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Decomposition of Gaussian processes, and factorization of positive definite kernels

Jorgensen Palie E. T., Tian Feng

Opuscula Mathematica

2019

Vol. 39, no. 4

497-–541

We establish a duality for two lactorization questions, one for general positive definite (p.d.) kernels K, and the other for Gaussian processes, say V. The latter notion, for Gaussian processes is stated via Ito-integration. Our approach to factorization for p.d. kernels is intuitively motivated by matrix factorizations, but in infinite dimensions, subtle measure theoretic issues must be addressed. Consider a given p.d. kernel K, presented as a covariance kernel for a Gaussian process V. We then give an explicit duality for these two seemingly different notions of factorization, for p.d. kernel K, vs for Gaussian process V. Our result is in the form of an explicit correspondence. It states that the analytic data which determine the variety of factorizations for K is the exact same as that which yield factorizations for V. Examples and applications are included: point-processes, sampling schemes, constructive discretization, graph-Laplacians, and boundary-value problems.

An improved ant colony optimization algorithm and its application to text-independent speaker verification system

Aghdam M. H.

Journal of Artificial Intelligence and Soft Computing Research

2012

Vol. 2, No. 4

301--315

With the growing trend toward remote security verification procedures for telephone banking, biometric security measures and similar applications, automatic speaker verification (ASV) has received a lot of attention in recent years. The complexity of ASV system and its verification time depends on the number of feature vectors, their dimensionality, the complexity of the speaker models and the number of speakers. In this paper, we concentrate on optimizing dimensionality of feature space by selecting relevant features. At present there are several methods for feature selection in ASV systems. To improve performance of ASV system we present another method that is based on ant colony optimization (ACO) algorithm. After feature selection phase, feature vectors are applied to a Gaussian mixture model universal background model (GMM-UBM) which is a text-independent speaker verification model. The performance of proposed algorithm is compared to the performance of genetic algorithm on the task of feature selection in TIMIT corpora. The results of experiments indicate that with the optimized feature set, the performance of the ASV system is improved. Moreover, the speed of verification is significantly increased since by use of ACO, number of features is reduced over 80% which consequently decrease the complexity of our ASV system.

Model częstotliwości podstawowej traktu głosowego zbudowany metodą grupowania argumentów (GMDH)

Wiliński A., Samborska-Owczarek A.

Metody Informatyki Stosowanej

2007

nr 2(Tom 12)

189-202

This paper concerns the problem of parameters estimation for a certain model, aiming at the approximation of output variable at the acceptable accuracy level. What distinguishes the way this common scientific task is here dealt with, is the usage of GMDH - Group Method of Data Handling (or more specifically the GMDH-based algorithm developed by the authors), which allows for simultaneous determination of both the structure and numerical characteristics of the model. The feature space under consideration is the matrix of repetitively observed attributes, describing the physical characteristics of voice samples, collected in order to determine the frequency of laryngeal tone for the purpose of medical diagnosis.