We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher-Bingham distribution on the unit sphere and make use of the partial di...

The texture of rotary-veneer can interference in defects detection, this paper presented a modified semi-fuzzy clustering (SFC) algorithm. SFC algorithm incorporates Fisher discrimination method with fuzzy theory using fuzzy scatter matrix. By iteratively optimizing the fuzzy Fisher criterion function, the final clustering results are obtained. SFC algorithm exhibits its robustness and capabili...

We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density functions for an arbitrary Riemannian Fisher information metric tensor. We note further that this construction is extremely unconstrained, depending only on...

In this paper, a new technique called Two Dimensional Gabor Fisher Discriminant (2DGFD) is derived and implemented for image representation and recognition. In our approach, the Gabor wavelets are used to extract facial features. The Principal Component Analysis (PCA) is applied directly on the Gabor transformed matrices to remove redundant information from the image rows and a new direct two d...

The problem how to derive a generic lower bound for the Fisher information measure is considered. We review a recent approach by two examples and identify a connection between the construction of strong Fisher information bounds and the sufficient statistics of the underlying system model. In order to present the problem of such information bounds within a broad scope, we discuss the properties...

This letter analyzes the Fisher kernel from a statistical point of view. The Fisher kernel is a particularly interesting method for constructing a model of the posterior probability that makes intelligent use of unlabeled data (i.e., of the underlying data density). It is important to analyze and ultimately understand the statistical properties of the Fisher kernel. To this end, we first establ...

The technical merits of weak-value-amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak-value-amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which use all of them). Using the Fisher-information metric, we demonstrate that weak-value t...

We report on an extensive simulation study comparing eight statistical classiication methods, focusing on problems where the number of observations is less than the number of variables. Using a wide range of artiicial and real data, two types of classiiers were contrasted; methods that classify using all variables, and methods that rst reduce the number of dimensions to two or three. The full f...

We present a new method for fitting peculiar velocity models to complete flux limited magnitude-redshifts catalogues, using the luminosity function of the sources as a distance indicator. The method is characterised by its robustness. In particular, no assumptions are made concerning the spatial distribution of sources and their luminosity function. Moreover, selection effects in redshift are a...