A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the left and right singular value bases of the given pattern matrix are generated independently and uniformly from Haar measures. This assumption makes it possible...

If is a random variable with values in a compact matrix group K , then the traces Tr( j ) ( j ∈ N) are real or complex valued random variables. As a crucial step in their approach to random matrix eigenvalues, Diaconis and Shahshahani computed the joint moments of any fixed number of these traces if is distributed according to Haar measure and if K is one of Un, On or Spn , where n is large eno...

This paper reviews minimax best equivariant estimation in these invariant problems: a location parameter, scale parameter and (Wishart) covariance matrix. We briefly review development of the estimator as generalized Bayes relative to right Haar measure each case. Then we prove minimaxity procedure by giving least favorable prior sequence based on non-truncated Gaussian distributions. The resul...

In this paper, we obtain a complete list of inequivalent irreducible representations the compact quantum group [Formula: see text] for nonzero complex deformation parameters text], which are not roots unity. The matrix coefficients these described in terms little text]-Jacobi polynomials. Haar state is shown to be faithful and an orthonormal basis obtained. Thus, have explicit description Peter...

The problems of systems identification, analysis and optimal control have been recently studied using orthogonal functions. The specific orthogonal functions used up to now are the Walsh, the block-pulse, the Laguerre, the Legendre, Haar and many other functions. In the present paper, several operational matrices for integration and differentiation are studied. we introduce the Kronecker convol...

The Weyl criterion is shown in the terms of Price functions and Haar type functions. We define the so-called modified integrals of Price and Haar type functions and obtain the analogues of the criterion of Weyl, the inequalities of LeVeque and Erdös-Turan and the formula of Koksma in the terms of the modified integrals of Price and Haar type functions.

While optical character recognition is field where machine learning algorithms are easily applied, it might not always be cost effective to do so. While Viola and Jones explored Haar features in their face detection algorithm, selecting from the thousands of features is quite time consuming. This paper compares their feature set with a baseline of pixel learners as well as another set of Haar f...

A numerical method for solving nonlinear mixed Hammerstein integral equations is presented in this paper. The method is based upon hybrid of rationalized Haar functions approximations. The properties of hybrid functions which are the combinations of block-pulse functions and rationalized Haar functions are first presented. The Newton-Cotes nodes and Newton-Cotes integration method are then util...

A non-linear transform, called ‘‘sign Haar transform’’ has recently been introduced. The transform is unique and converts binary/ternary vectors into ternary spectral domain. Recursive definitions for the calculation of sign Haar transform are developed. Essential properties of logic functions and variables in the spectral domain of a quantized transform based on Haar functions are presented. S...