Robustness in Statistical Pattern Recognition by Yurij Kharin (auth.)

By Yurij Kharin (auth.)

This booklet is anxious with very important difficulties of sturdy (stable) statistical pat­ tern reputation while hypothetical version assumptions approximately experimental information are violated (disturbed). development attractiveness idea is the sector of utilized arithmetic within which prin­ ciples and techniques are built for type and id of gadgets, phenomena, tactics, events, and signs, i. e. , of gadgets that may be laid out in a finite set of positive factors, or homes characterizing the gadgets (Mathematical Encyclopedia (1984)). levels in improvement of the mathematical conception of trend attractiveness can be saw. on the first degree, till the center of the Nineteen Seventies, development recogni­ tion thought was once replenished normally from adjoining mathematical disciplines: mathe­ matical facts, practical research, discrete arithmetic, and data concept. This improvement level is characterised through profitable answer of trend reputation difficulties of alternative actual nature, yet of the easiest shape within the experience of used mathematical versions. one of many major techniques to unravel development popularity difficulties is the statisti­ cal technique, which makes use of stochastic versions of function variables. lower than the statistical method, the 1st degree of development popularity thought improvement is characterised through the idea that the chance info version is understood precisely or it's esti­ mated from a consultant pattern of enormous measurement with negligible estimation error (Das Gupta, 1973, 1977), (Rey, 1978), (Vasiljev, 1983)).

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No The sample A is obtained by a series of n independent experiments on observation of objects from all classes 0 1 , ... , OL. The result of the j-th experiment is a composed (N + I)-vector (x;:7jf, where Xj is a vector of random feature variables and is a value in some way associated with the class number Vj E 5 of the observed object. Sometimes the classes to which the observed data belong are fixed in advance. In these situations 71, ... ,7L are nonrandom. •. ,X n are independent random vectors.

1. Tukey-Huber Type Distortions The family of admissible distorted densities for the i-th class has a nonparametric description: 0:::; Ei:::;E+i,hi(x) 20, r hi (x)dx=l}. JRN Thus, the distorted density Pi(X) is a mixture of the hypothetical (expected) distribution pi(x) and an arbitrary distribution hi(x) describing data contamination by outliers. 2. distribution is Gaussian: pi(x) = n1(x I l"i,a'j2). (Huber, 1981) generalized this distortion type. , 1986), (Krasnenker, 1980), (Launer, 1979), (Ershov, 1978), (Zypkin, 1984).

L-type distortions. The parametric E-nonhomogeneity of the training sample is produced, for example, by instability of experiment conditions when this sample is being recorded. 2. , 1988)). In Chapter 6 the following kinds of statistical dependence of training sample elements are defined and used: • stationary vector time series, • Markov sequence, • vector autoregressive time series. 3. Misclassification of Training Sample In the training sample A; of size only (1 - Ei) . i( i E S), and the remaining Ei .

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