Sparse Estimation of the Precision Matrix and Plug-In Principle in Linear Discriminant Analysis for Hyperspectral Image Classification

PICCO, M. L.; RUIZ, M. S.

doi:10.5540/tcam.2022.023.03.00595

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Articles • Trends Comput. Appl. Math. 23 (3) • Jul-Sep 2022 • https://doi.org/10.5540/tcam.2022.023.03.00595 linkcopy

Sparse Estimation of the Precision Matrix and Plug-In Principle in Linear Discriminant Analysis for Hyperspectral Image Classification

Authorship SCIMAGO INSTITUTIONS RANKINGS

In this paper, a new method for supervised classification of hyperspectral images is proposed for the case in which the size of the training sample is small. It consists of replacing in the Mahalanobis distance the maximum likelihood estimator of the precision matrix by a sparse estimator. The method is compared with two other existing versions of LDA sparse, both in real and simulated images.

Keywords:
hight dimensionality; linear discriminant analysis; hyperspectral image

	1	2	...	k	Total
Predicted class	1	2	...	k	Total
1	n ₁₁	n ₁₂	...	n _1k	n _1.
2	n ₂₁	n ₂₂	...	n _2k	n _2.
...	...	...	...	...	...
k	n _k1	n _k2	...	n _kk	n _k.
Total	n _.1	n _.2	...	n _.k	N

training sample	RF	SDA	Pen-LDA	Plug-in LDA
	36.3	11.3	6.3	17.4
	(0.953)	(0.995)	(0.998)	(0.989)

	LDA	RF	SDA	Pen-LDA	Plug-in LDA
wF₁ score	0.43	0.90	0.94	0.94	0.92
$\hat{κ}$	0.34	0.87	0.92	0.92	0.90

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