Enhancing timbre model using MFCC and its time derivatives for music similarity estimation

One of the popular methods for content-based music similarity estimation is to model timbre with MFCC as a single multivariate Gaussian with full covariance matrix, then use symmetric Kullback-Leibler divergence. From the field of speech recognition, we propose to use the same approach on the MFCCs’ time derivatives to enhance the timbre model. The Gaussian models for the delta and acceleration coefficients are used to create their respective distance matrix. The distance matrices are then combined linearly to form a full distance matrix for music similarity estimation. In our experiments on two datasets, our novel approach performs better than using MFCC alone.Moreover, performing genre classification using k-NN showed that the accuracies obtained are already close to the state-of-the-art

The Burbea-Rao and Bhattacharyya centroids

We study the centroid with respect to the class of information-theoretic Burbea-Rao divergences that generalize the celebrated Jensen-Shannon divergence by measuring the non-negative Jensen difference induced by a strictly convex and differentiable function. Although those Burbea-Rao divergences are symmetric by construction, they are not metric since they fail to satisfy the triangle inequality. We first explain how a particular symmetrization of Bregman divergences called Jensen-Bregman distances yields exactly those Burbea-Rao divergences. We then proceed by defining skew Burbea-Rao divergences, and show that skew Burbea-Rao divergences amount in limit cases to compute Bregman divergences. We then prove that Burbea-Rao centroids are unique, and can be arbitrarily finely approximated by a generic iterative concave-convex optimization algorithm with guaranteed convergence property. In the second part of the paper, we consider the Bhattacharyya distance that is commonly used to measure overlapping degree of probability distributions. We show that Bhattacharyya distances on members of the same statistical exponential family amount to calculate a Burbea-Rao divergence in disguise. Thus we get an efficient algorithm for computing the Bhattacharyya centroid of a set of parametric distributions belonging to the same exponential families, improving over former specialized methods found in the literature that were limited to univariate or "diagonal" multivariate Gaussians. To illustrate the performance of our Bhattacharyya/Burbea-Rao centroid algorithm, we present experimental performance results for $k$-means and hierarchical clustering methods of Gaussian mixture models.Comment: 13 page

Optimal Kullback-Leibler Aggregation via Information Bottleneck

In this paper, we present a method for reducing a regular, discrete-time Markov chain (DTMC) to another DTMC with a given, typically much smaller number of states. The cost of reduction is defined as the Kullback-Leibler divergence rate between a projection of the original process through a partition function and a DTMC on the correspondingly partitioned state space. Finding the reduced model with minimal cost is computationally expensive, as it requires an exhaustive search among all state space partitions, and an exact evaluation of the reduction cost for each candidate partition. Our approach deals with the latter problem by minimizing an upper bound on the reduction cost instead of minimizing the exact cost; The proposed upper bound is easy to compute and it is tight if the original chain is lumpable with respect to the partition. Then, we express the problem in the form of information bottleneck optimization, and propose using the agglomerative information bottleneck algorithm for searching a sub-optimal partition greedily, rather than exhaustively. The theory is illustrated with examples and one application scenario in the context of modeling bio-molecular interactions.Comment: 13 pages, 4 figure

KL-Divergence Guided Two-Beam Viterbi Algorithm on Factorial HMMs

This thesis addresses the problem of the high computation complexity issue that arises when decoding hidden Markov models (HMMs) with a large number of states. A novel approach, the two-beam Viterbi, with an extra forward beam, for decoding HMMs is implemented on a system that uses factorial HMM to simultaneously recognize a pair of isolated digits on one audio channel. The two-beam Viterbi algorithm uses KL-divergence and hierarchical clustering to reduce the overall decoding complexity. This novel approach achieves 60% less computation compared to the baseline algorithm, the Viterbi beam search, while maintaining 82.5% recognition accuracy.Ope

The Diagonalized Newton Algorithm for Nonnegative Matrix Factorization

Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative data is approximated by the low-rank product of two matrices with non-negative entries. In this paper, the approximation quality is measured by the Kullback-Leibler divergence between the data and its low-rank reconstruction. The existence of the simple multiplicative update (MU) algorithm for computing the matrix factors has contributed to the success of NMF. Despite the availability of algorithms showing faster convergence, MU remains popular due to its simplicity. In this paper, a diagonalized Newton algorithm (DNA) is proposed showing faster convergence while the implementation remains simple and suitable for high-rank problems. The DNA algorithm is applied to various publicly available data sets, showing a substantial speed-up on modern hardware.Comment: 8 pages + references; International Conference on Learning Representations, 201