0].) In [7], the only roles played by the seond order Baum- Welh statistis are in the alulation of the likelihood funtion (Proposition 2) and in the estimation of the ovariane matries Σ (Proposition 3). In pratie, for eah mixture omponent, m and Σ an be opied from the UBM and only the matrix V needs to be estimated from the training data. Furthermore, the ontribution of the seond order statistis an be dropped from the expression for the likelihood funtion without ompromising its usefulness. Thus the seond order statistis do not play an essential role in most implementations i-vetor extration Proposition of [7] shows how to alulate the posterior distribution of y for a given utterane on the assumption that the prior is standard normal. (There is no gain in generality by assuming a non-standard normal prior.) The posterior ovariane matrix Cov (y, y) and mean vetor y are given by Cov (y, y) = I + N V y = Cov (y, y) Σ V Σ V! (F N m ).() The usual proedure to alleviate the omputational burden is to store the matries V Σ V and, for eah utterane s, use these matries together with the 0 order Baum-Welh statistis to evaluate the preision matrix I + N (s)v Σ V for the given utterane. Beause of symmetry, only R(R+)/2 real numbers (i.e. the upper triangular part of V Σ V ) need to be stored for eah mixture omponent. Of ourse it would be possible to eonomize on memory by alulating the preision matrix for eah utterane from srath but this is not done in pratie as the omputational burden would be exessive Whitening the Baum-Welh statistis A simplifiation whih an be applied if the mean vetors and ovariane matries m and Σ are taken as given (rather than estimated in the ourse of training the i-vetor extrator) is that the first order statistis an be pre-whitened by subjeting them to the transformation where F L (F N m ) L L = Σ is the Cholesky deomposition of Σ. (Of ourse hanging the Baum-Welh statistis in this way will hange the the estimates of the matries V produed by the eigenvoie training algorithm summarized below. But these hanges anel eah other out in the sense that, for eah utterane, the posterior distribution of the hidden variables y remains unhanged. Thus the point estimate of the i-vetor that is, the mean of the posterior remains unhanged whih is all that we require.) Performing this transformation enables us to take m = 0 and Σ = I in all of the equations in [7]. This simplifies the implementation and, more importantly, it failitates building i- vetor extrators whih do not have to distinguish between full ovariane and diagonal ovariane UBMs. (It was shown in [] that full ovariane UBMs outperform diagonal ovariane UBMs in speaker reognition.) We will assume heneforth that the Baum-Welh statistis have been whitened Training the ivetor extrator As for estimating the matries V, suppose we have a training set where for eah utterane s, the first and seond order moments y(s) and y(s)y (s) have been alulated. The maximum likelihood update formula for V is!! V = F (s) y (s) N (s) y(s)y (s) s s

3 where the sums over s extend over all utteranes in the training set, and for eah utterane s, N (s) and F (s) are the Baum- Welh statistis of order 0 and for mixture omponent. Calulating the first and seond moments is just a matter of evaluating the posterior of y(s). For example, y(s)y (s) = Cov (y(s), y(s)) + y(s) y (s). As for minimum divergene estimation, the idea is to modify the matries V in suh a way as to fore the empirial distribution of the i-vetors to onform to the standard normal prior [2, 3]. Let LL be the Cholesky deomposition of the matrix S y(s)y (s) s where S is the number of training utteranes and the sum extends over all utteranes in the training set. The transformations V V L y(s) L y(s) have the desired effet. Both maximum likelihood and minimum divergene estimation inrease the likelihood of the training set where the likelihood is evaluated as in Proposition 2 of [7]. Note that, just as for run-time i-vetor extration, alulating i-vetor posteriors is the prinipal omputation for both maximum likelihood and minimum divergene training. 3. The variational Bayes algorithm We will show how the memory requirements of the posterior alulation an be substantially redued at the ost of a modest omputational overhead by working with a basis of the i-vetor spae with respet to whih the i-vetor posterior ovariane matries are approximately diagonal, so that the i-vetor omponents are approximately statistially independent in the posterior. The variational Bayes (VB) method is a standard way of enforing this type of posterior independene assumption. In the ase at hand, variational Bayes produes an approximation to the true posterior whih is of very high quality in the sense that, at onvergene, the mean of the posterior distribution that is, the point estimate of the i-vetor is alulated exatly. The only inauray is in the posterior ovariane matrix whih is only approximately diagonal. These posterior ovarianes are used in training the i-vetor extrator (not at run time) but the effet of the diagonal approximation is minimal so that it turns out that using the VB method in training i-vetor extrators leads to no degradation in speaker reognition auray. If the VB algorithm is initialized properly, very few iterations (typially 3, independently of the i-vetor dimension) are needed to obtain aurate i-vetor estimates. Beause the off-diagonal elements of the posterior ovariane matrix are ignored, it follows that the omputational and memory requirements of the VB method sale linearly rather than quadratially in the i-vetor dimension. 3.. VB updates Suppose we are given an utterane represented as a sequene of aousti feature vetors,..., T or for short. We suppose that the prior distribution of y is standard normal. Assume provisionally that it is reasonable to impose diagonal onstraints on the posterior ovariane matrix of y given so that we an write y = (y,..., y R ) Q(y) = Q(y )... Q(y R ). where Q(y) approximates the true posterior P(y ). We will return to the question of why this assumption is reasonable in the next setion. Meantime, we derive a variational Bayes algorithm to alulate Q(y). We introdue the following notation. For r =,..., R, we denote the rth olumn of V by V r so that and diag (V V ) = V y = 0 R r= V V V r y r... V R V R C A. The memory overhead of the VB algorithm is the ost of storing this diagonal matrix for eah mixture omponent, rather than (the upper triangle of) V V as required by the standard posterior alulation outlined in Setion 2.2. Following the standard proedure given in [9] the VB update for Q(y r ) is ln Q(y r ) = E y\y r [ln P(y, )] + onstant. So using to indiate equality up to an additive onstant, we have ln Q(y r ) 2 Letting 2 + E y\y r ( + NV r " # ( t V y) ( t V y) 2 (yr ) 2 t V r ) (y r ) 2 F N r r L r = + y r V r y r. N V r V r, we an read off the posterior expetation and variane of y r from this expression: y r = F L r N y r V r Var(y r ) = L r. r r A omplete VB update iteration onsists in applying this for r =,..., R. Readers familiar with the Jaobi method in numerial linear algebra will reognize that suessive VB iterations implement the Jaobi method for solving the linear system (). It is well known (and easy to verify) that, if the Jaobi method onverges, then it onverges to the solution of the linear system. Convergene in this ase is guaranteed by variational Bayes [9]. Thus, if is run to onvergene, the VB method alulates i-vetors exatly.

4 For effiient implementation, we an use the following reformulation. Set R = F N V y for eah mixture omponent (R for remainder). The VB update of y onsists in performing the following operations for r =,..., R:. R R + N y r V r ( =,..., C) 2. y r P = L r V r R 3. R R N y r V r ( =,..., C) More effiiently (sine diag (V V ) has been preomputed), ) and 2) an be ombined as y r new = L r = L r = L r V r (R + N y r old V r ) R + y r old R + L r L «y r r old N V r V r so that the VB update of y redues to performing the following operations for r =,..., R:. y r P new = L r V r R + ` L y r r old 2. R R N ( y r new y r old ) V r ( =,..., C) VB Initialization The VB algorithm is guaranteed to alulate i-vetors exatly but a good initialization is needed to ensure that it does so quikly. We are free to postmultiply the matries V by any orthogonal matrix without affeting the assumption that y has a standard normal prior distribution; in partiular we an hoose a basis of the i-vetor spae suh that the matrix w V V is diagonal where, for eah mixture omponent, w is the orresponding mixture weight (i.e. prior probability). Sine, for a given utterane of suffiiently long duration, N Nw it follows that the posterior ovariane matrix for an utterane, namely Cov (y, y) in (), is approximately diagonal (as we mentioned in Setion 3.). Note that the quality of the approximation may degrade in the ase of very short utteranes (for whih it may not be the ase that N Nw for eah mixture omponent omponent). Thus a reasonable initial estimate of y for VB is the approximate solution of () obtained by ignoring the off-diagonal elements in Cov (y, y). (Solving a system of equations with a diagonal oeffiient matrix is omputationally trivial.) Unlike the approximation used in [8], this is only an initial estimate hosen so as to ensure rapid onvergene of the VB algorithm. Note that in [8] the approximation is only for extrating i-vetors at run time; it turns out to be too rude to use in training i-vetor extrators. On the other hand, sine the variational Bayes approah to alulating i-vetors is exat, it an be used in off-line training of i-vetor extrators. This is the reason why we are able to experiment with i-vetors of very high dimensionality The variational lower bound The variational Bayes updates are guaranteed to inrease the variational lower bound L on ln P() defined by» P(y, ) L = E ln Q(y) where the expetation is taken with respet to Q(y). Ignoring the ontribution of the seond order statistis (whih does not hange from one VB iteration to the next), the variational lower bound an be expressed in terms of the posterior mean and ovariane as follows L = (V y ) F N (V y ) V y 2 2 tr (N V V Cov (y, y)) D (Q(y) P(y)) where D (Q(y) P(y)) is the Kullbak-Leibler divergene between the posterior Q(y) and the standard normal prior P(y) whih (by the formula for the divergene of two multivariate Gaussians [3]) is given by D (Q(y) P(y)) = R 2 ln Cov (y, y) tr ([ Cov (y, y) + y y ]). Evaluating the variational lower bound on eah VB update turns out to be rather expensive so in pratie it is more useful for troubleshooting than for monitoring onvergene of the VB algorithm at run time. (A simple, effetive run-time onvergene riterion is the Eulidean norm of the differene between suessive i-vetor estimates y new y old.) In onstruting an i-vetor extrator, the usual riterion used to monitor onvergene of the maximum likelihood and minimum divergene training algorithms is the exat likelihood funtion desribed in Proposition 2 of [7] whose evaluation requires omputing exat posterior ovarianes. If the posteriors are alulated with the VB algorithm, the appropriate riterion to use is the aggregate variational lower bound alulated by summing the variational lower bound over all training utteranes. If posteriors are evaluated with the VB method, this riterion is guaranteed to inrease from one training iteration to the next (both for maximum likelihood training and minimum divergene training) so it is useful for troubleshooting. 4.. Testbed 4. Experimental Results We report the results of experiments onduted on the det 2 trials (normal voal effort telephone speeh) in the female portion of the extended ore ondition of the NIST 200 speaker reognition evaluation (thus using a larger set of trials than was provided for in the original evaluation plan ). Results are reported using the following metris: the equal error rate (EER), the normalized detetion ost funtion used in evaluations prior to 200 (2008 NDCF) and the normalized detetion ost funtion defined for the 200 evaluation (200 NDCF) whih severely penalizes false alarms. The purpose of the experiments was to ompare the performane of the VB i-vetor extrator with that of our earlier JFA-based implementation and to investigate the SRE0 evalplan.r6.pdf

5 question of whether improvements in speaker verifiation auray ould be ahieved with very high dimensional i-vetors. Speaker verifiation was arried out with heavy-tailed PLDA, using the front end and data sets for training the UBM, the i-vetor extrators and the PLDA lassifiers desribed in [3]. In omparing the VB i-vetor extrator with the JFA-based implementation, we used the in house CRIM voie ativity detetor (VAD) in extrating Baum-Welh statistis. However we learned in the ourse of the Bosaris workshop at BUT in 200 that the CRIM voie ativity detetor did not perform as well as the elebrated BUT Hungarian phoneme reognizer and BUT kindly made their transripts available to us for the experiments with very high dimensional i-vetors Auray of VB We evaluated the auray of the variational Bayes method by omparing it with our original i-vetor implementation, where the i-vetor extrator was built using exeutables written for Joint Fator Analysis. (The sripts were modified in suh a way as to ignore the speaker labels attahed to reordings in the Swithboard and Mixer training orpora.) We used a standard UBM onfiguration (2048 diagonal Gaussians, 60 dimensional aousti feature vetors) to extrat Baum-Welh statistis. However, in our JFA implementation, the Baum-Welh statistis were not whitened, the means and ovarianes assoiated with the various mixture omponents were re-estimated in the ourse of fator analysis training rather than opied form the UBM (and only UBMs with diagonal ovariane matries were supported). To test the auray of the variational Bayes method we used it in onjuntion with the diagonal ovariane UBM both to train an i-vetor extrator and to alulate the i-vetors at run time. Our implementation in this ase used whitened Baum- Welh statistis so the means and ovarianes assoiated with the various mixture omponents were not re-estimated in the ourse of training the i-vetor extrator. We used 5 iterations of variational Bayes to extrat i-vetors. The i-vetor dimensionality was 400 in both ases, redued to 00 by linear disriminant analysis as in [, ] and heavytailed PLDA lassifiers [3] were used for verifiation. The results were essentially idential: an equal error rate of 3.% for the JFA implementation versus 3.0% for VB and a detetion ost of 0.50 for JFA versus 0.49 for VB (where the detetion ost was measured with the 200 NIST ost funtion). The slight edge observed for the VB method may seem surprising. It appears to be attributable to the fat that the varianes were opied from the UBM in this ase but not in the ase of the JFA-based implementation. The effet of this opying is to overestimate the varianes in the i-vetor extrator by about 5%. (Copying results in overestimates sine the UBM varianes are estimated in a way whih takes no aount of inter-utterane variability.) It is well known that overestimating varianes often proves to be helpful in speeh modeling Effiieny of VB We evaluated the effiieny of the VB method by performing a omparison with the standard approah summarized in (), using whitened Baum-Welh statistis in both ases. On a 2.40 GHz Intel eon CPU, the time taken to extrat an i-vetor with the standard approah was about 0.5 seonds. Almost all of the time was spent in BLAS routines (in partiular 75% of the omputational burden is spent aumulating the ovariane matrix in ()). An estimate of about 0.25 seonds is given [8] whih appears to indiate that ompiler optimization might be useful. For the VB approah we performed 5 VB updates at run time. Under these onditions the time taken to extrat an i- vetor was 0.9 seonds. Thus, as expeted, the VB method is slower (by about a fator of 2 in the ase of 400 dimensional i-vetors) but still quite quik ompared with the ost of extrating Baum-Welh statistis using a large UBM. In working with higher dimensional i-vetors, we always found that 3 5 variational Bayes iterations were suffiient. (The exat number of iterations performed was determined by the Eulidean norm stopping riterion mentioned in Setion 3.3). It follows that, like the memory requirements, the omputational overhead of the VB method sales linearly rather than quadratially in the i-vetor dimension. So the omputational advantage of the standard implementation relative to the VB method atually dereases as the i-vetor dimension inreases High dimensional i-vetors Sine the VB method enables very high dimensional i-vetor extrators to be trained with relatively modest omputational resoures, we onduted some experiments to see if any gains in auray ould be ahieved by inreasing the i-vetor dimensionality. We used the same 2048 omponent diagonal UBM as in the previous setions but we replaed the CRIM VAD with the BUT VAD whih aounts for the lower error rates. In every ase we redued the number of dimensions to 00 by linear disriminant analysis (LDA). Table shows the results of inreasing the i-vetor dimension from 400 to 600 in steps of 400. The equal error rates degrade, but there is a minor improvement in the 200 NDCF. Table : EER / NDCF female extended ore ondition, 200 NIST evaluation. 00 dimensional LDA. Diagonal UBM, 2048 Gaussians. i-vetor EER 2008 NDCF 200 NDCF % % % % Conlusion We have shown how a variational Bayes approah enables exat i-vetor extration to performed in suh a way that omputational and memory requirements sale linearly rather than quadratially in the i-vetor dimensionality. Beause it is an exat method, the variational Bayes algorithm an be used in training i-vetor extrators as well as at run-time. This makes it possible to experiment with i-vetors of muh higher dimension than has previously been envisaged, yielding modest improvements in speaker verifiation auray as measured by the NIST 200 detetion ost funtion. Aknowledgements We would like to thank Brno University of Tehnology for hosting the 200 Bosaris workshop where this work was begun. Speial thanks to Ondrej Glembek who suggested the initialization in Setion 3.2.

6 6. Referenes [] N. Dehak, P. Kenny, R. Dehak, P. Dumouhel, and P. Ouellet, Front-end fator analysis for speaker verifiation, IEEE Trans. Audio, Speeh, Lang. Proess., vol. 9, no. 4, pp , May 20. [2] N. Dehak, P. Torres-Carrasquillo, D. Reynolds, and R. Dehak, Language reognition via ivetors and dimensionality redution, in Pro. Interspeeh, Florene, Aug. 20. [3] G. Martnez, O. Plhot, L. Burget, O. Glembek, and P. Matejka, Language reognition in ivetors spae, in Pro. Interspeeh, Florene, Aug. 20. [4] F. Castaldo, D. Colibro, E. Dalmasso, P. Lafae, and C. Vair, Stream-based speaker segmentation using speaker fators and eigenvoies, in Pro. ICASSP, Las Vegas, Nevada, Mar. 2008, pp [5] C. Vaquero, A. Ortega, and E. Lleida, Intra-session variability ompensation and a hypothesis generation and seletion strategy for speaker segmentation, in Pro. ICASSP, 20, pp [6] S. Shum, N. Dehak, E. Chuangsuwanih, D. Reynolds, and J. Glass, Exploiting intra-onversation variability for speaker diarization, in Pro. Interspeeh, Florene, Aug. 20. [7] P. Kenny, G. Boulianne, and P. Dumouhel, Eigenvoie modeling with sparse training data, IEEE Trans. Speeh Audio Proessing, vol. 3, no. 3, pp , May [8] O. Glembek, L. Burget, P. Matejka, M. Karafiat, and P. Kenny, Simplifiation and optimization of i-vetor extration, in Proeedings ICASSP, 20. [9] C. Bishop, Pattern Reognition and Mahine Learning. New York, NY: Springer Siene+Business Media, LLC, [0]. Zhao, Y. Dong, J. Zhao, L. Lu, J. Liu, and H. Wang, Variational Bayesian Joint Fator Analysis for Speaker Verifiation, in Pro. ICASSP 2009, Taipei, Taiwan, Apr [] P. Matejka, O. Glembek, F. Castaldo, J. Alam, O. Plhot, P. Kenny, L. Burget, and J. Cernoky, Full-ovariane UBM and heavy-tailed PLDA in i-vetor speaker verifiation, in Proeedings ICASSP, 20. [2] P. Kenny, P. Ouellet, N. Dehak, V. Gupta, and P. Dumouhel, A study of inter-speaker variability in speaker verifiation, IEEE Trans. Audio, Speeh and Lang. Proess., vol. 6, no. 5, pp , July [Online]. Available: [3] P. Kenny, Bayesian speaker verifiation with heavy tailed priors, in Pro. Odyssey 200: The speaker and Language Reognition Workshop, Brno, Czeh Rebubli, June 200.