Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering

State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with $\ell_1$, $\ell_2$ or nuclear norms. $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be connected. $\ell_2$ and nuclear norm regularization often improve connectivity, but give a subspace-preserving affinity only for independent subspaces. Mixed $\ell_1$, $\ell_2$ and nuclear norm regularizations offer a balance between the subspace-preserving and connectedness properties, but this comes at the cost of increased computational complexity. This paper studies the geometry of the elastic net regularizer (a mixture of the $\ell_1$ and $\ell_2$ norms) and uses it to derive a provably correct and scalable active set method for finding the optimal coefficients. Our geometric analysis also provides a theoretical justification and a geometric interpretation for the balance between the connectedness (due to $\ell_2$ regularization) and subspace-preserving (due to $\ell_1$ regularization) properties for elastic net subspace clustering. Our experiments show that the proposed active set method not only achieves state-of-the-art clustering performance, but also efficiently handles large-scale datasets.Comment: 15 pages, 6 figures, accepted to CVPR 2016 for oral presentatio

Adaptive speaker diarization of broadcast news based on factor analysis

The introduction of factor analysis techniques in a speaker diarization system enhances its performance by facilitating the use of speaker specific information, by improving the suppression of nuisance factors such as phonetic content, and by facilitating various forms of adaptation. This paper describes a state-of-the-art iVector-based diarization system which employs factor analysis and adaptation on all levels. The diarization modules relevant for this work are: the speaker segmentation which searches for speaker boundaries and the speaker clustering which aims at grouping speech segments of the same speaker. The speaker segmentation relies on speaker factors which are extracted on a frame-by-frame basis using eigenvoices. We incorporate soft voice activity detection in this extraction process as the speaker change detection should be based on speaker information only and we want it to disregard the non-speech frames by applying speech posteriors. Potential speaker boundaries are inserted at positions where rapid changes in speaker factors are witnessed. By employing Mahalanobis distances, the effect of the phonetic content can be further reduced, which results in more accurate speaker boundaries. This iVector-based segmentation significantly outperforms more common segmentation methods based on the Bayesian Information Criterion (BIC) or speech activity marks. The speaker clustering employs two-step Agglomerative Hierarchical Clustering (AHC): after initial BIC clustering, the second cluster stage is realized by either an iVector Probabilistic Linear Discriminant Analysis (PLDA) system or Cosine Distance Scoring (CDS) of extracted speaker factors. The segmentation system is made adaptive on a file-by-file basis by iterating the diarization process using eigenvoice matrices adapted (unsupervised) on the output of the previous iteration. Assuming that for most use cases material similar to the recording in question is readily available, unsupervised domain adaptation of the speaker clustering is possible as well. We obtain this by expanding the eigenvoice matrix used during speaker factor extraction for the CDS clustering stage with a small set of new eigenvoices that, in combination with the initial generic eigenvoices, models the recurring speakers and acoustic conditions more accurately. Experiments on the COST278 multilingual broadcast news database show the generation of significantly more accurate speaker boundaries by using adaptive speaker segmentation which also results in more accurate clustering. The obtained speaker error rate (SER) can be further reduced by another 13% relative to 7.4% via domain adaptation of the CDS clustering. (C) 2017 Elsevier Ltd. All rights reserved