Principal Component Analysis (PCA) aims to learn compact and informative representations for data and has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods cannot deal with dense noise effectively. In this paper, we propose Cauchy Principal Compo...

The classic Leftover Hash Lemma (LHL) is often used to argue that certain distributions arising from modular subset-sums are close to uniform over their finite domain. Though very powerful, the applicability of the leftover hash lemma to lattice based cryptography is limited for two reasons. First, typically the distributions we care about in lattice-based cryptography are discrete Gaussians, n...

In this paper, we propose a new score normalization method for text-independent speaker verification using GMM (Gaussian Mixture Model). In the proposed method, cohort model is designed as virtual speaker model based on the similarity of local acoustic information between the reference speaker and other customers. The similarity is determined using statistical distance between model components ...

Abstract As artificial intelligence (AI) becomes ubiquitous, it will be increasingly involved in novel, morally significant situations. Thus, understanding what means for a machine to responsible is important ethics. Any method ascribing moral responsibility AI must intelligible and intuitive the humans who interact with it. We argue that appropriate approach determine how AIs might fare on sta...

we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

This is a brief and concise account of the basic concepts and results on statistical convergence, strong Cesàro summability and Walsh-Fourier series. To emphasize the significance of statistical convergence, for example we mention the fact that the one-dimensional Walsh-Fourier series of an integrable (in Lebesgue’s sense) function may be divergent almost everywhere, but it is statistically con...

in this paper, we present legendre wavelet method to obtain numerical solution of a singular integro-differential equation. the singularity is assumed to be of the cauchy type. the numerical results obtained by the present method compare favorably with those obtained by various galerkin methods earlier in the literature.