面向高光谱分类的局部几何稀疏保持嵌入

黄鸿; 唐玉枭; 段宇乐

doi:10.16383/j.aas.c190594

面向高光谱分类的局部几何稀疏保持嵌入

doi: 10.16383/j.aas.c190594

1.
重庆大学光电工程学院光电技术与系统教育部重点实验室重庆 400044

基金项目: 国家自然科学基金(42071302), 重庆市基础研究与前沿探索项目(cstc2018jcyjAX0093)资助

详细信息

作者简介:
黄鸿：重庆大学光电工程学院教授. 主要研究方向为流形学习, 模式识别, 遥感影像智能化处理. 本文通信作者. E-mail: hhuang@cqu.edu.cn

唐玉枭：重庆大学光电工程学院硕士研究生. 主要研究方向为模式识别和图像处理.E-mail: tangyuxiao@cqu.edu.cn

段宇乐：重庆大学光电工程学院博士研究生. 主要研究方向为机器学习, 模式识别和遥感图像处理.E-mail: duanyule@cqu.edu.cn

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出版历程
- 收稿日期: 2019-08-18
- 录用日期: 2020-04-06
- 网络出版日期: 2022-09-22
- 刊出日期: 2022-10-14

Local Geometry and Sparsity Preserving Embedding for Hyperspectral Image Classification

1.
Key Laboratory of Optoelectronic Technique System of the Ministry of Education, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044

Funds: Supported by National Natural Science Foundation of China (42071302) and Chongqing Basic Research and Frontier Exploration Project (cstc2018jcyjAX0093)

More Information

Author Bio:
HUANG Hong　Professor at the College of Optoelectronic Engineering, Chongqing University. His research interest covers manifold learning, pattern recognition, and intelligent processing of remote sensing images. Corresponding author of this paper

TANG Yu-Xiao　Master student at the College of Optoelectronic Engineering, Chongqing University. His research interest covers pattern recognition and image processing

DUAN Yu-Le　Ph.D. candidate at the College of Optoelectronic Engineering, Chongqing University. His research interest covers machine learning, pattern recognition, and remote sensing image processing

摘要

摘要: 大量维数约简(Dimensionality reducion, DR)方法表明保持数据间稀疏特性的同时, 确保几何结构的保持能更有效提取出具有鉴别性的特征, 为此本文提出一种联合局部几何近邻结构和局部稀疏流形的维数约简方法. 该方法首先通过局部线性嵌入方法重构每个样本以保持数据的局部线性关系, 同时计算样本邻域内的局部稀疏流形结构, 在此基础上通过图嵌入框架保持数据的局部几何近邻结构和稀疏结构, 最后在低维嵌入空间中使类内数据尽可能聚集, 提取低维鉴别特征, 从而提升地物分类性能. 在Indian Pines和PaviaU高光谱数据集上的实验结果表明, 本文方法相较于传统维数约简方法能明显提高地物的分类性能, 总体分类可达到83.02%和91.20%, 有利于实际应用.
- 高光谱图像 /
- 维数约简 /
- 稀疏表示 /
- 流形学习 /
- 协同嵌入
Abstract: A large number of dimensionality reduction methods show that while maintaining the sparse characteristics between data, ensuring that the geometry is maintained can more effectively extract discriminative features. To address this issue, a dimensionality reduction (DR) method combining joint local geometry neighbor structure and local sparse manifold is proposed. The method first reconstructs each sample by local linear embedding to maintain the local linear relationship, and calculates the local sparse manifold structure in the neighbors. Then the local geometry neighbor structure and sparse manifold structure are maintained by the graph embedding frame. Finally, in the low-dimensional embedded space, the intra-class data is compacted as much as possible, so that the low-dimensional discriminative features are extracted to improve the classification performance. The experimental results on the Indian Pines and PaviaU hyperspectral datasets show that the proposed method can significantly improve the classification precision compared with the traditional DR methods. The overall classification can reach 83.02% and 91.20%, respectively, which is beneficial to practical applications.
- Hyperspectral image /
- dimensionality reduction (DR) /
- sparse representation /
- manifold learning /
- collaborative embedding

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图 1 局部几何稀疏保持嵌入(LGSPE)方法流程图

Fig. 1 Flowchart of the LGSPE method

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图 2 Indian Pines高光谱图像

Fig. 2 Indian Pines hyperspectral image

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图 3 PaviaU 高光谱图像

Fig. 3 PaviaU hyperspectral image

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图 4 不同参数$\lambda $和$\beta $在两个数据集上的总体分类精度

Fig. 4 OAs with different parameters$\lambda $and$\beta $on two datasets

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图 5 不同参数${S_n}$和${C_n}$在两个数据集上的总体分类精度

Fig. 5 OAs with different parameters ${S_n}$ and ${C_n}$ on two datasets

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图 6 各算法在Indian Pines数据集上的分类结果图

Fig. 6 Classification maps of different method on Indian Pines dataset

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图 7 PaviaU数据集上各算法的分类结果图

Fig. 7 Classification maps of different method on PaviaU dataset

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表 1 不同算法在Indian Pines数据集上的分类结果(总体分类精度±标准差(%) ($p,h$))

Table 1 Classification results with different methods on Indian Pines dataset (OA ± Std (%) ($p,h$))

算法	2%	4%	6%	8%	10%
RAW	58.08±1.01 (1.5×10⁻⁰⁸, 1)	63.17±0.95 (5.8×10⁻¹², 1)	64.97±0.65 (1.2×10⁻¹⁴, 1)	66.11±0.57 (2.2×10⁻¹⁷, 1)	67.88±0.55 (3.9×10⁻²⁰, 1)
PCA	58.02±1.03 (1.1×10⁻⁰⁸, 1)	62.99±1.04 (8.7×10⁻¹², 1)	64.83±0.53 (4.6×10⁻¹⁵, 1)	66.09±0.70 (7.2×10⁻¹⁷, 1)	67.80±0.53 (2.3×10⁻²⁰, 1)
LDA	47.39±1.49 (5.9×10⁻¹⁶, 1)	63.15±1.47 (1.5×10⁻⁰⁹, 1)	68.52±1.19 (1.3×10⁻⁰⁹, 1)	71.05±1.03 (7.5×10⁻¹¹, 1)	73.53±0.63 (2.2×10⁻¹⁴, 1)
LFDA	57.68±0.80 (2.3×10⁻¹⁰, 1)	63.00±1.26 (2.1×10⁻¹¹, 1)	65.17±0.84 (9.3×10⁻¹⁴, 1)	67.25±0.63 (3.5×10⁻¹⁶, 1)	68.78±0.79 (1.5×10⁻¹⁷, 1)
SNPE	47.29±1.82 (1.5×10⁻¹⁴, 1)	65.04±1.29 (2.1×10⁻⁰⁸, 1)	68.72±1.28 (2.3×10⁻⁰⁹, 1)	70.19±0.73 (6.2×10⁻¹³, 1)	71.67±0.44 (1.7×10⁻¹⁷, 1)
SPP	51.95±1.04 (8.0×10⁻¹⁴, 1)	60.00±0.80 (1.6×10⁻¹⁵, 1)	64.29±0.96 (6.2×10⁻¹⁵, 1)	65.98±0.59 (2.8×10⁻¹⁷, 1)	67.97±0.55 (5.2×10⁻²⁰, 1)
DLSP	57.47±1.36 (2.1×10⁻⁰⁶, 1)	63.63±1.18 (1.5×10⁻¹⁰, 1)	66.05±0.58 (7.6×10⁻¹⁴, 1)	67.65±0.74 (1.4×10⁻¹⁵, 1)	69.35±0.94 (1.6×10⁻¹⁶, 1)
SDL	57.56±1.08 (8.8×10⁻⁰⁹, 1)	64.04±0.52 (2.3×10⁻¹³, 1)	69.05±0.97 (2.4×10⁻¹¹, 1)	71.27±0.88 (9.0×10⁻¹¹, 1)	74.03±0.72 (3.3×10⁻¹³, 1)
DSPE	61.66±1.80 (2.5×10⁻⁰¹, 0)	65.63±1.89 (5.5×10⁻⁰⁶, 1)	69.00±1.37 (3.8×10⁻⁰⁹, 1)	69.25±1.28 (1.7×10⁻¹¹, 1)	70.84±1.15 (3.9×10⁻¹³, 1)
MSME	51.66±1.34 (2.4×10⁻¹³, 1)	57.76±1.38 (1.3×10⁻¹⁴, 1)	61.65±0.84 (1.7×10⁻¹⁶, 1)	64.36±0.57 (8.0×10⁻¹⁹, 1)	66.57±0.99 (4.5×10⁻¹⁸, 1)
LGSFA	58.44±1.64 (3.7×10⁻⁰⁶, 1)	68.17±1.69 (6.0×10⁻⁰³, 1)	72.77±1.13 (3.4×10⁻⁰³, 1)	75.45±0.90 (4.6×10⁻⁰³, 1)	77.24±0.59 (2.4×10⁻⁰⁵, 1)
SDME	58.99±1.41 (3.8×10⁻⁰⁶, 1)	66.84±1.34 (4.0×10⁻⁰⁶, 1)	72.71±1.09 (1.5×10⁻⁰³, 1)	76.05±0.55 (7.2×10⁻⁰³, 1)	78.30±0.30 (2.0×10⁻⁰³, 1)
LGSPE	62.79±1.25	70.34±1.05	74.64±1.25	77.04±0.86	79.13±0.53

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表 2 不同算法在Indian Pine数据集上各类地物的分类结果

Table 2 Classification results of each class samples via different methods on Indian Pines dataset

类别	RAW	PCA	LDA	LFDA	SNPE	SPP	DLSP	SDL	DSPE	MSME	LGSFA	SDME	LGSPE
1	58.33	66.67	72.22	61.11	47.22	63.89	58.33	58.33	55.56	52.78	75.00	77.78	77.78
2	55.68	55.93	67.13	60.38	62.36	59.06	58.90	70.76	66.97	58.07	77.35	77.18	79.98
3	58.01	58.16	63.55	59.86	63.26	58.01	58.16	64.40	60.57	59.43	67.52	68.65	70.35
4	38.31	37.31	51.74	36.32	40.80	32.84	43.28	51.74	39.80	32.84	52.24	54.73	61.19
5	83.70	84.18	87.83	84.18	83.94	83.94	86.62	88.56	86.62	82.00	89.29	90.51	91.24
6	93.23	93.71	96.77	94.68	93.71	94.68	94.52	96.94	95.16	92.74	97.58	97.26	97.90
7	77.78	77.78	72.22	55.56	88.89	55.56	83.33	83.33	88.89	66.67	88.89	88.89	88.89
8	94.83	95.57	99.01	93.60	94.83	94.09	96.06	94.83	95.57	92.36	96.06	96.31	96.80
9	50	60.00	90	70	70	40	60	100	90	60	100	80	70
10	66.59	65.38	61.74	68.77	69.61	69.85	65.98	74.21	67.43	67.43	74.33	77.24	77.60
11	70.82	70.96	73.50	72.83	75.13	73.41	72.21	81.74	74.75	74.70	80.88	81.60	82.89
12	43.25	43.85	70.63	46.63	53.77	46.43	49.80	63.10	62.30	43.45	69.64	72.42	75.99
13	89.08	86.78	97.13	86.78	87.93	93.68	85.63	95.98	94.83	82.76	94.83	95.98	95.98
14	88.93	88.56	94.05	90.23	90.88	89.58	90.33	96.65	91.53	90.33	94.60	94.33	95.26
15	35.37	34.76	59.15	39.94	38.11	39.02	35.06	46.04	42.99	33.54	50.91	50.00	56.71
16	92.41	92.41	88.61	91.14	89.87	88.61	92.41	91.14	86.08	86.08	86.08	88.61	89.87
OA (%)	69.65	69.65	76.17	71.62	73.34	71.43	71.28	79.12	74.63	70.65	80.57	81.32	83.02
AA (%)	68.52	69.50	77.83	69.50	71.89	67.67	70.66	78.61	74.94	67.20	80.95	80.72	81.78
Kappa	0.654	0.654	0.728	0.676	0.695	0.674	0.673	0.761	0.710	0.664	0.778	0.787	0.806
DR 时间 (s)	—	0.01	0.01	0.06	0.13	21.94	39.76	3.67	2.07	6.18	5.52	36.64	12.28

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表 3 不同算法在PaviaU数据集上的分类结果(总体分类精度±标准差(%) ($p,h$))

Table 3 Classification results with different methods on PaviaU dataset (OA ± Std (%) ($p,h$))

算法	0.4%	0.8%	1.2%	1.6%	2%
RAW	76.16±1.28 (1.8×10⁻⁰⁹, 1)	78.13±0.69 (2.4×10⁻¹⁵, 1)	80.50±0.53 (5.2×10⁻¹⁷, 1)	81.11±0.65 (4.7×10⁻¹⁶, 1)	82.20±0.54 (3.0×10⁻¹⁷, 1)
PCA	76.15±1.27 (1.7×10⁻⁰⁹, 1)	78.12±0.69 (2.4×10⁻¹⁵, 1)	80.49±0.54 (6.7×10⁻¹⁷, 1)	81.10±0.64 (4.1×10⁻¹⁶, 1)	82.18±0.54 (2.5×10⁻¹⁷, 1)
LDA	68.06±1.49 (1.2×10⁻¹⁴, 1)	76.24±1.65 (1.1×10⁻¹², 1)	78.73±1.21 (4.2×10⁻¹⁴, 1)	80.36±0.64 (7.0×10⁻¹⁷, 1)	81.88±0.64 (1.1×10⁻¹⁶, 1)
LFDA	79.10±1.16 (3.8×10⁻⁰⁶, 1)	81.60±0.57 (1.0×10⁻¹¹, 1)	83.41±0.26 (6.6×10⁻¹⁵, 1)	84.25±0.68 (1.7×10⁻¹¹, 1)	85.25±0.48 (3.7×10⁻¹³, 1)
SNPE	75.17±1.00 (4.5×10⁻¹¹, 1)	78.32±1.23 (1.2×10⁻¹², 1)	80.48±0.56 (9.0×10⁻¹⁷, 1)	82.15±1.20 (1.9×10⁻¹¹, 1)	83.09±0.68 (7.7×10⁻¹⁵, 1)
SPP	67.23±0.44 (1.9×10⁻¹⁷, 1)	73.63±1.27 (6.1×10⁻¹⁶, 1)	76.24±0.96 (1.6×10⁻¹⁷, 1)	78.13±0.48 (5.7×10⁻²⁰, 1)	79.19±0.92 (5.4×10⁻¹⁷, 1)
DLSP	74.32±1.80 (6.8×10⁻¹⁰, 1)	77.73±1.10 (1.0×10⁻¹³, 1)	80.47±0.80 (5.7×10⁻¹⁵, 1)	79.69±1.39 (4.9×10⁻¹³, 1)	81.52±1.02 (3.9×10⁻¹⁴, 1)
SDL	57.30±2.31 (9.4×10⁻¹⁷, 1)	60.73±4.15 (2.2×10⁻¹³, 1)	62.80±2.30 (1.4×10⁻¹⁷, 1)	65.46±1.89 (2.2×10⁻¹⁸, 1)	67.28±2.63 (1.3×10⁻¹⁵, 1)
DSPE	79.50±1.52 (6.0×10⁻⁰⁵, 1)	80.50±2.31 (6.6×10⁻⁰⁷, 1)	80.75±1.56 (1.8×10⁻¹⁰, 1)	82.09±1.42 (1.7×10⁻¹⁰, 1)	83.62±1.67 (2.1×10⁻⁰⁸, 1)
MSME	75.24±1.76 (3.2×10⁻⁰⁹, 1)	79.32±1.90 (3.3×10⁻⁰⁹, 1)	82.94±1.01 (2.6×10⁻¹⁰, 1)	83.94±1.12 (1.9×10⁻⁰⁹, 1)	85.41±0.64 (2.8×10⁻¹¹, 1)
LGSFA	73.90±1.05 (4.7×10⁻¹², 1)	78.26±1.80 (1.6×10⁻¹⁰, 1)	81.40±0.93 (5.3×10⁻¹³, 1)	82.59±0.65 (2.7×10⁻¹⁴, 1)	83.28±0.78 (9.5×10⁻¹⁴, 1)
SDME	79.67±1.84 (3.2×1⁰⁻⁰⁴, 1)	82.32±0.74 (9.0×10⁻¹⁰, 1)	83.57±0.68 (2.2×10⁻¹¹, 1)	84.67±0.78 (4.6×10⁻¹⁰, 1)	85.35±0.60 (9.7×10⁻¹², 1)
LGSPE	82.96±1.46	86.24±0.78	87.34±0.47	88.23±0.52	88.74±0.36

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表 4 不同算法在PaviaU数据集上各类地物的分类结果

Table 4 Classification results of each class samples via different methods on PaviaU dataset

类别	RAW	PCA	LDA	LFDA	SNPE	SPP	DLSP	SDL	DSPE	MSME	LGSFA	SDME	LGSPE
1	85.76	85.74	87.59	86.28	86.17	83.60	86.25	66.85	76.28	85.33	89.17	85.24	89.08
2	93.48	93.33	93.76	95.49	94.65	93.19	93.28	94.19	93.52	96.14	97.27	93.50	97.92
3	63.09	62.99	62.24	69.26	64.69	57.37	62.69	49.00	58.48	64.54	66.10	63.29	74.12
4	83.10	83.24	84.40	84.40	84.95	80.87	83.37	75.78	79.66	83.72	90.45	87.29	88.94
5	98.75	98.75	99.84	99.30	98.67	99.22	98.75	99.69	99.61	99.77	99.77	99.69	99.61
6	63.02	63.16	68.84	72.35	68.04	67.06	62.89	34.72	73.73	76.81	58.04	72.48	82.52
7	83.93	83.69	74.51	86.22	85.59	76.80	83.45	54.87	71.81	82.34	78.62	84.40	88.28
8	80.70	80.93	76.62	83.16	81.68	76.53	80.85	75.61	70.10	78.90	75.04	74.30	83.59
9	100	100	100	100	100	99.67	99.67	87	97	99.33	99	98.89	100
OA (%)	85.37	85.34	85.90	88.13	86.88	84.38	85.35	76.63	83.40	88.03	87.29	86.20	91.20
AA (%)	83.50	83.50	83.04	86.25	84.90	81.59	83.47	70.91	80.07	85.21	83.79	84.34	89.21
Kappa	0.804	0.804	0.812	0.841	0.824	0.791	0.804	0.682	0.778	0.840	0.828	0.816	0.883
DR 时间 (s)	—	0.009	0.01	0.10	0.28	23.72	71.13	7.30	6.54	8.26	6.31	33.18	12.17

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表 5 不同算法在 Indian Pines 和 PaviaU 数据集上的分类结果(总体分类精度±标准差(%) (Kappa))

Table 5 Classification results with different methods on PaviaU and Indian Pines dataset (OA ± Std (%) (Kappa))

			5	10	20	40	60
		RAW	44.02±3.74 (0.376)	48.69±1.92 (0.430)	55.25±2.36 (0.499)	58.78±0.91 (0.538)	61.10±0.33 (0.562)
	未滤波	SSRSHE	43.65±5.79 (0.375)	49.16±5.34 (0.436)	56.58±4.33 (0.515)	59.91±2.70 (0.550)	66.90±1.69 (0.626)
Indian		LGSPE	45.58±2.97 (0.342)	52.80±2.47 (0.470)	61.82±2.88 (0.572)	70.26±1.42 (0.664)	73.29±1.09 (0.697)
Pines		RAW	48.97±2.10 (0.432)	58.53±1.92 (0.535)	65.27±1.66 (0.609)	70.14±1.65 (0.663)	74.30±1.04 (0.709)
	滤波后	SSRSHE	65.04±4.15 (0.610)	71.50±2.87 (0.680)	79.30±1.63 (0.767)	86.64±2.85 (0.848)	87.75±1.15 (0.860)
		LGSPE	69.17±2.72 (0.657)	78.96±1.82 (0.763)	85.48±1.48 (0.836)	90.68±1.00 (0.894)	93.92±0.50 (0.930)
		RAW	56.85±7.57 (0.474)	65.12±3.46 (0.564)	68.82±2.72 (0.609)	71.78±0.79 (0.644)	74.58±0.59 (0.676)
	未滤波	SSRSHE	62.49±3.39 (0.538)	64.29±1.73 (0.559)	67.81±3.25 (0.599)	71.21±1.71 (0.638)	75.36±2.44 (0.685)
PaviaU		LGSPE	65.58±6.08 (0.567)	69.91±6.06 (0.622)	75.70±1.98 (0.690)	81.76±1.71 (0.765)	81.45±1.30 (0.760)
		RAW	60.41±2.85 (0.514)	67.39±2.46 (0.590)	71.27±3.06 (0.639)	76.11±1.14 (0.696)	77.86±2.17 (0.718)
	滤波后	SSRSHE	71.18±4.85 (0.639)	75.17±2.96 (0.686)	82.86±2.07 (0.730)	84.24±0.71 (0.795)	87.02±0.97 (0.803)
		LGSPE	76.10±3.53 (0.697)	80.21±3.05 (0.700)	86.70±2.18 (0.828)	91.02±1.95 (0.883)	93.72±0.93 (0.917)

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