International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 4, Pages 239-247

Classification of reduction invariants with improved backpropagation

S. M. Shamsuddin,1 M. Darus,2 and M. N. Sulaiman3

1Faculty of Computer Science and Information System, Universiti Teknologi, Malaysia
2Faculty of Sciences and Technology, Universiti Kebangsaan, Malaysia
3Faculty of Computer Science and Information Technology, Universiti Putra, Malaysia

Received 3 November 2000

Copyright © 2002 S. M. Shamsuddin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Data reduction is a process of feature extraction that transforms the data space into a feature space of much lower dimension compared to the original data space, yet it retains most of the intrinsic information content of the data. This can be done by using a number of methods, such as principal component analysis (PCA), factor analysis, and feature clustering. Principal components are extracted from a collection of multivariate cases as a way of accounting for as much of the variation in that collection as possible by means of as few variables as possible. On the other hand, backpropagation network has been used extensively in classification problems such as XOR problems, share prices prediction, and pattern recognition. This paper proposes an improved error signal of backpropagation network for classification of the reduction invariants using principal component analysis, for extracting the bulk of the useful information present in moment invariants of handwritten digits, leaving the redundant information behind. Higher order centralised scale- invariants are used to extract features of handwritten digits before PCA, and the reduction invariants are sent to the improved backpropagation model for classification purposes.