Statistical discrimination analysis using the maximum function.(English)Zbl 1132.62049
Summary: The maximum of \(k\) functions defined on \(\mathbb R^n\), \(n\geq 1,\) by \[f_{\max} (x) = \max\{ f_{1} (x),\dots , f_k (x)\},\;\forall x \in\mathbb R^n,\] can have important roles in statistics, particularly in classification. Through its relation with the Bayes error, which is the reference error in classification, it can serve to compute numerical bounds for errors in other classification schemes. It can also serve to define the joint \(L^1\)-distance between more than two densities, which, in turn, will serve as a useful tool in classification and cluster analyses. It has a vast potential application in digital image processing too. Finally, its versatile role can be seen in several numerical examples, related to the analysis of Fisher’s classical iris data in multidimensional spaces.
MSC:
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 62F15 | Bayesian inference |
| 68T10 | Pattern recognition, speech recognition |
Keywords:
Bayes error;discriminant function;L\(^{1}\)-norm;linear;maximum;normal distribution;pattern classification;quadratic;space curves;Hammax softwareCite
Full Text:DOI
References:
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