Fisher Discriminant Criterion Research Articles

A theorem on the uncorrelated optimal discriminant vectors

This paper proposes a theorem on the uncorrelated optimal discriminant vectors (UODVs). It is proved that the classical optimal discriminant vectors are equivalent to UODV, which can be used to extract ( L−1) uncorrelated discriminant features for L-class problems without losing any discriminant information in the meaning of Fisher discriminant criterion function. Experiments on Concordia University CENPARMI handwritten numeral database indicate that UODVs are much more powerful than the Foley–Sammon optimal discriminant vectors. It is believed that when the number of training samples is large, the conjugate orthogonal set of discriminant vectors can be much more powerful than the orthogonal set of discriminant vectors.

Feature Extraction Method Based on the Generalised Fisher Discriminant Criterion and Facial Recognition

In this paper we view the optimal set of discriminant vectors as a global transform, and consider its separability from a global view point. Based on this idea, the concept of a generalised Fisher discriminant criterion and that of a generalised optimal set of discriminant vectors is introduced. After that, a new algorithm is given to calculate the generalised optimal set of discriminant vectors defined in this paper, which is particularly suited to the case of a small number of samples where the scatter matrix is singular. It is then applied to an experiment on human facial recognition, and the results show that the new algorithm is superior to existing methods in terms of correct classification rate.

Colour filtering using local density information

A multichannel filtering technique is proposed based on local density estimation. The window data are ordered according to their distance from that of the maximum density, and the samples to be averaged are selected using the Fisher discriminant criterion. The method has been evaluated in several real images.

Quantitative assessment of mineral resources with an application to petroleum geology

The probability of occurrence of natural resources, such as petroleum deposits, can be assessed by a combination of multivariate statistical and geostatistical techniques. The area of study is partitioned into regions that are as homogeneous as possible internally while simultaneously as distinct as possible. Fisher's discriminant criterion is used to select geological variables that best distinguish productive from nonproductive localities, based on a sample of previously drilled exploratory wells. On the basis of these geological variables, each wildcat well is assigned to the production class (dry or producer in the two-class case) for which the Mahalanobis' distance from the observation to the class centroid is a minimum. Universal kriging is used to interpolate values of the Mahalanobis' distances to all locations not yet drilled. The probability that an undrilled locality belongs to the productive class can be found, using the kriging estimation variances to assess the probability of misclassification. Finally, Bayes' relationship can be used to determine the probability that an undrilled location will be a discovery, regardless of the production class in which it is placed. The method is illustrated with a study of oil prospects in the Lansing/Kansas City interval of western Kansas, using geological variables derived from well logs.