Discrimination and Classification, Round 2

  • Bernard Flury
Part of the Springer Texts in Statistics book series (STS)

Abstract

In this chapter we continue the theory of classification developed in Chapter 5 on a somewhat more general level. We start out with some basic consideration of optimality. In the notation introduced in Section 5.4, Y will denote a p-variate random vector measured in k groups (or populations). Let X denote a discrete random variable that indicates group membership, i.e., takes values 1, … , k. The probabilities
$$ {\pi _j} = \Pr \left[ {X = j} \right]\quad j = 1, \ldots ,k, $$
(1)
will be referred to as prior probabilities, as usual. Suppose that the distribution of Y in the jth group is given by a pdf f j (y), which may be regarded as the conditional pdf of Y, given X = j. Assume for simplicity that Y is continuous with sample space ℝ p in each group. Then the joint pdf of X and Y, as seen from Sec tion 2.8, is
$$ {f_{XY}}\left( {j,y} \right) = \left\{ \begin{gathered} {\pi _j}{f_j}\left( y \right)\;for{\kern 1pt} j = 1, \ldots ,k,y \in {\mathbb{R}^p} \hfill \\ 0\quad otherwise. \hfill \\ \end{gathered} \right. $$
(2)

Keywords

Covariance Matrice Canonical Variate Classification Rule Classification Region Standard Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Suggested Further Reading

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Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • Bernard Flury
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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