Optimum linear and non-linear transformations in feature extraction
de Figueiredo, Rui J. P.
Master of Science
In pattern recognition one tries to classify a pattern based on a certain number of observed variables. The observed variables are more often than not redundant. The method of reducing the number of observed variables, or features, is called "Feature Extraction." The solution of the above problem requires the aid of a distance measure. Here a distance measure is obtained geometrically and is compared with the Bhattacharya distance and the Divergence for the n-dimensional Gaussian random variable. Then a method is given to optimally select the features of gaussian random process. A special case of this result gives the optimum linear transformation to reduce the dimension of an n-dimensional Gaussian random vector. The distance measure derived geometrically was used to obtain an optimum non-linear transformation to reduce the number of observed variables. An example was solved on the computer to give a certain amount of comparison among the different methods.