Informatica

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.

The smoothing constant λ is the most important characteristic of the nonparametric Parzen window classifier (PWC). The PWC tends to a one-nearest neighbour classifier as λ tends to zero and to a parametric linear Eucliden distance classifier as λ tends to infinity. An asymptotic probability of misclassification of the PWC decreases with the decrease in λ. A sensitivity of the PWC to a finiteness of the training data depends on a true-intrinsic dimensionality of the data, and it increases with the decrease in the value of λ. It is proposed to determine an optimal value of the smoothing constant from a smoothed empirical graph of the dependence of an expected probability of misclassification on the value of λ. The graph can be estimated by means of leaving-one-out or hold-out methods simultaneously for a number of values of λ chosen from the interval (0.001–1000) in a logarithmic scale.