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Unsupervised Feature Selection Based on Ultrametricity and Sparse Training Data: A Case Study for the Classification of High-Dimensional Hyperspectral Data
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Remote Sens. 2019, 11(2), 109;

Locally Weighted Discriminant Analysis for Hyperspectral Image Classification

School of Computer Science, China University of Geosciences, Wuhan 430074, China
School of Computer, Wuhan University, Wuhan 430072, China
Department of Computing, The Hong Kong Polytechnic University, Kowloon, Hong Kong 999077, China
Author to whom correspondence should be addressed.
Received: 26 November 2018 / Revised: 27 December 2018 / Accepted: 3 January 2019 / Published: 9 January 2019
(This article belongs to the Special Issue Dimensionality Reduction for Hyperspectral Imagery Analysis)
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A hyperspectral image (HSI) contains a great number of spectral bands for each pixel, which will limit the conventional image classification methods to distinguish land-cover types of each pixel. Dimensionality reduction is an effective way to improve the performance of classification. Linear discriminant analysis (LDA) is a popular dimensionality reduction method for HSI classification, which assumes all the samples obey the same distribution. However, different samples may have different contributions in the computation of scatter matrices. To address the problem of feature redundancy, a new supervised HSI classification method based on locally weighted discriminant analysis (LWDA) is presented. The proposed LWDA method constructs a weighted discriminant scatter matrix model and an optimal projection matrix model for each training sample, which is on the basis of discriminant information and spatial-spectral information. For each test sample, LWDA searches its nearest training sample with spatial information and then uses the corresponding projection matrix to project the test sample and all the training samples into a low-dimensional feature space. LWDA can effectively preserve the spatial-spectral local structures of the original HSI data and improve the discriminating power of the projected data for the final classification. Experimental results on two real-world HSI datasets show the effectiveness of the proposed LWDA method compared with some state-of-the-art algorithms. Especially when the data partition factor is small, i.e., 0.05, the overall accuracy obtained by LWDA increases by about 20 % for Indian Pines and 17 % for Kennedy Space Center (KSC) in comparison with the results obtained when directly using the original high-dimensional data. View Full-Text
Keywords: hyperspectral image (HSI) classification; linear discriminant analysis (LDA); dimensionality reduction; spatial-spectral information hyperspectral image (HSI) classification; linear discriminant analysis (LDA); dimensionality reduction; spatial-spectral information

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Li, X.; Zhang, L.; You, J. Locally Weighted Discriminant Analysis for Hyperspectral Image Classification. Remote Sens. 2019, 11, 109.

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