Alpha-divergence two-dimensional nonnegative matrix factorization for biomedical blind source separation

An alpha-divergence two-dimensional nonnegative matrix factorization (NMF2D) for biomedical signal separation is presented. NMF2D is a popular approach for retrieving low-rank approximations of nonnegative data such as image pixel, audio signal, data mining, pattern recognition and so on. In this paper, we concentrate on biomedical signal separation by using NMF2D with alpha-divergence family which decomposes a mixture into two-dimensional convolution factor matrices that represent temporal code and the spectral basis. The proposed iterative estimation algorithm (alpha-divergence algorithm) is initialized with random values, and it updated using multiplicative update rules until the values converge. Simulation experiments were carried out by comparing the original and estimated signal in term of signal-to-distortion ratio (SDR). The performances have been evaluated by including and excluding the sparseness constraint which sparseness is favored by penalizing nonzero gains. As a result, the proposed algorithm improved the iteration speed and sparseness constraints produce slight improvement of SDR

Statistical Traffic State Analysis in Large-scale Transportation Networks Using Locality-Preserving Non-negative Matrix Factorization

Statistical traffic data analysis is a hot topic in traffic management and control. In this field, current research progresses focus on analyzing traffic flows of individual links or local regions in a transportation network. Less attention are paid to the global view of traffic states over the entire network, which is important for modeling large-scale traffic scenes. Our aim is precisely to propose a new methodology for extracting spatio-temporal traffic patterns, ultimately for modeling large-scale traffic dynamics, and long-term traffic forecasting. We attack this issue by utilizing Locality-Preserving Non-negative Matrix Factorization (LPNMF) to derive low-dimensional representation of network-level traffic states. Clustering is performed on the compact LPNMF projections to unveil typical spatial patterns and temporal dynamics of network-level traffic states. We have tested the proposed method on simulated traffic data generated for a large-scale road network, and reported experimental results validate the ability of our approach for extracting meaningful large-scale space-time traffic patterns. Furthermore, the derived clustering results provide an intuitive understanding of spatial-temporal characteristics of traffic flows in the large-scale network, and a basis for potential long-term forecasting.Comment: IET Intelligent Transport Systems (2013

Stochastic Behavior of the Nonnegative Least Mean Fourth Algorithm for Stationary Gaussian Inputs and Slow Learning

Some system identification problems impose nonnegativity constraints on the parameters to estimate due to inherent physical characteristics of the unknown system. The nonnegative least-mean-square (NNLMS) algorithm and its variants allow to address this problem in an online manner. A nonnegative least mean fourth (NNLMF) algorithm has been recently proposed to improve the performance of these algorithms in cases where the measurement noise is not Gaussian. This paper provides a first theoretical analysis of the stochastic behavior of the NNLMF algorithm for stationary Gaussian inputs and slow learning. Simulation results illustrate the accuracy of the proposed analysis.Comment: 11 pages, 8 figures, submitted for publicatio

Clustering and Latent Semantic Indexing Aspects of the Nonnegative Matrix Factorization

This paper provides a theoretical support for clustering aspect of the nonnegative matrix factorization (NMF). By utilizing the Karush-Kuhn-Tucker optimality conditions, we show that NMF objective is equivalent to graph clustering objective, so clustering aspect of the NMF has a solid justification. Different from previous approaches which usually discard the nonnegativity constraints, our approach guarantees the stationary point being used in deriving the equivalence is located on the feasible region in the nonnegative orthant. Additionally, since clustering capability of a matrix decomposition technique can sometimes imply its latent semantic indexing (LSI) aspect, we will also evaluate LSI aspect of the NMF by showing its capability in solving the synonymy and polysemy problems in synthetic datasets. And more extensive evaluation will be conducted by comparing LSI performances of the NMF and the singular value decomposition (SVD), the standard LSI method, using some standard datasets.Comment: 28 pages, 5 figure