Error estimation is a crucial part of classification methodology and it becomes problematic with small samples. We demonstrate here that the complexity of the decision boundary plays a key role on the performance of error estimation methods. First, a model is developed which quantifies the complexity of a classification problem purely in terms of the geometry of the decision boundary, without r...

Marketing problems often involve binary classification of customers into “buyers” versus “non-buyers” or “prefers brand A” versus “prefers brand B”. These cases require binary classification models such as logistic regression, linear, and quadratic discriminant analysis. A promising recent technique for the binary classification problem is the Support Vector Machine (Vapnik (1995)), which has a...

Introduction Discriminant function analysis is used to determine which continuous variables discriminate between two or more naturally occurring groups. For example, a researcher may want to investigate which variables discriminate between fruits eaten by (1) primates, (2) birds, or (3) squirrels. For that purpose, the researcher could collect data on numerous fruit characteristics of those spe...

We study the Galois groups of polynomials arising from a compatible family representations with big orthogonal monodromy. show that are usually as large possible given constraints imposed on them by functional equation and discriminant considerations. As an application, we consider Frobenius middle étale cohomology hypersurfaces in [Formula: see text] degree at least three. also text]-functions...

This study deals with the relation between the spectral representation and the perceptual identification of the Spanish fricatives and affricates. Several spectral representations have been analyzed: FFT-derived linear cepstrum, mel cepstrum coefficients, LPC cepstral coefficients and the first four statistical moments. Quadratic discriminant analysis including the leaveone-out method have been...

This chapter establishes Gauss’s Law of Quadratic Reciprocity, the theory of binary quadratic forms, and Dirichlet’s Theorem on primes in arithmetic progressions. Section 1 outlines how the three topics of the chapter occurred in natural sequence and marked a transition as the subject of number theory developed a coherence and moved toward the kind of algebraic number theory that is studied tod...

In classification, with an increasing number of variables, the required number of observations grows drastically. In this paper we present an approach to put into effect the maximal possible variable selection, by splitting a K class classification problem into pairwise problems. The principle makes use of the possibility that a variable that discriminates two classes will not necessarily do so...

The interaction of consonantal and vocalic segments in FV syllables regarding identification of place of articulation of fricatives has been studied. A probabilistic model for integration of acoustic information in both segments is proposed. The model weights each segment’s contribution and integrates them in order to resemble listeners’ perception. First, the perceptual validity of the model h...