Related papers: Correlated Wishart Matrices Classification via an …

Covariance matrices provide a valuable source of information about complex interactions and dependencies within the data. However, from a clustering perspective, this information has often been underutilized and overlooked. Indeed, commonly…

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…

We propose a new method for PolSAR (Polarimetric Synthetic Aperture Radar) imagery classification based on stochastic distances in the space of random matrices obeying complex Wishart distributions. Given a collection of prototypes…

Geostatistical modeling for continuous point-referenced data has been extensively applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging characterizing…

Linear Discriminant Analysis (LDA) on Electronic Health Records (EHR) data is widely-used for early detection of diseases. Classical LDA for EHR data classification, however, suffers from two handicaps: the ill-posed estimation of LDA…

Computational visual aesthetics has recently become an active research area. Existing state-of-art methods formulate this as a binary classification task where a given image is predicted to be beautiful or not. In many applications such as…

Collaborative representation-based classification (CRC) has demonstrated remarkable progress in the past few years because of its closed-form analytical solutions. However, the existing CRC methods are incapable of processing the nonlinear…

Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…

A Wishart kernel density estimator (KDE) is introduced for density estimation in the cone of positive definite matrices. The estimator is boundary-aware and mitigates the boundary bias suffered by conventional KDEs, while remaining simple…

This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a…

This paper proposes improved methods for the maximum likelihood (ML) estimation of the equivalent number of looks $L$. This parameter has a meaningful interpretation in the context of polarimetric synthetic aperture radar (PolSAR) images.…

In this paper, we obtain a property of the expectation of the inverse of compound Wishart matrices which results from their orthogonal invariance. Using this property as well as results from random matrix theory (RMT), we derive the…

Although various clustering methods have been successfully applied to polarimetric synthetic aperture radar (PolSAR) image clustering tasks, most of the available approaches fail to realize automatic determination of cluster number, nor…

Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an…

We present an analytic method to determine spectral properties of the covariance matrices constructed of correlated Wishart random matrices. The method gives, in the limit of large matrices, exact analytic relations between the spectral…

This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We…

WISDoM (Wishart Distributed Matrices) is a new framework for the quantification of deviation of symmetric positive-definite matrices associated to experimental samples, like covariance or correlation matrices, from expected ones governed by…

The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been…

Image captioning aims at automatically generating descriptions of an image in natural language. This is a challenging problem in the field of artificial intelligence that has recently received significant attention in the computer vision…

Retrieving similar images from a large dataset based on the image content has been a very active research area and is a very challenging task. Studies have shown that retrieving similar images based on their shape is a very effective…