# An efficient multivariate generalized Gaussian distribution estimator: Application to IVA

@article{Boukouvalas2015AnEM, title={An efficient multivariate generalized Gaussian distribution estimator: Application to IVA}, author={Zois Boukouvalas and Gengshen Fu and T. Adalı}, journal={2015 49th Annual Conference on Information Sciences and Systems (CISS)}, year={2015}, pages={1-4} }

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… Expand

#### 22 Citations

An adaptive fixed-point IVA algorithm applied to multi-subject complex-valued FMRI data

- Mathematics, Computer Science
- 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2016

An adaptive fixed-point IVA algorithm is proposed by taking into account the extremely noisy nature, large variability of the source component vector (SCV) distribution, and non-circularity of the complex-valued fMRI data. Expand

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

- Mathematics, Computer Science
- 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)
- 2016

This work develops 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 and quantifies performance against other algorithms while varying noncircularity, shape parameter and data dimensionality. Expand

Globally Convergent Algorithms for Learning Multivariate Generalized Gaussian Distributions

- Computer Science
- 2021 IEEE Statistical Signal Processing Workshop (SSP)
- 2021

The multivariate generalized Gaussian distribution has been used intensively in various data analytics fields. Due to its flexibility in modeling different distributions, developing efficient methods… Expand

Adaptive independent vector analysis for multi-subject complex-valued fMRI data

- Computer Science, Medicine
- Journal of Neuroscience Methods
- 2017

This work proposes an adaptive fixed-point IVA algorithm suitable for decomposing multi-subject complex-valued fMRI data, and has great potential for capturing additional subject variability. Expand

Development of ICA and IVA Algorithms with Application to Medical Image Analysis

- Computer Science, Mathematics
- 2018

This work introduces a flexible ICA algorithm that uses an effective PDF estimator to accurately capture the underlying statistical properties of the data and discusses several techniques to accurately estimate the parameters of the multivariate generalized Gaussian distribution, and how to integrate them into the IVA model. Expand

Adaptive Constrained Independent Vector Analysis: An Effective Solution for Analysis of Large-Scale Medical Imaging Data

- Computer Science, Medicine
- IEEE Journal of Selected Topics in Signal Processing
- 2020

Adaptive cIVA (acIVA) is proposed that can reliably estimate high-dimensional multivariate sources from large-scale simulated datasets, when compared with standard IVA, and successfully extracts meaningful functional networks from a large- scale fMRI dataset for which standardIVA did not converge. Expand

Multimodal Data Fusion Using Source Separation: Two Effective Models Based on ICA and IVA and Their Properties

- Computer Science, Medicine
- Proceedings of the IEEE
- 2015

Two multivariate solutions for multimodal data fusion that let multiple modalities fully interact for the estimation of underlying features that jointly report on all modalities are focused on. Expand

Blind Speech Extraction Based on Rank-Constrained Spatial Covariance Matrix Estimation With Multivariate Generalized Gaussian Distribution

- Mathematics, Computer Science
- IEEE/ACM Transactions on Audio, Speech, and Language Processing
- 2020

A new blind speech extraction method that robustly extracts a directional speech from background diffuse noise by combining independent low-rank matrix analysis (ILRMA) and efficient rank-constrained spatial covariance matrix (SCM) estimation is proposed. Expand

Multi-modal data fusion using source separation: Two effective models based on ICA and IVA and their properties

- 2018

Fusion of information from multiple sets of data in order to extract a set of features that are most useful and relevant for the given task is inherent to many problems we deal with today. Since,… Expand

Generalized independent low-rank matrix analysis using heavy-tailed distributions for blind source separation

- Mathematics, Computer Science
- EURASIP J. Adv. Signal Process.
- 2018

This paper introduces a heavy-tailed property by replacing the conventional Gaussian source distribution with a generalized Gaussian or Student’s t distribution in the source model estimation, and proposes two extensions of the source distribution assumed in ILRMA. Expand

#### References

SHOWING 1-10 OF 18 REFERENCES

Parameter Estimation For Multivariate Generalized Gaussian Distributions

- Mathematics, Computer Science
- IEEE Transactions on Signal Processing
- 2013

It is proved that the maximum likelihood estimator (MLE) of the scatter matrix exists and is unique up to a scalar factor, for a given shape parameter β ∈ (0,1). Expand

Independent vector analysis, the Kotz distribution, and performance bounds

- Mathematics, Computer Science
- 2013 IEEE International Conference on Acoustics, Speech and Signal Processing
- 2013

The use of the Kotz distribution family is introduced as a more flexible source distribution model which exploits both second and higher-order statistics and the Cramér-Rao lower bound for IVA performance prediction is shown to be analogous to the bound for blind source separation. Expand

A maximum likelihood approach for independent vector analysis of Gaussian data sets

- Mathematics, Computer Science
- 2011 IEEE International Workshop on Machine Learning for Signal Processing
- 2011

Following a maximum likelihood (ML) approach, it is shown that the cost function to be minimized by the proposed GML-IVA algorithm reduces to an estimate of the mutual information among the different sets of latent variables. Expand

Diversity in Independent Component and Vector Analyses: Identifiability, algorithms, and applications in medical imaging

- Mathematics, Computer Science
- IEEE Signal Processing Magazine
- 2014

This overview article presents ICA, and then its generalization to multiple data sets, IVA, both using mutual information rate, and presents conditions for the identifiability of the given linear mixing model and derive the performance bounds. Expand

Joint Blind Source Separation With Multivariate Gaussian Model: Algorithms and Performance Analysis

- Mathematics, Computer Science
- IEEE Transactions on Signal Processing
- 2012

This paper proposes to use the multivariate Gaussian source prior to achieve JBSS of sources that are linearly dependent across datasets, and introduces both Newton and quasi-Newton optimization algorithms for the general IVA framework. Expand

Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination

- Mathematics, Computer Science
- International Journal of Computer Vision
- 2011

The modeling of the interband correlation significantly improves classification efficiency, while the GD is shown to consistently outperform the KLD as a similarity measure. Expand

Joint Blind Source Separation by Multiset Canonical Correlation Analysis

- Mathematics, Medicine
- IEEE Transactions on Signal Processing
- 2009

A generative model of joint BSS based on the correlation of latent sources within and between datasets using multiset canonical correlation analysis (M-CCA) and its utility in estimating meaningful brain activations from a visuomotor task is proposed. Expand

On the Geometry of Multivariate Generalized Gaussian Models

- Mathematics, Computer Science
- Journal of Mathematical Imaging and Vision
- 2011

The geometry of the zero-mean multivariate generalized Gaussian distribution (MGGD) and the calculation of geodesic distances on the MGGD manifold are concerns and an application to image texture similarity measurement in the wavelet domain is briefly discussed. Expand

Independent Vector Analysis: An Extension of ICA to Multivariate Components

- Computer Science
- ICA
- 2006

This paper solves an ICA problem where both source and observation signals are multivariate, thus, vectorized signals and proposes the frequency domain blind source separation (BSS) for convolutive mixtures as an application of IVA. Expand

An effective decoupling method for matrix optimization and its application to the ICA problem

- Mathematics, Computer Science
- 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
- 2012

The decoupling procedure is utilized to develop a new decoupled ICA algorithm that uses Newton optimization enabling superior performance when the sample size is limited. Expand