21 August 1987 Comparative Study Of Various Linear Mapping Algorithms For Hybrid Statistical Pattern Recognition
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Proceedings Volume 0754, Optical and Digital Pattern Recognition; (1987) https://doi.org/10.1117/12.939981
Event: OE LASE'87 and EO Imaging Symposium, 1987, Los Angeles, CA, United States
Abstract
We study the relations among various linear mapping-based algorithms by formulating a more general unified pseudo-inverse algorithm. We show that the least-square linear mapping technique, the simplified least-square linear mapping technique, the synthetic discriminant function, the equal correlation peak method and the Caulfield-Maloney filter are in fact all special cases of the unified pseudo-inverse algorithm. When the total number of the training images (KM, where K is the number of classes and M is the number of training images in each class) is larger than the dimension of the images (N), the overdetermined case of the unified pseudo-inverse algorithm is the same as the least-square linear mapping technique, due to the fact that both algorithms are based on optimization processes of minimization of the least square error. When KM < N, the underdetermined case of the unified pseudo-inverse algorithm is the same as the least-square linear mapping technique and the synthetic discriminant function. Furthermore, when KM < N, the synthetic discriminant function method can be considered as the degenerated case of the least-square linear mapping technique. Experimental results on classification using the linear mapping-based algorithms are provided and show good agreement with the theoretical analysis.
© (1987) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Q. Tian, Q. Tian, Y. Fainman, Y. Fainman, Z. H. Gu, Z. H. Gu, Sing H. Lee, Sing H. Lee, } "Comparative Study Of Various Linear Mapping Algorithms For Hybrid Statistical Pattern Recognition", Proc. SPIE 0754, Optical and Digital Pattern Recognition, (21 August 1987); doi: 10.1117/12.939981; https://doi.org/10.1117/12.939981
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