Recently, the mathematical tool from fractal geometry (i.e., fractal dimension) has been employed to investigate optimization trajectory-dependent generalization ability for some pointwise learning models with independent and identically distributed (i.i.d.) observations. This paper goes beyond the limitations of pointwise learning and i.i.d. samples, and establishes generalization bounds for pairwise learning with uniformly strong mixing samples. The derived theoretical results fill the gap of trajectory-dependent generalization analysis for pairwise learning, and can be applied to wide learning paradigms, e.g., metric learning, ranking and gradient learning. Technically, our framework brings concentration estimation with Rademacher complexity and trajectory-dependent fractal dimension together in a coherent way for felicitous learning theory analysis. In addition, the efficient computation of fractal dimension can be guaranteed for random algorithms (e.g., stochastic gradient descent algorithm for deep neural networks) by bridging topological data analysis tools and the trajectory-dependent fractal dimension.

Recent years have witnessed an explosion of Multi- view Subspace Classification (MSCla) and Multi-view Subspace Clustering (MSClu) methods for various applications. However, their theoretical foundation have not been well explored and understood. In this paper, we investigate the multi-view subspace-preserving recovery theory, which is the theoretical underpinnings for MSCla and MSClu methods. Specifically, we derive novel geometrically interpretable conditions for the success of multi-view subspace-preserving recovery. Compared with prior related works, we make the following innovations: First, our theory does not require the equality constraint, which is a common requirement in prior theoretical works and may be too restrictive in reality. Second, we provide both Individual Theoretical Guarantee (ITG) and Universal Theoretical Guarantee (UTG) for multi-view subspace-preserving recovery while prior works only give the UTG. Third, we also apply the proposed theory to establish theoretical guarantees for MSCla and MSClu, respectively. Numerical results validate the proposed theory for multi-view subspace-preserving recovery.

Learning discriminative 3D representations that generalize well to unknown testing categories is an emerging requirement for many real-world 3D applications. Existing well-established methods often struggle to attain this goal due to insufficient 3D training data from broader concepts. Meanwhile, pre-trained large vision-language models (e.g., CLIP) have shown remarkable zero-shot generalization capabilities. Yet, they are limited in extracting suitable 3D representations due to substantial gaps between their 2D training and 3D testing distributions. To address these challenges, we propose Testing-time Distribution Alignment (TeDA), a novel framework that adapts a pretrained 2D vision-language model CLIP for unknown 3D object retrieval at test time. To our knowledge, it is the first work that studies the test-time adaptation of a vision-language model for 3D feature learning. TeDA projects 3D objects into multi-view images, extracts features using CLIP, and refines 3D query embeddings with an iterative optimization strategy by confident query-target sample pairs in a self-boosting manner. Additionally, TeDA integrates textual descriptions generated by a multimodal language model (InternVL) to enhance 3D object understanding, leveraging CLIP's aligned feature space to fuse visual and textual cues. Extensive experiments on four open-set 3D object retrieval benchmarks demonstrate that TeDA greatly outperforms state-of-the-art methods, even those requiring extensive training. We also experimented with depth maps on Objaverse-LVIS, further validating its effectiveness. Code is available at https://github.com/wangzhichuan123/TeDA.

Open-set 3D object retrieval (3DOR) aims to learn discriminative and generalizable embeddings for unseen categories of 3D objects. However, attaining this objective typically requires the costly acquisition of large-scale 3D object datasets and associated resources for model training. Building upon the strong open-world representation capabilities of CLIP, we introduce CLIP-AdaM, which, to our knowledge, represents the first attempt to adapt a CLIP model for open-set 3DOR with minimal effort. We first find that a pretrained CLIP already delivers a surprisingly acceptable performance on multi-view images. To further unleash its potential, we design a customized adapter for learning to aggregate and adapt its pretrained features towards better 3D embeddings. For aggregation, it learns two sets of view scores to weigh the contributions of view images for fusion. One is learned by a tiny view-score network at the instance level, and the other is learned implicitly at the dataset level, aiding generalization to unseen categories. The adaptation component comprises only a basic linear layer yet yields superior results. During training, the adapter with such a small amount of parameters can be efficiently fine-tuned with limited 3D closed-set data, effectively mitigating the overfitting issue while harnessing the prior knowledge from pretrained models. Without bells and whistles, CLIP-AdaM attains state-of-the-art performance on four open-set 3DOR benchmarks. Additionally, it demonstrates strong extensibility to broader scenarios, including zero-shot, few-shot, and seen/unseen 3D representation learning.

Numerous representation-based classification (RC) methods have been developed for face recognition due to their decent model interpretability and robustness against noise. Most existing RC methods primarily characterize the gray-scale reconstruction error image (single-channel data) in two ways: the one-dimensional (1D) pixel-based error model and the two-dimensional (2D) gray-scale image-matrix-based error model. The former measures the reconstruction error pixel by pixel, while the latter leverages 2D structural information of the gray-scale error image, such as the low-rank property. However, when applying these methods to different color channels of a test color face image (multi-channel data) separately and independently, they neglect the three-dimensional (3D) structural correlations among distinct color channels. In real-world scenarios, face images are often contaminated with complex noise, including contiguous occlusion and random pixel corruption, which pose significant challenges to these approaches and can lead to a decline in performance. In this paper, we propose a Tensor Nuclear Norm based Robust Multi-channel Atomic Representation (TNN-RMAR) framework with application to color face recognition. The proposed method has the following three critical ingredients: 1) We propose a 3D color image-tensor-based error model, which can take full advantage of the 3D structural information of the color error image. 2) To leverage the 3D structural information of the color error image, we model it as a 3-order tensor and exploit its low-rank property with the tensor nuclear norm. Given that multiple color channels in a color image are generally corrupted at the same positions, we design a tube-wise tailored loss function to further leverage its tube-wise structure. 3) We devise the multi-channel atomic norm (MAN) regularization for the representation coefficient matrix, which allows us to jointly harness the correlation information of coefficients in different color channels. In addition, we also devise an efficient algorithm to solve the TNN-RMAR framework based on the alternating direction method of multipliers (ADMM) framework. By leveraging TNN-RMAR as a general platform, we also develop several novel robust multi-channel RC methods. Experimental results on benchmark real-world databases validate the effectiveness and robustness of the proposed framework for robust color face recognition.

This paper proposes a unified Superposed Atomic Representation (SAR) framework for high-dimensional data recovery with multiple low-dimensional structures. The data can be in various forms ranging from vectors to tensors. The goal of SAR is to recover different components from their sum, where each component has a low-dimensional structure, such as sparsity, low-rankness or be lying a low-dimensional subspace. Examples of SAR include, but not limited to, Robust Sparse Representation (RSR), Robust Principal Component Analysis (RPCA), Tensor RPCA (TRPCA), and Outlier Pursuit (OP). We establish the theoretical guarantee for SAR. To further improve SAR, we also develop a Weighted SAR (WSAR) framework by paying more attention and penalizing less on significant atoms of each component. An effective optimization algorithm is devised for WSAR and the convergence of the algorithm is rigorously proved. By leveraging WSAR as a general platform, several new methods are proposed for high-dimensional data recovery. The experiments on real data demonstrate the superiority of WSAR for various data recovery problems.

Vertical Federated Learning (VFL) has garnered significant attention due to its applicability in multi-party collaborative learning and the increasing demand for privacy-preserving measures. Most existing VFL algorithms primarily focus on accuracy as the training model metric. However, the data we access is often imbalanced in the real world, making it difficult for models based on accuracy to correctly classify minority samples. The Area Under the Curve (AUC) serves as an effective metric to evaluate the performance of a model on imbalanced data. Therefore, optimizing AUC can enhance the model's ability to handle imbalanced data. Besides, computational resources within VFL systems are also imbalanced, which makes synchronous VFL algorithms are difficult to apply in the real world. To address the double imbalance issue, we propose Asynchronous Vertical Federated Kernelized AUC Maximization (AVFKAM). Specifically, AVFKAM asynchronously updates a kernel model based on triply stochastic gradients with respect to (w.r.t.) the pairwise loss and random feature approximation. To facilitate theoretical analysis, we transfer the asynchrony of model coefficients to the functional gradient through a dual relationship between coefficients and objective function. Furthermore, we demonstrate that AVFKAM converges to the optimal solution at a rate of O(1/t), where t represents the global iteration number, and discuss the security of the model. If t is denoted as the global iteration number, we provide that it converges to the optimal solution with the rate of O(1/t). Finally, experimental results on various benchmark datasets demonstrate that AVFKAM maintains high AUC performance and efficiency.

Tensor Robust Principal Component Analysis (TRPCA), which aims to recover the low-rank and sparse components from their sum, has drawn intensive interest in recent years. Most existing TRPCA methods adopt the tensor nuclear norm (TNN) and the tensor ℓ1 norm as the regularization terms for the low-rank and sparse components, respectively. However, TNN treats each singular value of the low-rank tensor L equally and the tensor ℓ1 norm shrinks each entry of the sparse tensor S with the same strength. It has been shown that larger singular values generally correspond to prominent information of the data and should be less penalized. The same goes for large entries in S in terms of absolute values. In this paper, we propose a Double Auto-weighted TRPCA (DATRPCA) method. Instead of using predefined and manually set weights merely for the low-rank tensor as previous works, DATRPCA automatically and adaptively assigns smaller weights and applies lighter penalization to significant singular values of the low-rank tensor and large entries of the sparse tensorsimultaneously. We have further developed an efficient algorithm to implement DATRPCA based on the Alternating Direction Method of Multipliers (ADMM) framework. In addition, we have also established the convergence analysis of the proposed algorithm. The results on both synthetic and real-world data demonstrate the effectiveness of DATRPCA for low-rank tensor recovery, color image recovery and background modelling.

Recently, the scheme of model-X knockoffs was proposed as a promising solution to address controlled feature selection under high-dimensional finite-sample settings. However, the procedure of model-X knockoffs depends heavily on the coefficient-based feature importance and only concerns the control of false discovery rate (FDR). To further improve its adaptivity and flexibility, in this paper, we propose an error-based knockoff inference method by integrating the knockoff features, the error-based feature importance statistics, and the stepdown procedure together. The proposed inference procedure does not require specifying a regression model and can handle feature selection with theoretical guarantees on controlling false discovery proportion (FDP), FDR, or k-familywise error rate (k-FWER). Empirical evaluations demonstrate the competitive performance of our approach on both simulated and real data.

This article presents a generalized collaborative representation-based classification (GCRC) framework, which includes many existing representation-based classification (RC) methods, such as collaborative RC (CRC) and sparse RC (SRC) as special cases. This article also advances the GCRC theory by exploring theoretical conditions on the general regularization matrix. A key drawback of CRC and SRC is that they fail to use the label information of training data and are essentially unsupervised in computing the representation vector. This largely compromises the discriminative ability of the learned representation vector and impedes the classification performance. Guided by the GCRC theory, we propose a novel RC method referred to as discriminative RC (DRC). The proposed DRC method has the following three desirable properties: 1) discriminability: DRC can leverage the label information of training data and is supervised in both representation and classification, thus improving the discriminative ability of the representation vector; 2) efficiency: it has a closed-form solution and is efficient in computing the representation vector and performing classification; and 3) theory: it also has theoretical guarantees for classification. Experimental results on benchmark databases demonstrate both the efficacy and efficiency of DRC for multiclass classification.

Sparse representation has achieved great success across various fields including signal processing, machine learning and computer vision. However, most existing sparse representation methods are confined to the real valued data. This largely limit their applicability to the quaternion valued data, which has been widely used in numerous applications such as color image processing. Another critical issue is that their performance may be severely hampered due to the data noise or outliers in practice. To tackle the problems above, in this work we propose a robust quaternion valued sparse representation (RQVSR) method in a fully quaternion valued setting. To handle the quaternion noises, we first define a new robust estimator referred as quaternion Welsch estimator to measure the quaternion residual error. Compared to the conventional quaternion mean square error, it can largely suppress the impact of large data corruption and outliers. To implement RQVSR, we have overcome the difficulties raised by the noncommutativity of quaternion multiplication and developed an effective algorithm by leveraging the half-quadratic theory and the alternating direction method of multipliers framework. The experimental results show the effectiveness and robustness of the proposed method for quaternion sparse signal recovery and color image reconstruction.

Representation-based classification (RC) methods, such as sparse RC, have shown great potential in face recognition (FR) in recent years. Most previous RC methods are based on the conventional regression models, such as lasso regression, ridge regression, or group lasso regression. These regression models essentially impose a predefined assumption on the distribution of the noise variable in the query sample, such as the Gaussian or Laplacian distribution. However, the complicated noises in practice may violate the assumptions and impede the performance of these RC methods. In this paper, we propose a modal regression (MR)-based atomic representation and classification (MRARC) framework to alleviate such limitations. MR is a robust regression framework which aims to reveal the relationship between the input and response variables by regressing toward the conditional mode function. Atomic representation is a general atomic norm regularized linear representation framework which includes many popular representation methods, such as sparse representation, collaborative representation, and low-rank representation as special cases. Unlike previous RC methods, the MRARC framework does not require the noise variable to follow any specific predefined distributions. This gives rise to the capability of MRARC in handling various complex noises in reality. Using MRARC as a general platform, we also develop four novel RC methods for unimodal and multimodal FR, respectively. In addition, we devise a general optimization algorithm for the unified MRARC framework based on the alternating direction method of multipliers and half-quadratic theory. The experiments on real-world data validate the efficacy of MRARC for robust FR and reconstruction.

Collecting labeled samples is quite costly and time-consuming for hyperspectral image (HSI) classification task. Semisupervised learning framework, which combines the intrinsic information of labeled and unlabeled samples, can alleviate the deficient labeled samples and increase the accuracy of HSI classification. In this letter, we propose a novel semisupervised learning framework that is based on spectral-spatial graph convolutional networks (S2GCNs). It explicitly utilizes the adjacency nodes in graph to approximate the convolution. In the process of approximate convolution on graph, the proposed method makes full use of the spatial information of the current pixel. The experimental results on three real-life HSI data sets, i.e., Botswana Hyperion, Kennedy Space Center, and Indian Pines, show that the proposed S2GCN can significantly improve the classification accuracy. For instance, the overall accuracy on Indian data is increased from 66.8% (GCN) to 91.6%.

Representation-based classification (RC) methods such as sparse RC (SRC) have attracted great interest in pattern recognition recently. Despite their empirical success, few theoretical results are reported to justify their effectiveness. In this paper, we establish the theoretical guarantees for a general unified framework termed as atomic representation-based classification (ARC), which includes most RC methods as special cases. We introduce a new condition called atomic classification condition (ACC), which reveals important geometric insights for the theory of ARC. We show that under such condition ARC is provably effective in correctly recognizing any new test sample, even corrupted with noise. Our theoretical analysis significantly broadens the range of conditions under which RC methods succeed for classification in the following two aspects: (1) prior theoretical advances of RC are mainly concerned with the single SRC method while our theory can apply to the general unified ARC framework, including SRC and many other RC methods; and (2) previous works are confined to the analysis of noiseless test data while we provide theoretical guarantees for ARC using both noiseless and noisy test data. Numerical results are provided to validate and complement our theoretical analysis of ARC and its important special cases for both noiseless and noisy test data.

Various greedy algorithms have been developed for sparse signal recovery in recent years. However, most of them utilize the l2 norm based loss function and sensitive to non-Gaussian noises and outliers. This paper proposes a Cauchy matching pursuit (CauchyMP) algorithm for robust sparse representation and classification. By leveraging a Cauchy estimator based loss function, the proposed approach can robustly learn the sparse representation of noisy data corrupted by various severe noises. As a greedy algorithm, CauchyMP is also computationally efficient. We also develop a CauchyMP based classifier for robust classification with application to face recognition. The experiments on the datasets with gross corruptions demonstrate the efficacy and robustness of CauchyMP for learning robust sparse representation.

Big data research has become a globally hot topic in recent years. One of the core problems in big data learning is how to extract effective information from the huge data. In this paper, we propose a Markov resampling algorithm to draw useful samples for handling coefficient-based regularized regression (CBRR) problem. The proposed Markov resampling algorithm is a selective sampling method, which can automatically select uniformly ergodic Markov chain (u.e.M.c.) samples according to transition probabilities. Based on u.e.M.c. samples, we analyze the theoretical performance of CBRR algorithm and generalize the existing results on independent and identically distributed observations. To be specific, when the kernel is infinitely differentiable, the learning rate depending on the sample size $m$ can be arbitrarily close to $\mathcal {O}(m^{-1})$ under a mild regularity condition on the regression function. The good generalization ability of the proposed method is validated by experiments on simulated and real data sets.

Matrix factorization is a popular low dimensional representation approach that plays an important role in many pattern recognition and computer vision domains. Among them, convex and semi-nonnegative matrix factorizations have attracted considerable interest, owing to its clustering interpretation. On the other hand, the generalized correlation function (correntropy) as the error measure does not depend on the assumption of Gaussianity, which the mean square error (MSE) heavily depends on. In this paper, we propose two novel algorithms, called Maximum Correntropy Criterion based Convex and Semi-Nonnegative Matrix Factorization (MCC-ConvexNMF, MCC-SemiNMF). Compared with the mean square error based convex and semi-nonnegative matrix factorization, the proposed methods can extract more information from the data and produce more accurate solutions. Experimental results on both synthetic dataset and the popular face database illustrate the effectiveness of our methods.

Owing to its simplicity and efficacy, orthogonal matching pursuit (OMP) has been a popular sparse representation method for compressed sensing and pattern classification. As a recent extension of OMP, generalized OMP (GOMP) improves the efficiency of OMP by identifying multiple atoms each iteration. Nonetheless, GOMP utilizes the mean square error (MSE) criterion as the loss function, which has been proven to rely on the Gaussianity assumption of the noise distribution and sensitive to non-Gaussian noise. In this paper, we propose a robust sparse representation method, called information-theoretic generalized OMP (ITGOMP), to reduce the limitation of GOMP. The key idea is to minimize the correntropy based information-theoretic loss function, which is independent of the noise distribution. We also devise a half-quadratic based algorithm to tackle the optimization problem. Finally, an ITGOMP based classifier is developed for robust pattern classification. The experiments on public real-world databases verify the effectiveness and robustness of the proposed method for classification.

As an efficient sparse representation algorithm, orthogonal matching pursuit (OMP) has attracted massive attention in recent years. However, OMP and most of its variants estimate the sparse vector using the mean square error criterion, which depends on the Gaussianity assumption of the error distribution. A violation of this assumption, e.g., non-Gaussian noise, may lead to performance degradation. In this paper, a correntropy matching pursuit (CMP) method is proposed to alleviate this problem of OMP. Unlike many other matching pursuit methods, our method is independent of the error distribution. We show that CMP can adaptively assign small weights on severely corrupted entries of data and large weights on clean ones, thus reducing the effect of large noise. Our another contribution is to develop a robust sparse representation-based recognition method based on CMP. Experiments on synthetic and real data show the effectiveness of our method for both sparse approximation and pattern recognition, especially for noisy, corrupted, and incomplete data.

Representation-based classifiers (RCs) including sparse RC (SRC) have attracted intensive interest in pattern recognition in recent years. In our previous work, we have proposed a general framework called atomic representation-based classifier (ARC) including many popular RCs as special cases. Despite the empirical success, ARC and conventional RCs utilize the mean square error (MSE) criterion and assign the same weights to all entries of the test data, including both severely corrupted and clean ones. This makes ARC sensitive to the entries with large noise and outliers. In this work, we propose an information-theoretic ARC (ITARC) framework to alleviate such limitation of ARC. Using ITARC as a general platform, we develop three novel representation-based classifiers. The experiments on public real-world datasets demonstrate the efficacy of ITARC for robust pattern recognition.

A improved swarm optimization method based on particle swarm optimization (PSO) and simplified swarm optimization (SSO) is proposed to adjust the weight in artificial neural network. This method is a modification of traditional PSO and SSO, and combines them to a new optimization method (PSOSSO for short). The proposed method overcomes some of the drawbacks of SSO and improves its ability to train the weight of ANN. In the experiments, the PSOSSO is employed to train fuzzy wavelet neural network (FWNN) forecasting model to predict the prices of Hong Kong Hang Seng Index. The experimental results present that the PSOSSO is more efficient than traditional PSO and SSO methods.

A novel approach called Spectral-Spatial 1-D Manifold Embedding (SS1DME) is proposed in this paper for remotely sensed hyperspectral image (HSI) classification. This novel approach is based on a generalization of the recently developed smooth ordering model, which has gathered a great interest in the image processing area. In the proposed approach, first, we employ the spectral-spatial information-based affinity metric to learn the similarity of HSI pixels, where the contextual information is encoded into the affinity metric using spatial information. In our derived model, based on the obtained affinity metric, the created multiple 1-D manifold embeddings (1DMEs) consist of several different versions of 1DME of the same set of all HSI points. Since each 1DME of the data is a 1-D sequence, a label function on the data can be obtained by applying the simple 1-D signal processing tools (such as interpolation/regression). By collecting the predicted labels from these label functions, we build a subset of the current unlabeled points, on which the labels are correctly labeled with high confidence. Next, we add a proportion of the elements from this subset to the original labeled set to get the updated labeled set, which is used for the next running instance. Repeating this process for several loops, we get an extended labeled set, where the new members are correctly labeled by the label functions with much high confidence. Finally, we utilize the extended labeled set to build the target classifier for the whole HSI pixels. In the whole process, 1DME plays the role of learning data features from the given affinity metric. With the incrementation of learning features during iteration, the proposed scheme will gradually approximate the exact labels of all sample points. The proposed scheme is experimentally demonstrated using four real HSI data sets, exhibiting promising classification performance when compared with other recently introduced spatial analysis alternatives.

Collaborative representation-based classification (CRC) and sparse RC (SRC) have recently achieved great success in face recognition (FR). Previous CRC and SRC are originally designed in the real setting for grayscale image-based FR. They separately represent the color channels of a query color image and ignore the structural correlation information among the color channels. To remedy this limitation, in this paper, we propose two novel RC methods for color FR, namely, quaternion CRC (QCRC) and quaternion SRC (QSRC) using quaternion ℓ1minimization. By modeling each color image as a quaternionic signal, they naturally preserve the color structures of both query and gallery color images while uniformly coding the query channel images in a holistic manner. Despite the empirical success of CRC and SRC on FR, a few theoretical results are developed to guarantee their effectiveness. Another purpose of this paper is to establish the theoretical guarantee for QCRC and QSRC under mild conditions. Comparisons with competing methods on benchmark real-world databases consistently show the superiority of the proposed methods for both color FR and reconstruction.

Recently, a large family of representation-based classification methods have been proposed and attracted great interest in pattern recognition and computer vision. This paper presents a general framework, termed as atomic representation-based classifier (ARC), to systematically unify many of them. By defining different atomic sets, most popular representation-based classifiers (RCs) follow ARC as special cases. Despite good performance, most RCs treat test samples separately and fail to consider the correlation between the test samples. In this paper, we develop a structural ARC (SARC) based on Bayesian analysis and generalizing a Markov random field-based multilevel logistic prior. The proposed SARC can utilize the structural information among the test data to further improve the performance of every RC belonging to the ARC framework. The experimental results on both synthetic and real-database demonstrate the effectiveness of the proposed framework.

Representation-based classifiers (RCs) have attracted considerable attention in face recognition in recent years. However, most existing RCs use the mean square error (MSE) criterion as the cost function, which relies on the Gaussianity assumption of the error distribution and is sensitive to non-Gaussian noise. This may severely degrade the performance of MSE-based RCs in recognizing facial images with random occlusion and corruption. In this paper, we present a minimum error entropy-based atomic representation (MEEAR) framework for face recognition. Unlike existing MSE-based RCs, our framework is based on the minimum error entropy criterion, which is not dependent on the error distribution and shown to be more robust to noise. In particular, MEEAR can produce discriminative representation vector by minimizing the atomic norm regularized Renyi's entropy of the reconstruction error. The optimality conditions are provided for general atomic representation model. As a general framework, MEEAR can also be used as a platform to develop new classifiers. Two effective MEE-based RCs are proposed by defining appropriate atomic sets. The experimental results on popular face databases show that MEEAR can improve both the recognition accuracy and the reconstructed results compared with the state-of-the-art MSE-based RCs.

Protein retrieval is a difficult task and has become a hot issue recently due to the complex structure and large data size of proteins. This work helps biologists investigate the link between structure and function of a protein in a deeper level and can be used in lots of biomedical applications. The retrieval system gives scores to all proteins in the database, e.g. SCOP or PDB, by given a query protein to compare with them. In this paper, we propose a novel algorithm based on sparse coding to retrieve proteins in the database using tableau representation. Both unsupervised and supervised methods are studied in the proposed algorithm where the sparse coefficient is regarded as similarity measurement. Experiments are conducted on ASTRAL 1.73 95% database and show that the proposed algorithms can improve the original feature extraction method which only uses cosine similarity.

This paper presents a novel spectral-spatial destriping method for hyperspectral images. The ubiquitous striping noise in hyperspectral images might degrade the quality of the imagery and bring difficulties in hyperspectral data processing. Although numerous methods have been proposed for striping noise reduction recently, most of them fail to consider the spectral correlation and spatial information of the hyperspectral images simultaneously. In order to remedy this drawback, the proposed method integrates the spectral and spatial information to remove the striping noise in the hyperspectral images. To this end, firstly, the low-rank representation (LRR) is used to take advantage of the spectral information. Then, the spatial information is included using a Huber-Markov random field (MRF) prior model, which is convex and can well preserve the edge and texture information while removing the noise. The experimental results on simulated and real hyperspectral data sets demonstrate the effectiveness of the proposed method.

It is a significant issue to find similar proteins from a large scale of protein database efficiently. This paper presents a new algorithm of protein sequence which is based on fractal dimension and wavelet transform. A hybrid method consisting fractal dimension calculation, discrete wavelet transform and sliding window are applied to generate a new encoding feature. Through the computation between the feature vectors, we can obtain the distance matrix and the phylogenic tree can be constructed.We apply this approach by analyzing the ND5 (NADH dehydrogenase subunit 5) protein dataset. The experimental results show that the proposed model is more accurate than the existing ones such as Su's model, Zhang's model and Yao's model, and it is consistent with the result generated from MEGA software and some known facts.

Feature extraction is a promising technique for hyperspectral image classification. Recent research has shown that the criterion of sparse representation classification (SRC) can help to design a feature extraction method. This method is called the SRC steered discriminative projection (SRCDP). Motivated by the fact that kernel trick can exploit the nonlinear case of features, this paper generalizes SRCDP to its kernel case named KSRCDP. Extensive experiments show that KSRCDP can obtain excellent classification performance on two classic hyperspectral images.