Pub. online:1 Jan 2001Type:Research ArticleOpen Access
Volume 12, Issue 2 (2001), pp. 221–238
One of the main problems in pattern classification and neural network training theory is the generalization performance of learning. This paper extends the results on randomized linear zero empirical error (RLZEE) classifier obtained by Raudys, Dičiūnas and Basalykas for the case of centered multivariate spherical normal classes. We derive an exact formula for an expected probability of misclassification (PMC) of RLZEE classifier in a case of arbitrary (centered or non-centered) spherical normal classes. This formula depends on two parameters characterizing the “degree of non-centering” of data. We discuss theoretically and illustrate graphically and numerically the influence of these parameters on the PMC of RLZEE classifier. In particular, we show that in some cases non-centered data has smaller expected PMC than centered data.
Pub. online:1 Jan 2000Type:Research ArticleOpen Access
Volume 11, Issue 4 (2000), pp. 381–396
An estimation of the generalization performance of classifier is one of most important problems in pattern clasification and neural network training theory. In this paper we estimate the generalization error (mean expected probability of classification) for randomized linear zero empirical error (RLZEE) classifier which was considered by Raudys, Dičiūnas and Basalykas. Instead of “non-explicit” asymptotics of a generalization error of RLZEE classifier for centered multivariate spherically Gaussian classes proposed by Basalykas et al. (1996) we obtain an “explicit” and more simple asymptotics. We also present the numerical simulations illustrating our theoretical results and comparing them with each other and previously obtained results.
Pub. online:1 Jan 1998Type:Research ArticleOpen Access
Volume 9, Issue 3 (1998), pp. 315–324
We study invertibility of big n × n matrices. There exists a number of algorithms, especially in mathematical statistics and numerical mathematics, requiring to invert step by step large matrices which are closely related to each other. Standard inverting methods require O(n3) arithmetical operations therefore using of these algorithms for big values of n becomes problematic. In this paper we introduce some classes of matrices that can be inverted by O(n2) operations if we use inverse matrices of other closely related matrices. The most important among them are matrices having big common submatrix and modified sample covariance matrices. We apply our theoretical results constructing a fast algorithm for prediction. This algorithm demonstrates the advantage of our inverting methods and can be used, for example, for safety control in the plant.
Pub. online:1 Jan 1990Type:Research ArticleOpen Access
Volume 1, Issue 2 (1990), pp. 121–124
In this report an expert system AKU for diagnostics in acupuncture is described. The injured vital energy channels can be diagnosed using three independent methods: inquiring, Ryodoraku test and Akabane test. The inquiring is constructed as a set of trees whose internal vertices are questions while the leaves are the symptoms of diseases. The production rules describe the correspondence between the symptoms and the state of vital energy “qi” in the channels. AKU is realized by IBM PC computer and used for acupuncture treatment. The program is coded in Turbo Prolog.