Zois Boukouvalas

An efficient multivariate generalized Gaussian distribution estimator: Application to IVA

Due to its simple parametric form, multivariate generalized Gaussian distribution (MGGD) has been widely used for modeling vector-valued signals. Therefore, efficient estimation of its parameters is of significant interest for a number of applications. Independent vector analysis (IVA) is a generalization of independent component analysis (ICA) that makes full use of the statistical dependence across multiple datasets to achieve source separation, and can take both second and higher-order statistics into account. MGGD provides an effective model for IVA as well as for modeling the latent multivariate variables-sources-and the performance of the IVA algorithm highly depends on the estimation of the source parameters. In this paper, we propose an efficient estimation technique based on the Fisher scoring (FS) and demonstrate its successful application to IVA. We quantify the performance of MGGD parameter estimation using FS and further verify the effectiveness of the new IVA algorithm using simulations.

IVA for abandoned object detection: Exploiting dependence across color channels

Automated detection of abandoned object (AO) is an important application in video surveillance for security purposes. Because of its importance, a number of techniques have been proposed to automatically detect abandoned objects in the past years. However, these techniques require prior knowledge on the properties of the object such as its shape and color, in order to classify foreground objects as abandoned object. In contrast, independent component analysis (ICA) does not require such prior knowledge. However, it can only model one dataset at a time, thus limiting its usage to monochrome frames. In this paper, we propose to use independent vector analysis (IVA), a recent extension of ICA to multivariate data that takes the dependence across multiple datasets into account while retaining the independence within each dataset. We present a new framework for AO detection using IVA and show that it provides successful performance in complicated scenarios, such as for videos with crowd, illumination change, and occlusion.

Density estimation by entropy maximization with kernels

The estimation of a probability density function is one of the most fundamental problems in statistics. The goal is achieving a desirable balance between flexibility while maintaining as simple a form as possible to allow for generalization, and efficient implementation. In this paper, we use the maximum entropy principle to achieve this goal and present a density estimator that is based on two types of approximation. We employ both global and local measuring functions, where Gaussian kernels are used as local measuring functions. The number of the Gaussian kernels is estimated by the minimum description length criterion, and the parameters are estimated by expectation maximization and a new probability difference measure. Experimental results show the flexibility and desirable performance of this new method.

A New Riemannian Averaged Fixed-Point Algorithm for MGGD Parameter Estimation

Multivariate generalized Gaussian distribution (MGGD) has been an attractive solution to many signal processing problems due to its simple yet flexible parametric form, which requires the estimation of only a few parameters, i.e., the scatter matrix and the shape parameter. Existing fixed-point (FP) algorithms provide an easy to implement method for estimating the scatter matrix, but are known to fail, giving highly inaccurate results, when the value of the shape parameter increases. Since many applications require flexible estimation of the shape parameter, we propose a new FP algorithm, Riemannian averaged FP (RA-FP), which can effectively estimate the scatter matrix for any value of the shape parameter. We provide the mathematical justification of the convergence of the RA-FP algorithm based on the Riemannian geometry of the space of symmetric positive definite matrices. We also show using numerical simulations that the RA-FP algorithm is invariant to the initialization of the scatter matrix and provides significantly improved performance over existing FP and method-of-moments (MoM) algorithms for the estimation of the scatter matrix.

Non-orthogonal constrained independent vector analysis: Application to data fusion

The existence of complementary information across multiple sensors has driven the proliferation of multivariate datasets. Exploitation of this common information, while minimizing the assumptions imposed on the data has led to the popularity of data-driven methods. Independent vector analysis (IVA), in particular, provides a flexible and effective approach for the fusion of multivariate data. In many practical applications, important prior information about the data exists and incorporating this information into the IVA model is expected to yield improved separation performance. In this paper, we propose a general formulation for non-orthogonal constrained IVA (C-IVA) framework that can incorporate prior information about either the sources or the mixing coefficients into the IVA cost function. A powerful decoupling method is the major enabling factor in this task. We demonstrate the improved performance of C-IVA over the unconstrained IVA model using both simulated as well as real medical imaging data.

Enhancing ICA performance by exploiting sparsity: Application to FMRI analysis

Independent component analysis (ICA) is a powerful method for blind source separation based on the assumption that sources are statistically independent. Though ICA has proven useful and has been employed in many applications, complete statistical independence can be too restrictive an assumption in practice. Additionally, important prior information about the data, such as sparsity, is usually available. Sparsity is a natural property of the data, a form of diversity, which, if incorporated into the ICA model, can relax the independence assumption, resulting in an improvement in the overall separation performance. In this work, we propose a new variant of ICA by entropy bound minimization (ICA-EBM)—a flexible, yet parameter-free algorithm—through the direct exploitation of sparsity. Using this new SparseICA-EBM algorithm, we study the synergy of independence and sparsity through simulations on synthetic as well as functional magnetic resonance imaging (fMRI)-like data.

Power spectra constrained IVA for enhanced detection of SSVEP content

The detection of steady state visual evoked potentials (SSVEPs) has been identified as an effective solution for brain computer interface (BCI) systems as well as for neurocognitive investigations of visually related tasks. SSVEPs are induced at the same frequency as the visual stimuli and can be observed in the scalp-based recordings of electroencephalogram signals, though they are one component buried amongst the normal brain signals and complex noise. Variations in individual response latencies as well as the presence of multiple biological artifacts complicate the use of direct frequency analysis, thus making blind source separation methods, such as independent component (ICA) and independent vector analysis (IVA) desirable solutions. IVA is a recent extension of ICA that decomposes multiple datasets simultaneously and has been been shown to be capable of enhancing and improving the detection of SSVEPs by exploiting the complimentary information that exists across EEG channels. In this work, we present a novel extension of IVA which incorporates a priori information to constrain the power spectral density (PSD) of the source estimates, known as constrained PSD IVA (CP-IVA) and demonstrate its improved SSVEP detection performance as well as stability over standard IVA and temporally constrained IVA (C-IVA).

Sparsity and Independence: Balancing Two Objectives in Optimization for Source Separation with Application to fMRI Analysis

Abstract Because of its wide applicability in various disciplines, blind source separation (BSS), has been an active area of research. For a given dataset, BSS provides useful decompositions under minimum assumptions typically by making use of statistical properties—types of diversity—of the data. Two popular types of diversity that have proven useful for many applications are statistical independence and sparsity. Although many methods have been proposed for the solution of the BSS problem that take either the statistical independence or the sparsity of the data into account, there is no unified method that can take into account both types of diversity simultaneously. In this work, we provide a mathematical framework that enables direct control over the influence of these two types of diversity and apply the proposed framework to the development of an effective ICA algorithm that can jointly exploit independence and sparsity. In addition, due to its importance in biomedical applications, we propose a new model reproducibility framework for the evaluation of the proposed algorithm. Using simulated functional magnetic resonance imaging (fMRI) data, we study the trade-offs between the use of sparsity versus independence in terms of the separation accuracy and reproducibility of the algorithm and provide guidance on how to balance these two objectives in real world applications where the ground truth is not available.

On the characterization, generation, and efficient estimation of the complex multivariate GGD

The complex multivariate generalized Gaussian distribution (CMGGD) is a flexible parametrized distribution suitable for a variety of applications. Previous work in this area is either limited to the univariate case or, in the multivariate case, restricts the complex vectors, unjustifiably, to be circular. In both cases, algorithms for parameter estimation also suffer from convergence or accuracy limitations over the complete range of their parameters. In this work, we develop the probability density function (PDF) for CMGGD that properly describes noncircular complex data. We then develop a fixed-point algorithm for the estimation of parameters of the CMGGD that is both rapid in its convergence and accurate for the complete shape parameter range. We quantify performance against other algorithms while varying noncircularity, shape parameter and data dimensionality and demonstrate robustness and gains in performance, especially for noncircular data.