Fast approximate kernel PCA via wavelet decomposition

Aaron George; Wojciech Czaja

doi:10.1117/12.2556568

24 April 2020 Fast approximate kernel PCA via wavelet decomposition

Aaron George, Wojciech Czaja

Proceedings Volume 11392, Algorithms, Technologies, and Applications for Multispectral and Hyperspectral Imagery XXVI; 1139214 (2020) https://doi.org/10.1117/12.2556568
Event: SPIE Defense + Commercial Sensing, 2020, Online Only

Abstract

Kernel methods proved to be a useful tool in classification and analysis of large data sets arising in the context of hyperspectral imaging (HSI). Among them, kernel PCA is of particular interest as it is a robust tool that combines non-linearity with the advantages provided by the principal components. Unfortunately, one drawback of kernel PCA is its high computational complexity, with run times on the order of O(N ³), where N is the number of points in the data set. To resolve this problem, we propose to take advantage of the fast approximate factor analysis approach proposed by M. V. Wickerhauser in the context of traditional image processing. We adapt and implement this concept to the kernel PCA setting, yielding an approximation to a full kernel PCA decomposition of the data, with run times asymptotically on the order O(N ² log N ). Furthermore, we test this approximation on several standard HSI data sets to demonstrate that these approximations do not impact the classification accuracy, while at the same time providing significant computation time reductions.

Conference Presentation

Citation Download Citation

Aaron George and Wojciech Czaja "Fast approximate kernel PCA via wavelet decomposition", Proc. SPIE 11392, Algorithms, Technologies, and Applications for Multispectral and Hyperspectral Imagery XXVI, 1139214 (24 April 2020); https://doi.org/10.1117/12.2556568

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