Fast Dimension Reduction That Preserves Underdetermined Data Clusters

Richard M. Crownover; James M. Keller

doi:10.1117/12.936898

4 April 1986 Fast Dimension Reduction That Preserves Underdetermined Data Clusters

Richard M. Crownover, James M. Keller

Proceedings Volume 0696, Advanced Algorithms and Architectures for Signal Processing I; (1986) https://doi.org/10.1117/12.936898
Event: 30th Annual Technical Symposium, 1986, San Diego, United States

Abstract

An important technique for object recognition in electro-optics, signal processing, and image understanding is to use a training algorithm to create a data base against which to compare data for objects being tested. The data for each training and test object is represented as a vector in a space of possible high dimension, perhaps in the hundreds or thousands. It is usually desired to project this data onto a space of much lower dimension in such a way that separation of object clusters is preserved. The difficulty with using this approach as it is usually presented is that it leads to inordinately large generalized matrix eigensystems that must be analyzed. Just as drastic is the large amount of data required for implementation. For instance, Fisher's linear discriminant method usually requires having at least as many training vectors as the dimension of the representation space. This is a severe limitation in that it would be preferable to train on reasonable amounts of data, say on samples of 20 data vectors in each class of objects. In this paper, we present a new methodology based on the Fisher linear discriminant method, but for the underdetermined case; that is, for the case of having only relatively small amounts of training data for each cluster of objects. The new algorithm is based partly on the original Fisher algorithm and partly on more recent fast algorithms for matrix factorizations. We also present examples showing application of this algorithm to the problem of automatic target recognition using images from FLIR data.

Citation Download Citation

Richard M. Crownover and James M. Keller "Fast Dimension Reduction That Preserves Underdetermined Data Clusters", Proc. SPIE 0696, Advanced Algorithms and Architectures for Signal Processing I, (4 April 1986); https://doi.org/10.1117/12.936898

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