26 April 2018 Exact divide-and-conquer algorithm of multinomial logistic regression for hyperspectral image classification
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Abstract
Multinomial logistic regression (MLR) is an effective classifier in spatial–spectral-based hyperspectral image (HSI) classification. However, in some typical scenarios, such as Gaussian regularized MLR (GSMLR) and Laplacian graph regularized MLR (LPMLR), it hits a large   (  cd  )    ×    (  cd  )   linear system during the regressors learning procedure that is unbearable in both space and time complexity (c is the number of classes and d is the length of feature). Even if using middle-sized features, it often runs out of memory. To this end, we propose two exact divide-and-conquer (DC) algorithms, DC-GSMLR and DC-LPMLR, to reduce the computation complexity. Both decompose the regressors learning problem into a series of equivalent smaller subproblems, each of which can be solved in closed form. Unlike the approximation ones available, they provide exact merged solutions instead. With the same accuracy, DC-LPMLR and DC-GSMLR only need to solve c  +  1 and 2 d  ×  d linear systems, respectively, significantly reducing the peak memory usage by almost O  (  c  )   and O  (  c2  /  2  )   times. For time, experiments on two popular HSI datasets indicate considerable speedup ratio as high as one or two orders of magnitude, showing the practicability in real applications.
© 2018 Society of Photo-Optical Instrumentation Engineers (SPIE)
Xiaotao Wang, Fang Liu, "Exact divide-and-conquer algorithm of multinomial logistic regression for hyperspectral image classification," Journal of Applied Remote Sensing 12(2), 025005 (26 April 2018). https://doi.org/10.1117/1.JRS.12.025005 Submission: Received 26 November 2017; Accepted 22 March 2018
Submission: Received 26 November 2017; Accepted 22 March 2018
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