Informatica

The estimation of intrinsic dimensionality of high-dimensional data still remains a challenging issue. Various approaches to interpret and estimate the intrinsic dimensionality are developed. Referring to the following two classifications of estimators of the intrinsic dimensionality – local/global estimators and projection techniques/geometric approaches – we focus on the fractal-based methods that are assigned to the global estimators and geometric approaches. The computational aspects of estimating the intrinsic dimensionality of high-dimensional data are the core issue in this paper. The advantages and disadvantages of the fractal-based methods are disclosed and applications of these methods are presented briefly.

An analytical equation for a generalization error of minimum empirical error classifier is derived for a case when true classes are spherically Gaussian. It is compared with the generalization error of a mean squared error classifier – a standard Fisher linear discriminant function. In a case of spherically distributed classes the generalization error depends on a distance between the classes and a number of training samples. It depends on an intrinsic dimensionality of a data only via initialization of a weight vector. If initialization is successful the dimensionality does not effect the generalization error. It is concluded advantageous conditions to use artificial neural nets are to classify patterns in a changing environment, when intrinsic dimensionality of the data is low or when the number of training sample vectors is really large.