The Generalized Bayes Method for High-Dimensional Data Recognition with Applications to Audio Signal Recognition

High-dimensional data recognition problem based on the Gaussian Mixture model has useful applications in many area, such as audio signal recognition, image analysis, and biological evolution. The expectation-maximization algorithm is a popular approach to the derivation of the maximum likelihood estimators of the Gaussian mixture model (GMM). An alternative solution is to adopt a generalized Bayes estimator for parameter estimation. In this study, an estimator based on the generalized Bayes approach is established. A simulation study shows that the proposed approach has a performance competitive to that of the conventional method in high-dimensional Gaussian mixture model recognition. We use a musical data example to illustrate this recognition problem. Suppose that we have audio data of a piece of music and know that the music is from one of four compositions, but we do not know exactly which composition it comes from. The generalized Bayes method shows a higher average recognition rate than the conventional method. This result shows that the generalized Bayes method is a competitor to the conventional method in this real application.

Admissible estimators of a multivariate normal mean vector when the scale is unknown

We study admissibility of a subclass of generalized Bayes estimators of a multivariate normal vector when the variance is unknown, under scaled quadratic loss. Minimaxity is established for some of these estimators.

Wavelet shrinkage generalized Bayes estimation for elliptical distribution parameter’s under LINEX loss

In this paper, the generalized Bayes estimator of elliptical distribution parameter’s under asymmetric Linex error loss function is considered. The new shrinkage generalized Bayes estimator by applying wavelet transformation is investigated. We develop admissibility and minimaxity of shrinkage estimator on multivariate normal distribution.We present the simulation in order to test validity of purpose estimator.

A Robust Credal Assignment Solution Based on the Generalized Bayes’ Theorem

This paper proposes a new assignment solution based on the Generalized Bayes’ Theorem (GBT) which aims to establish the best matching between two sets of uncertain data. In order to estimate the effectiveness of the proposition, it is compared to the best credal assignment solutions and the well known Global Nearest Neighbor (GNN) algorithm, through synthetic data and a literature example of multi-target tracking scenarios. Given the same input data, the proposed solution gives better assignment results, especially when sensor imprecision increases. However, the proposed solution stills actually computationally more complex than the GNN and the solution proposed by Denoeux et al.