Cumulative global distance for dimension reduction in handwritten digits database

Authors:
Mahdi Yektaii;Prabir Bhattacharya
Affiliations:
Concordia Institute for Information Systems Engineering, Concordia University, Montreal, QC, Canada;Concordia Institute for Information Systems Engineering, Concordia University, Montreal, QC, Canada
Venue:
VISUAL'07 Proceedings of the 9th international conference on Advances in visual information systems
Year:
2007

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Abstract

The various techniques used to determine the reduced number of features in principal component analysis are usually ad-hoc and subjective. In this paper, we use a method of finding the number of features which is based on the saturation behavior of a graph and hence is not ad-hoc. It gives a lower bound on the number of features to be selected. We use a database of handwritten digits and reduce the dimensions of the images in this database based on the above method. A comparison with some conventional methods such as scree and cumulative percentage is also performed. These two methods are based on the values of the eigenvalues of the database covariance matrix. The Mahalanobis and Bhattacharyya distances will be shown to be of little use in determining the number of reduced dimensions.