Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Joint & Progressive Learning from High-Dimensional Data for Multi-Label Classification

Despite the fact that nonlinear subspace learning techniques (e.g. manifold learning) have successfully applied to data representation, there is still room for improvement in explainability (explicit mapping), generalization (out-of-samples), and cost-effectiveness (linearization). To this end, a novel linearized subspace learning technique is developed in a joint and progressive way, called \textbf{j}oint and \textbf{p}rogressive \textbf{l}earning str\textbf{a}teg\textbf{y} (J-Play), with its application to multi-label classification. The J-Play learns high-level and semantically meaningful feature representation from high-dimensional data by 1) jointly performing multiple subspace learning and classification to find a latent subspace where samples are expected to be better classified; 2) progressively learning multi-coupled projections to linearly approach the optimal mapping bridging the original space with the most discriminative subspace; 3) locally embedding manifold structure in each learnable latent subspace. Extensive experiments are performed to demonstrate the superiority and effectiveness of the proposed method in comparison with previous state-of-the-art methods.Comment: accepted in ECCV 201

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

HB-PLS: A statistical method for identifying biological process or pathway regulators by integrating Huber loss and Berhu penalty with partial least squares regression

Gene expression data features high dimensionality, multicollinearity, and non-Gaussian distribution noise, posing hurdles for identification of true regulatory genes controlling a biological process or pathway. In this study, we integrated the Huber loss function and the Berhu penalty (HB) into partial least squares (PLS) framework to deal with the high dimension and multicollinearity property of gene expression data, and developed a new method called HB-PLS regression to model the relationships between regulatory genes and pathway genes. To solve the Huber-Berhu optimization problem, an accelerated proximal gradient descent algorithm with at least 10 times faster than the general convex optimization solver (CVX), was developed. Application of HB-PLS to recognize pathway regulators of lignin biosynthesis and photosynthesis in Arabidopsis thaliana led to the identification of many known positive pathway regulators that had previously been experimentally validated. As compared to sparse partial least squares (SPLS) regression, an efficient method for variable selection and dimension reduction in handling multicollinearity, HB-PLS has higher efficacy in identifying more positive known regulators, a much higher but slightly less sensitivity/(1-specificity) in ranking the true positive known regulators to the top of the output regulatory gene lists for the two aforementioned pathways. In addition, each method could identify some unique regulators that cannot be identified by the other methods. Our results showed that the overall performance of HB-PLS slightly exceeds that of SPLS but both methods are instrumental for identifying real pathway regulators from high-throughput gene expression data, suggesting that integration of statistics, machine leaning and convex optimization can result in a method with high efficacy and is worth further exploration

Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure

Enhancing Domain Word Embedding via Latent Semantic Imputation

We present a novel method named Latent Semantic Imputation (LSI) to transfer external knowledge into semantic space for enhancing word embedding. The method integrates graph theory to extract the latent manifold structure of the entities in the affinity space and leverages non-negative least squares with standard simplex constraints and power iteration method to derive spectral embeddings. It provides an effective and efficient approach to combining entity representations defined in different Euclidean spaces. Specifically, our approach generates and imputes reliable embedding vectors for low-frequency words in the semantic space and benefits downstream language tasks that depend on word embedding. We conduct comprehensive experiments on a carefully designed classification problem and language modeling and demonstrate the superiority of the enhanced embedding via LSI over several well-known benchmark embeddings. We also confirm the consistency of the results under different parameter settings of our method.Comment: ACM SIGKDD 201