Exact divide-and-conquer algorithm of multinomial logistic regression for hyperspectral image classification

Xiaotao Wang; Fang Liu

doi:10.1117/1.JRS.12.025005

26 April 2018 Exact divide-and-conquer algorithm of multinomial logistic regression for hyperspectral image classification

Xiaotao Wang, Fang Liu

Author Affiliations +

Journal of Applied Remote Sensing, Vol. 12, Issue 2, 025005 (April 2018). https://doi.org/10.1117/1.JRS.12.025005

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.

Citation Download Citation

Xiaotao Wang and 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

Received: 26 November 2017; Accepted: 22 March 2018; Published: 26 April 2018

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $24.00

Non-members: $28.00 ADD TO CART

JOURNAL ARTICLE
11 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Hyperspectral imaging

Image classification

Error analysis

Image sensors

Matrix multiplication

Visualization

Algorithms

Show All Keywords

Keywords/Phrases

Search In:

Publication Years