Feature Extraction Based on Linear Embedding and Tensor Manifold for Hyperspectral Image

Shixin Ma; Chuntong Liu; Hongcai Li; Geng Zhang; Zhenxin He

doi:10.3788/AOS201939.0412001

Acta Optica Sinica, Volume. 39, Issue 4, 0412001(2019)

Feature Extraction Based on Linear Embedding and Tensor Manifold for Hyperspectral Image

Shixin Ma^1、*, Chuntong Liu¹, Hongcai Li¹, Geng Zhang², and Zhenxin He¹

Author Affiliations

¹ College of Missile Engineering, Rocket Force University of Engineering, Xi′an, Shaanxi 710025, China

² Key Laboratory of Spectral Imaging Technology, Xian Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi′an, Shaanxi 710119, China

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Figures & Tables(12)

Fig. 1. Diagrams of manifold difference. (a) LLE algorithm; (b) GLE algorithm

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Fig. 2. Dimensionality reduction frame of tensor manifold

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Fig. 3. Indian Pines hyperspectral data. (a) Pseudo-color image; (b) ground-truth map

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Fig. 4. PaviaU hyperspectral data. (a) Pseudo-color image; (b) ground-truth map

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Fig. 5. Influence of sparse parameters λ on classification performance (Indian Pines data)

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Fig. 6. Dimensionality reduction performance of Indian Pines data obtained with different algorithms. (a) Ground-truth map; (b) PCA algorithm; (c) MNF algorithm; (d) LLE algorithm; (e) LE algorithm; (f) LPP algorithm; (g) RP algorithm; (h) proposed algorithm

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Fig. 7. Dimensionality reduction performance of PaviaU data obtained with different algorithms. (a) Ground-truth map; (b) PCA algorithm; (c) MNF algorithm; (d) LLE algorithm; (e) LE algorithm; (f) LPP algorithm; (g) RP algorithm; (h) proposed algorithm

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Fig. 8. Projection results obtained with different dimensionality reduction algorithms (Indian Pines data). (a) Original data (band 1 & 2); (b) PCA algorithm; (c) MNF algorithm; (d) LLE algorithm; (e) LE algorithm; (f) LPP algorithm; (g) RP algorithm; (h) proposed algorithm

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Fig. 9. Classification accuracy of different algorithms obtained at different embedding dimensions. (a) Indian Pines data; (b) PaviaU data

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Table 1. Classification accuracy of different dimensionality reduction algorithms

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Table 1. Classification accuracy of different dimensionality reduction algorithms

Dataset	SVM classification	PCA	MNF	LLE	LE	LPP	RP	LETM
Indian Pines (M=30)	OCA /%	76.69	83.74	71.44	68.88	79.09	81.16	85.10
Indian Pines (M=30)	ACA /%	69.26	79.74	70.08	63.52	75.48	77.95	81.96
PaviaU(M=20)	OCA /%	92.46	93.09	85.67	82.58	93.56	90.56	95.55
PaviaU(M=20)	ACA /%	89.04	91.94	82.15	75.98	90.55	86.98	93.93

Table 2. Time complexity of different algorithms
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Table 2. Time complexity of different algorithms
Algorithm Time complexity
PCA O(N²D)
MNF O(2N²D)
LLE O[NDlb k·lb D+NDk³+DN²+N³]
LE O[NDlb k·lb D+NDk³+MD²]
LPP O[NDlb k·lb D+NDk³+2DMN+kMD²]
RP O(DMN)
LETM O(t⁴N⁴+t²N²D²+2t³N³+2t²N²D+kMD²)

Table 3. Computation time of different algorithms

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Table 3. Computation time of different algorithms

Data	Reduced dimensionality	Computation times /s
Data	Reduced dimensionality	PCA	NMF	LLE	LE	LPP	RP	LETM
Indian Pines	10	0.273	0.386	44.912	13.520	13.065	0.079	42.367
	30	0.274	0.391	45.774	13.733	13.177	0.079	42.803
	50	0.277	0.403	46.265	14.210	13.313	0.090	43.116
PaviaU	10	0.763	1.039	3633.611	2187.667	2454.708	0.239	304.150
	30	0.807	1.068	3672.186	2193.203	2454.845	0.294	307.489
	50	0.811	1.085	3714.503	2199.186	2454.896	0.401	310.316

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Shixin Ma, Chuntong Liu, Hongcai Li, Geng Zhang, Zhenxin He. Feature Extraction Based on Linear Embedding and Tensor Manifold for Hyperspectral Image[J]. Acta Optica Sinica, 2019, 39(4): 0412001

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