Nmf-Based Blind Source Separation Using A Linear Predictive Coding Error Clustering Criterion

Non-negative matrix factorization (NMF) based sound source separation involves two phases: First, the signal spectrum is decomposed into components which, in a second step, are clustered in order to obtain estimates of the source signal spectra. The major challenge with this approach is the accuracy of the clustering algorithm in the second step, especially as most previously used clustering algorithms are focusing on the frequency part of NMF only and, hence, are missing the information of the time activation matrix. In this paper, we propose a novel clustering criterion which combines the frequency and time activation part of NMF. It is based on the linear predictive coding compression error and we show that it allows a good clustering of the NMF components while at the same time can be efficiently computed. Our new clustering criterion shows an overall improved performance compared with the current state-of-the-art clustering algorithms as we experiment on the TRIOS dataset.

Fast high-dimensional Bayesian classification and clustering

Vahid Partovi Nia

We introduce a fast approach to classification and clustering applicable to high-dimensional continuous data, based on Bayesian mixture models for which explicit computations are available. This permits us to treat classification and clustering in a single framework, and allows calculation of unobserved class probability. The new classifier is robust to adding noise variables as a drawback of the built-in spike-and-slab structure of the proposed Bayesian model. The usefulness of classification using our method is shown on metabololomic example, and on the Iris data with and without noise variables. Agglomerative hierarchical clustering is used to construct a dendrogram based on the posterior probabilities of particular partitions, to provide a dendrogram with a probabilistic interpretation. An extension to variable selection is proposed which summarises the importance of variables for classification or clustering and has probabilistic interpretation. Having a simple model provides estimation of the model parameters using maximum likelihood and therefore yields a fully automatic algorithm. The new clustering method is applied to metabolomic, microarray, and image data and is studied using simulated data motivated by real datasets. The computational difficulties of the new approach are discussed, solutions for algorithm acceleration are proposed, and the written computer code is briefly analysed. Simulations shows that the quality of the estimated model parameters depends on the parametric distribution assumed for effects, but after fixing the model parameters to reasonable values, the distribution of the effects influences clustering very little. Simulations confirms that the clustering algorithm and the proposed variable selection method is reliable when the model assumptions are wrong. The new approach is compared with the popular Bayesian clustering alternative, MCLUST, fitted on the principal components using two loss functions in which our proposed approach is found to be more efficient in almost every situation.

EPFL2009

Robust Principal Component Analysis on Graphs

Xavier Bresson, Michael Bronstein, Vasilis Kalofolias, Nauman Shahid, Pierre Vandergheynst

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization model, which is however non-convex. Besides, PCA based clustering can also be enhanced by using a graph of data similarity. In this article, we introduce a new model called "Robust PCA on Graphs" which incorporates spectral graph regularization into the Robust PCA framework. Our proposed model benefits from 1) the robustness of principal components to occlusions and missing values, 2) enhanced low-rank recovery, 3) improved clustering property due to the graph smoothness assumption on the low-rank matrix, and 4) convexity of the resulting optimization problem. Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery tasks.

2015

Fast high-dimensional Bayesian classification and clustering

Vahid Partovi Nia

EPFL2009