Brain and Nature-inspired Learning, Computation and Recognition

Brain and Nature-Inspired Learning, Computation and Recognition
Copyright
1. Introduction
	1.1 A brief introduction to the neural network
		1.1.1 The development of neural networks
		1.1.2 Neuron and feedforward neural network
		1.1.3 Backpropagation algorithm
		1.1.4 The learning paradigm of neural networks
	1.2 Natural inspired computation
		1.2.1 Fundamentals of nature-inspired computation
		1.2.2 Evolutionary algorithm
		1.2.3 Artificial immune system (AIS)
		1.2.4 Other methods
	1.3 Machine learning
		1.3.1 Development of machine learning
		1.3.2 Dimensionality reduction
		1.3.3 Sparseness and low-rank
		1.3.4 Semisupervised learning
	1.4 Compressive sensing learning
		1.4.1 The development of compressive sensing
		1.4.2 Sparse representation
		1.4.3 Compressive observation
		1.4.4 Sparse reconstruction
	1.5 Applications
		1.5.1 Community detection
		1.5.2 Capacitated arc routing optimization
		1.5.3 Synthetic aperture radar image processing
		1.5.4 Hyperspectral image processing
	References
2. The models and structure of neural networks
	2.1 Ridgelet neural network
	2.2 Contourlet neural network
		2.2.1 Nonsubsampled contourlet transforms
		2.2.2 Deep contourlet neural network
	2.3 Convolutional neural network
		2.3.1 Convolution
		2.3.2 Pooling
		2.3.3 Activation function
		2.3.4 Batch normalization
		2.3.5 LeNet5
	2.4 Recurrent artificial neural network
	2.5 Generative adversarial nets
		2.5.1 Biological description—human behavior
		2.5.2 Data augmentation
		2.5.3 Model description
	2.6 Autoencoder
		2.6.1 Layer-wise pretraining
		2.6.2 Autoencoder network
	2.7 Restricted Boltzmann machine and deep belief network
	Further reading
3. Theoretical basis of natural computation
	3.1 Evolutionary algorithms
		3.1.1 Pattern theorem
		3.1.2 Implicit parallelism
		3.1.3 Building block assumption
	3.2 Artificial immune system
		3.2.1 Markov chain-based convergence analysis
		3.2.2 Nonlinear dynamic model
	3.3 Multiobjective optimization
		3.3.1 Introduction
		3.3.2 Mathematical concepts
		3.3.3 Multiobjective optimization algorithms
			3.3.3.1 The first generation of evolutionary multiobjective optimization algorithms
				3.3.3.1.1 MOGA
				3.3.3.1.2 NSGA
				3.3.3.1.3 NPGA
			3.3.3.2 The second generation of evolutionary multiobjective optimization algorithms
				3.3.3.2.1 SPEA and SPEA2
				3.3.3.2.2 PAES, PESA, and PESA-II
				3.3.3.2.3 NSGA-II
	References
4. Theoretical basis of machine learning
	4.1 Dimensionality reduction
		4.1.1 Subspace segmentation
		4.1.2 Nonlinear dimensionality reduction
	4.2 Sparseness and low rank
		4.2.1 Sparse representation
		4.2.2 Matrix recovery and completion
	4.3 Semisupervised learning and kernel learning
		4.3.1 Semisupervised learning
		4.3.2 Nonparametric kernel learning
	References
5. Theoretical basis of compressive sensing
	5.1 Sparse representation
		5.1.1 Stationary dictionary
		5.1.2 Learning dictionary
	5.2 Compressed observation
	5.3 Sparse reconstruction
		5.3.1 Relaxation methods
		5.3.2 Greedy methods
		5.3.3 Natural computation methods
		5.3.4 Other methods
	References
6. Multiobjective evolutionary algorithm (MOEA)-based sparse clustering
	6.1 Introduction
		6.1.1 The introduction of MOEA on constrained multiobjective optimization problems
		6.1.2 An introduction to MOEA on clustering learning and classification learning
		6.1.3 The introduction of MOEA on sparse spectral clustering
	6.2 Modified function and feasible-guiding strategy-based constrained MOPs
		6.2.1 Problem description
		6.2.2 Modified objective function
		6.2.3 The feasible-guiding strategy
		6.2.4 Procedure for the proposed algorithm
	6.3 Learning simultaneous adaptive clustering and classification learning via MOEA
		6.3.1 Objective functions of MOASCC
		6.3.2 The framework of MOASCC
		6.3.3 Computational complexity
	6.4 A sparse spectral clustering framework via MOEA
		6.4.1 Mathematical description of SRMOSC
		6.4.2 Extension on semisupervised clustering
		6.4.3 Initialization
		6.4.4 Crossover
		6.4.5 Mutation
		6.4.6 Laplacian matrix construction
		6.4.7 Final solution selection phase
		6.4.8 Complexity analysis
	6.5 Experiments
		6.5.1 The experiments of MOEA on constrained multiobjective optimization problems
			6.5.1.1 Experimental setup
			6.5.1.2 Performance metrics
				6.5.1.2.1 IGD
				6.5.1.2.2 Minimal spacing
				6.5.1.2.3 Coverage of two sets (ς)
			6.5.1.3 Comparison experiment results
		6.5.2 The experiments of MOEA on clustering learning and classification learning
			6.5.2.1 Experiment setup
			6.5.2.2 Experiment on a synthetic datasets
			6.5.2.3 Experiment on real-life datasets
		6.5.3 The experiments of MOEA on sparse spectral clustering
			6.5.3.1 Detailed analysis of SRMOSC
			6.5.3.2 Experimental comparison between SRMOSC and other algorithms
	6.6 Summary
	References
7. MOEA-based community detection
	7.1 Introduction
	7.2 Multiobjective community detection based on affinity propagation
		7.2.1 Background to APMOEA
			7.2.1.1 Affinity propagation method
			7.2.1.2 Multiobjective optimization
		7.2.2 Objective functions
		7.2.3 The selection method for nondominated solutions
		7.2.4 Preliminary partition by the AP method
		7.2.5 Further search using multiobjective evolutionary algorithm
			7.2.5.1 Representation and initialization
			7.2.5.2 Genetic operators
		7.2.6 Elitist strategy of the external archive
	7.3 Multiobjective community detection based on similarity matrix
		7.3.1 Background of GMOEA-net
			7.3.1.1 Structural balance theory
			7.3.1.2 Tchebycheff approach
		7.3.2 Objective functions
		7.3.3 The construction of similarity matrix and k-nodes update policy
			7.3.3.1 The function of node similarity
			7.3.3.2 The k-nodes update policy
		7.3.4 Evolutionary operators
			7.3.4.1 The cross-merging operator based on local node sets
			7.3.4.2 The mutation operator based on similarity matrix
		7.3.5 The whole framework of GMOEA-net
	7.4 Experiments
		7.4.1 Evaluation index
		7.4.2 Networks for simulation
			7.4.2.1 Computer-generated networks
			7.4.2.2 Real-world networks
		7.4.3 Comparison algorithms and parameter settings
			7.4.3.1 Comparison algorithms
			7.4.3.2 Parameter settings
		7.4.4 Experiments on computer-generated networks
			7.4.4.1 Experiments on APMOEA
			7.4.4.2 Experiments on GMOEA-net
		7.4.5 Experiments on real-world networks
	7.5 Summary
	References
8. Evolutionary computation-based multiobjective capacitated arc routing optimizations
	8.1 Introduction
	8.2 Multipopulation cooperative coevolutionary algorithm
		8.2.1 Related works
			8.2.1.1 The model of MO-CARP
			8.2.1.2 The description of direction vector
		8.2.2 Initial population and subpopulations partition
		8.2.3 The fitness evaluation in each subpopulation
		8.2.4 The elitism archiving mechanism
			8.2.4.1 The external elitism archive
			8.2.4.2 The internal elitism archive
		8.2.5 The cooperative coevolutionary process
			8.2.5.1 Construct evolutionary pool for each subregion
			8.2.5.2 Crossover
			8.2.5.3 Local search
			8.2.5.4 The selection of offspring solutions and diversity preservation mechanism
		8.2.6 The processing flow of MPCCA
	8.3 Immune clonal algorithm via directed evolution
		8.3.1 Antibody initialization
		8.3.2 Immune clonal operation
		8.3.3 Immune gene operations
			8.3.3.1 The decomposition operation of the population
			8.3.3.2 Gene recombination operator
			8.3.3.3 Gene mutation operator
			8.3.3.4 Directed comparison operator
			8.3.3.5 Clonal selection operator
		8.3.4 The processing flow of DE-ICA
	8.4 Improved memetic algorithm via route distance grouping
		8.4.1 Solutions for the timely replacement of IRDG-MAENS
		8.4.2 Determine the regions which individuals belong to
		8.4.3 The processing flow of IRDG-MAENS
	8.5 Experiments
		8.5.1 Test problems and experimental setup
			8.5.1.1 MPCCA
			8.5.1.2 DE-ICA
			8.5.1.3 IRDG-MAENS
		8.5.2 The performance metrics
			8.5.2.1 The distance to the reference set (ID)
			8.5.2.2 Purity
			8.5.2.3 Hypervolume (HV)
		8.5.3 Wilcoxon signed rank test
		8.5.4 Comparison of the evaluation metrics
			8.5.4.1 MPCCA
			8.5.4.2 DE-ICA
			8.5.4.3 IRDG-MAENS
		8.5.5 Comparison of nondominant solutions
			8.5.5.1 MPCCA
			8.5.5.2 DE-ICA
			8.5.5.3 IRDG-IDMAENS
	8.6 Summary
	References
9. Multiobjective optimization algorithm-based image segmentation
	9.1 Introduction
	9.2 Multiobjective evolutionary fuzzy clustering with MOEA/D
		9.2.1 Fuzzy-C means clustering algorithms with local information
		9.2.2 Framework of MOEFC
		9.2.3 Opposition-based learning operator
		9.2.4 Mixed population initialization
		9.2.5 The time complexity analysis
	9.3 Multiobjective immune algorithm for SAR image segmentation
		9.3.1 Definitions of AIS-based, multiobjective optimization
		9.3.2 The stage of features extraction and preprocessing
			9.3.2.1 Watershed raw segmentation
			9.3.2.2 Feature extraction using Gabor filters and GLCP
		9.3.3 The immune multiobjective framework for SAR imagery segmentation
	9.4 Experiments
		9.4.1 The MOEFC experiments
			9.4.1.1 Experimental setting of MOEFC
			9.4.1.2 Segmentation results on synthetic images
			9.4.1.3 Segmentation results on natural images
			9.4.1.4 Segmentation results on medical images
			9.4.1.5 Segmentation results on SAR images
		9.4.2 The IMIS experiments
			9.4.2.1 IMIS experimental settings
			9.4.2.2 Analysis of experimental results
	9.5 Summary
	References
10. Graph-regularized feature selection based on spectral learning and subspace learning
	10.1 Nonnegative spectral learning and subspace learning-based graph-regularized feature selection
		10.1.1 Dual-graph nonnegative spectral learning
		10.1.2 Dual-graph sparse regression
		10.1.3 Feature selection
		10.1.4 Optimization
		10.1.5 Local structure preserving
		10.1.6 Update rules for SGFS
	10.2 Experiments of spectral learning and subspace learning methods for feature selection
		10.2.1 Experiments and analysis of NSSRD
			10.2.1.1 Experimental settings
			10.2.1.2 Simple illustrative example problem
			10.2.1.3 Evaluating the effectiveness of NSSRD
			10.2.1.4 Clustering results and analysis
		10.2.2 Experiments and analysis of SGFS
			10.2.2.1 Experimental setting
			10.2.2.2 Convergence test
			10.2.2.3 AT&T face dataset example
			10.2.2.4 Experimental results and analysis
			10.2.2.5 Robustness test of algorithms
			10.2.2.6 Parameter sensitivity analysis
	References
11. Semisupervised learning based on nuclear norm regularization
	11.1 Framework of semisupervised learning (SSL) with nuclear norm regularization
		11.1.1 A general framework
		11.1.2 Nuclear norm regularized model
		11.1.3 Modified fixed point algorithm
		11.1.4 Implementation
		11.1.5 Label propagation
		11.1.6 Valid kernel
	11.2 Experiments and analysis
		11.2.1 Compared algorithms and parameter settings
		11.2.2 Synthetic data
		11.2.3 Real-world data sets
		11.2.4 Transduction classification results
	References
12. Fast clustering methods based on learning spectral embedding
	12.1 Learning spectral embedding for semisupervised clustering
		12.1.1 Graph construction and spectral embedding
			12.1.1.1 Symmetry-favored graph
			12.1.1.2 Spectral embedding of graph Laplacian
		12.1.2 Problem formulation
			12.1.2.1 The unit hypersphere
			12.1.2.2 Squared loss model
			12.1.2.3 Hinge loss model
			12.1.2.4 Clustering
		12.1.3 Algorithm
		12.1.4 Experiments
			12.1.4.1 Parameter selection
			12.1.4.2 Vector-based clustering
			12.1.4.3 Graph-based clustering
	12.2 Fast semisupervised clustering with enhanced spectral embedding
		12.2.1 Problem formulation
			12.2.1.1 Objective function
			12.2.1.2 Solving the objective function
			12.2.1.3 Clustering
		12.2.2 Algorithm
			12.2.2.1 Experimental results
			12.2.2.2 Parameter selection
			12.2.2.3 Toy examples
			12.2.2.4 Vector-based clustering
			12.2.2.5 Graph-based clustering
	References
Chapter 13 - Fast clustering methods based on affinity propagation and density weighting
	13.1 The framework of fast clustering methods based on affinity propagation and density weighting
		13.1.1 Related works
			13.1.1.1 AP clustering
			13.1.1.2 Spectral clustering
			13.1.1.3 Nyström method
			13.1.1.4 Local length and global distance
		13.1.2 Fast AP algorithm
			13.1.2.1 Coarsening phase
				13.1.2.1.1 Fast sampling algorithm
				13.1.2.1.2 Determine the number of representative exemplars
			13.1.2.2 Exemplar-clustering phase
			13.1.2.3 Refinement phase
		13.1.3 Fast two-stage spectral clustering framework
			13.1.3.1 Fast two-stage AP algorithm
			13.1.3.2 Determine the number of representative exemplars
			13.1.3.3 Sampling phase
			13.1.3.4 Fast-weighted approximation spectral clustering phase
			13.1.3.5 Robustness
			13.1.3.6 Fast nearest-neighbors research
	13.2 Experiments and analysis
		13.2.1 Experiments on the method based on affinity propagation
			13.2.1.1 Synthetic data sets
			13.2.1.2 Compared algorithms and parameter settings
			13.2.1.3 Vector-based clustering
			13.2.1.4 Evaluation metrics
			13.2.1.5 Experimental results
			13.2.1.6 Graph-based clustering
		13.2.2 Experiments on the method based on density-weighting
			13.2.2.1 Intertwined spirals data set
			13.2.2.2 Real-world data sets
			13.2.2.3 Compared algorithms
			13.2.2.4 Algorithm performances
			13.2.2.5 Spectral embedding
	References
14. SAR image processing based on similarity measures and discriminant feature learning
	14.1 SAR image retrieval based on similarity measures
		14.1.1 Semantic classification and region-based similarity measures
			14.1.1.1 Semisupervised learning
			14.1.1.2 Classification recovery scheme
			14.1.1.3 Improved integrated region matching measure
				14.1.1.3.1 Self-adapting k-means segmentation
				14.1.1.3.2 Region-based IRM distance computation
				14.1.1.3.3 Improved IRM scheme
				14.1.1.3.4 Edge regions calculation
				14.1.1.3.5 IIRM computation
			14.1.1.4 Methodology summary
				14.1.1.4.1 Off-line process
				14.1.1.4.2 On-line process
			14.1.1.5 Experiment
				14.1.1.5.1 Performance of improved integrated region matching (IIRM) measure
				14.1.1.5.2 Query example (proposed method, IRM, one of the latest retrieval methods)
				14.1.1.5.3 Land cover statistical analysis
		14.1.2 Fusion similarity-based reranking for SAR image retrieval
			14.1.2.1 Fusion similarity-based reranking
				14.1.2.1.1 Preprocessing
				14.1.2.1.2 Reranking
					14.1.2.1.2.1 Modal-image matrix construction and fusion similarity calculation
					14.1.2.1.2.2 Reranking function and solution
			14.1.2.2 Experiments and discussion
				14.1.2.2.1 Experiment settings
				14.1.2.2.2 Numerical assessment
					14.1.2.2.2.1 Based on different retrieval methods
					14.1.2.2.2.2 Compared with different reranking algorithms
			14.1.2.3 Influence of different parameters
			14.1.2.4 Reranking efficiency
			14.1.2.5 Reranking examples
		14.1.3 SAR image content retrieval based on fuzzy similarity and relevance feedback
			14.1.3.1 Region-based fuzzy matching
				14.1.3.1.1 Introduction to the improved integrated region matching algorithm
				14.1.3.1.2 RFM measure
					14.1.3.1.2.1 Superpixel-based segmentation for brightness-texture regions
					14.1.3.1.2.2 Multiscale edge detector-based segmentation for edge regions
					14.1.3.1.2.3 Fuzzy region representation
					14.1.3.1.2.4 RFM similarity calculation
					14.1.3.1.2.5 RFM summarization and computational complexity
			14.1.3.2 Multiple relevance feedback (MRF)
			14.1.3.3 Experiments and discussion
				14.1.3.3.1 Setting parameters
				14.1.3.3.2 Evaluation criteria
				14.1.3.3.3 Retrieval examples
			14.1.3.4 Numerical evaluation
				14.1.3.4.1 Performance of the RFM
				14.1.3.4.2 Performance of the proposed retrieval method
				14.1.3.4.3 Importance of the multiple RF schemes\' integration
				14.1.3.4.4 Significance of the RFM Gaussian kernel
				14.1.3.4.5 Influences of different parameters
	14.2 SAR image change detection based on spatial coding and similarity
		14.2.1 Saliency-guided change detection for SAR imagery using a semisupervised Laplacian SVM
			14.2.1.1 Learning a pseudotraining set via saliency detection
			14.2.1.2 Obtaining change result via Laplacian support vector machine
			14.2.1.3 Experimental results
				14.2.1.3.1 Description of data sets
				14.2.1.3.2 Quantitative analysis
				14.2.1.3.3 Parameter selection
				14.2.1.3.4 Experiment results and analysis on three data sets
		14.2.2 SAR images change detection based on spatial coding and nonlocal similarity pooling
			14.2.2.1 Producing the difference image
			14.2.2.2 Learning dictionary via affinity propagation
			14.2.2.3 Creating feature vectors via sparse coding and nonlocal similarity pooling
				14.2.2.3.1 Obtaining a change map by k-means clustering
			14.2.2.4 Experimental results
				14.2.2.4.1 Quantitative analysis
				14.2.2.4.2 Parameter selection
				14.2.2.4.3 Experiment results and analysis of the first three data sets
				14.2.2.4.4 Experiment results and analysis on the last two image pairs
				14.2.2.4.5 Results and analysis on simulated images
				14.2.2.4.6 Experiment for sparse representation
	References
15. Hyperspectral image processing based on sparse learning and sparse graph
	15.1 Hyperspectral image denoising based on hierarchical sparse learning
		15.1.1 Spatial-spectral data extraction
		15.1.2 Hierarchical sparse learning for denoising each band-subset
		15.1.3 Experimental results and discussion
			15.1.3.1 Experiment on simulated data
			15.1.3.2 Experiment on real data
				15.1.3.2.1 Denoising for urban data
				15.1.3.2.2 Experimental results on Indian Pines data
	15.2 Hyperspectral image restoration based on hierarchical sparse Bayesian learning
		15.2.1 Beta process
			15.2.1.1 Full hierarchical sparse Bayesian model
		15.2.2 Experimental results
			15.2.2.1 Denoising
			15.2.2.2 Predicting the missing data
			15.2.2.3 Discussion
	15.3 Hyperspectral image dimensionality reduction using a sparse graph
		15.3.1 Sparse representation
		15.3.2 Sparse graph-based dimensionality reduction
		15.3.3 Sparse graph learning
		15.3.4 Spatial-spectral clustering
		15.3.5 Experimental results
			15.3.5.1 Introduction of hyperspectral datasets
			15.3.5.2 Classification results
			15.3.5.3 Influence of spatial-spectral clustering
			15.3.5.4 Convergence analysis
	References
16. Nonconvex compressed sensing framework based on block strategy and overcomplete dictionary
	16.1 Introduction
	16.2 The block compressed sensing framework based on the overcomplete dictionary
		16.2.1 Block compressed sensing
		16.2.2 Overcomplete dictionary
		16.2.3 Structured compressed sensing model
	16.3 Image sparse representation based on the ridgelet overcomplete dictionary
	16.4 Structured reconstruction model
		16.4.1 Structural sparse prior based on image self-similarity
		16.4.2 Reconstruction model based on an estimation of the direction structure of image blocks
	16.5 Nonconvex reconstruction strategy
	References
17. Sparse representation combined with fuzzy C-means (FCM) in compressed sensing
	17.1 Basic introduction to fuzzy C-means (FCM) and sparse representation (SR)
	17.2 Two versions combining FCM with SR
		17.2.1 FDCM_SSR
		17.2.2 SL_FCM
	17.3 Experimental results
		17.3.1 FDCM_SSR
			17.3.1.1 UCI data set
			17.3.1.2 Artificial images
			17.3.1.3 Natural images
	17.4 SAR images
		17.4.1 SL_FCM
			17.4.1.1 Artificial and natural images
			17.4.1.2 Synthetic aperture radar images
	References
18. Compressed sensing by collaborative reconstruction
	18.1 Introduction
	18.2 Methods
		18.2.1 Block CS of images
		18.2.2 Collaborative reconstruction method based on an overcomplete dictionary
		18.2.3 Geometric structure-guided collaborative reconstruction method
	18.3 Experiment
		18.3.1 Collaborative reconstruction method based on an overcomplete dictionary
		18.3.2 Geometric structure-guided collaborative reconstruction method
	References
19. Hyperspectral image classification based on spectral information divergence and sparse representation
	19.1 The research status and challenges of hyperspectral image classification
		19.1.1 The research status of hyperspectral image classification
		19.1.2 The challenges of hyperspectral image classification
	19.2 Motivation
	19.3 Spectral information divergence (SID)
	19.4 Sparse representation classification method based on SID
	19.5 Joint sparse representation classification method based on SID
	19.6 Experimental results and analysis
		19.6.1 Comparison of the measurements
		19.6.2 Comparison of the performance of sparse representation classification methods
		19.6.3 Analysis of parameters
		19.6.4 The proof of convergence
	References
20. Neural network-based synthetic aperture radar image processing
	20.1 Discriminant deep belief network for SAR image classification
		20.1.1 Weak classifiers training
		20.1.2 Discriminative projection
		20.1.3 High-level discriminative feature learning
		20.1.4 Experiment and result
	20.2 Convolutional-wavelet neural network for SAR image segmentation
		20.2.1 Overall framework
		20.2.2 Experiment and result
	20.3 Deep neural network for SAR image registration
		20.3.1 Train deep neural network
		20.3.2 Predicting the matching label and eliminate the wrong matching points
		20.3.3 Experiment and result
	References
21. Neural networks-based polarimetric SAR image classification
	21.1 PolSAR decomposition
	21.2 Autoencoder for PolSAR image classification
		21.2.1 Data processing and feature learning
		21.2.2 Experiment and result
	21.3 DBN for PolSAR image classification
		21.3.1 DBN structure and feature learning
		21.3.2 Experiment and result
	21.4 Wishart deep stacking networks for PolSAR image classification
		21.4.1 Wishart distance and network structure
		21.4.2 Experiment and results
	References
22. Deep neural network models for hyperspectral images
	22.1 Deep fully convolutional network
		22.1.1 Fully convolutional networks
		22.1.2 Deep multiscale spatial distribution prediction via FCN-8s
		22.1.3 Spatial-spectral feature fusion and classification for HSI
		22.1.4 Experiment and results
	22.2 Recursive autoencoders
		22.2.1 Unsupervised RAE
		22.2.2 Experiments and results
	22.3 Superpixel-based multiple local CNN
		22.3.1 Multiple local regions joint representation CNN model
		22.3.2 Experiments and results
	References
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	X
	Y
	Z
15.1 Hyperspectral image denoising based on hierarchical sparse learning
	15.1.1 Spatial-spectral data extraction
	15.1.2 Hierarchical sparse learning for denoising each band-subset
	15.1.3 Experimental results and discussion
		15.1.3.1 Experiment on simulated data
		15.1.3.2 Experiment on real data
15.2 Hyperspectral image restoration based on hierarchical sparse Bayesian learning
	15.2.1 Beta process
		15.2.1.1 Full hierarchical sparse Bayesian model
	15.2.2 Experimental results
		15.2.2.1 Denoising
		15.2.2.2 Predicting the missing data
		15.2.2.3 Discussion
15.3 Hyperspectral image dimensionality reduction using a sparse graph
	15.3.1 Sparse representation
	15.3.2 Sparse graph-based dimensionality reduction
	15.3.3 Sparse graph learning
	15.3.4 Spatial-spectral clustering
	15.3.5 Experimental results
		15.3.5.1 Introduction of hyperspectral datasets
		15.3.5.2 Classification results
		15.3.5.3 Influence of spatial-spectral clustering
		15.3.5.4 Convergence analysis
References