Introduction E9F5FC

Questions FFFFC0

• View
• Edit
• History
• Print

Šarūnas Raudys described a hierarchy of statistical methods that accord with divisions of everything and perhaps relate to Clifford algebras and Bott periodicity.

• Evolution and generalization of a single neurone: I. Single-layer perceptron as seven statistical classifiers
• Evolution and generalization of a single neurone:: II. Complexity of statistical classifiers and sample size considerations
• Evolution and generalization of a single neurone. III. Primitive, regularized, standard, robust and minimax regressions
  • (1) the Euclidean distance classifier;
  • (2) the standard Fisher linear discriminant function (DF);
  • (3) the Fisher linear DF with pseudo-inversion of the covariance matrix;
  • (4) regularized linear discriminant analysis;
  • (5) the generalized Fisher DF;
  • (6) the minimum empirical error classifier;
  • (7) the maximum margin classifier.
• Šarūnas Raudys. Statistical and Neural Classifiers: An Integrated Approach to Design Google Books VU Matematikos ir informatikos skaitykla (004.9/Ra256)

Statistical classification

• Statistical classification

Overview

Consider the nonlinear single-layer perceptron (SLP) as a process in which

• the weights of the perceptron are increasing
• the cost function of the sum of squares is changing gradually

During backpropagation training, the decision boundary of the SLP becomes identical or close to that of seven statistical classifiers.

A classifier distinguishes (two) classes. This is similar to a linear complex structure, which distinguishes what commutes with it from what does not commute with it.