Independent vector analysis

Abstract

In this dissertation, we propose a novel concept termed independent vector analysis (IVA) as an extension of independent component analysis (ICA) to multidimensional approach. IVA can be considered as an ICA problem where both source and observation signals are multivariate, thus, the components (sources) are vector sequences (random vectors). In the formulation, we assume the elements of a source vector are dependent, although each source vector itself is independent of the other source vectors. To measure dependence between vectors, we discuss some objective functions such as vector correlation and vector mutual information, where vector correlation can be defined by total covariance matrix and covariance matrices of individual sources, and vector mutual information can be defined by Kullback-Leibler divergence (KLD) between total joint probability and the product of marginal probabilities. We then derive a class of algorithms, which are similar to and slightly different from ordinary ICA algorithms, but have some interesting properties. In the algorithm, multivariate score functions caused by vector dependency models are defined. Here we propose vector density models that have dependencies, i.e. correlation and a kind of variance dependency, within a source vector. Then, we discuss some information-theoretic view of IVA and its objective functions. The simulation results show that the proposed model and algorithms successfully recovers the latent components. In most cases, IVA outperforms ICA. Even in the case that the components have Gaussian distributions, IVA is able to estimate the original sources, where ICA does not work properly. Additionally, IVA does not cause any permutation ambiguities between elements of source vectors. As an application of IVA, we suggest blind source separation (BSS) of convolutive mixtures. BSS is a challenging problem in real world environments where sources are time delayed and convolved. The problem becomes more diffi...