The Experts below are selected from a list of 30075 Experts worldwide ranked by ideXlab platform
Feiping Nie - One of the best experts on this subject based on the ideXlab platform.
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local structured feature learning with dynamic maximum entropy graph
Pattern Recognition, 2021Co-Authors: Zheng Wang, Feiping Nie, Rong Wang, Hui YangAbstract:Abstract In recent years, Linear Discriminant Analysis (LDA) has seen huge adoption in data mining applications. Due to its globality, it is incompetent to handle multimodal data. Besides, most of LDA’s variants learn the Projection Matrix based on the pre-defined similarity Matrix, which is easily affected by noisy and irrelevant features. To address above two issues, a novel local structured feature learning with Dynamic Maximum Entropy Graph (DMEG) method is developed which firstly develops a more discriminative LDA with whitening constraint that can minimize the within-class scatter while keeping the total samples scatter unchanged simultaneously. Second, for exploring the local structure of data, the l0-norm constraint is imposed on similarity Matrix to ensure the k connectivity on graph. More importantly, proposed model learns the similarity and Projection Matrix simultaneously to ensure that the neighborships can be found in the optimal subspace where the noise have been removed already. Moreover, a maximum entropy regularization is employed to reinforce the discriminability of graph and avoid the trivial solution. Last but not least, an efficient iterative optimization algorithm is provided to optimize proposed model with a NP-hard constraint. Extensive experiments conducted on synthetic and several real-world data sets demonstrate the efficiency in classification task and robustness to noise of proposed method.
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simultaneously learning neighborship and Projection Matrix for supervised dimensionality reduction
IEEE Transactions on Neural Networks, 2019Co-Authors: Yanwei Pang, Bo Zhou, Feiping NieAbstract:Explicitly or implicitly, most dimensionality reduction methods need to determine which samples are neighbors and the similarities between the neighbors in the original high-dimensional space. The Projection Matrix is then learnt on the assumption that the neighborhood information, e.g., the similarities, are known and fixed prior to learning. However, it is difficult to precisely measure the intrinsic similarities of samples in high-dimensional space because of the curse of dimensionality. Consequently, the neighbors selected according to such similarities and the Projection Matrix obtained according to such similarities and the corresponding neighbors might not be optimal in the sense of classification and generalization. To overcome this drawback, in this paper, we propose to let the similarities and neighbors be variables and model these in a low-dimensional space. Both the optimal similarity and Projection Matrix are obtained by minimizing a unified objective function. Nonnegative and sum-to-one constraints on the similarity are adopted. Instead of empirically setting the regularization parameter, we treat it as a variable to be optimized. It is interesting that the optimal regularization parameter is adaptive to the neighbors in a low-dimensional space and has an intuitive meaning. Experimental results on the YALE B, COIL-100, and MNIST data sets demonstrate the effectiveness of the proposed method.
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rank k 2 d multinomial logistic regression for Matrix data classification
IEEE Transactions on Neural Networks, 2018Co-Authors: Kun Song, Feiping Nie, Junwei HanAbstract:The amount of Matrix data has increased rapidly nowadays. How to classify Matrix data efficiently is an important issue. In this paper, by discovering the shortages of 2-D linear discriminant analysis and 2-D logistic regression, a novel 2-D framework named rank- $k$ 2-D multinomial logistic regression (2DMLR-RK) is proposed. The 2DMLR-RK is designed for a multiclass Matrix classification problem. In the proposed framework, each category is modeled by a left Projection Matrix and a right Projection Matrix with rank $k$ . The left Projection matrices capture the row information of Matrix data, and the right Projection matrices acquire the column information. We identify the parameter $k$ plays the role of balancing the capacity of learning and generalization of the 2DMLR-RK. In addition, we develop an effective framework for solving the proposed nonconvex optimization problem. The convergence, initialization, and computational complexity are discussed. Extensive experiments on various types of data sets are conducted. Comparing with 1-D methods, 2DMLR-RK not only achieves a better classification accuracy, but also costs less computation time. Comparing with other state-of-the-art 2-D methods, the 2DMLR-RK achieves a better performance for Matrix data classification.
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flexible manifold learning with optimal graph for image and video representation
IEEE Transactions on Image Processing, 2018Co-Authors: Wei Wang, Feiping Nie, Yan Yan, Shuicheng Yan, Nicu SebeAbstract:Graph-based dimensionality reduction techniques have been widely and successfully applied to clustering and classification tasks. The basis of these algorithms is the constructed graph which dictates their performance. In general, the graph is defined by the input affinity Matrix. However, the affinity Matrix derived from the data is sometimes suboptimal for dimension reduction as the data used are very noisy. To address this issue, we propose the projective unsupervised flexible embedding models with optimal graph (PUFE-OG). We build an optimal graph by adjusting the affinity Matrix. To tackle the out-of-sample problem, we employ a linear regression term to learn a Projection Matrix. The optimal graph and the Projection Matrix are jointly learned by integrating the manifold regularizer and regression residual into a unified model. The experimental results on the public benchmark datasets demonstrate that the proposed PUFE-OG outperforms state-of-the-art methods.
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simultaneously learning neighborship and Projection Matrix for supervised dimensionality reduction
arXiv: Computer Vision and Pattern Recognition, 2017Co-Authors: Yanwei Pang, Bo Zhou, Feiping NieAbstract:Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The Projection Matrix is then learned on the assumption that the neighborhood information (e.g., the similarity) is known and fixed prior to learning. However, it is difficult to precisely measure the intrinsic similarity of samples in high-dimensional space because of the curse of dimensionality. Consequently, the neighbors selected according to such similarity might and the Projection Matrix obtained according to such similarity and neighbors are not optimal in the sense of classification and generalization. To overcome the drawbacks, in this paper we propose to let the similarity and neighbors be variables and model them in low-dimensional space. Both the optimal similarity and Projection Matrix are obtained by minimizing a unified objective function. Nonnegative and sum-to-one constraints on the similarity are adopted. Instead of empirically setting the regularization parameter, we treat it as a variable to be optimized. It is interesting that the optimal regularization parameter is adaptive to the neighbors in low-dimensional space and has intuitive meaning. Experimental results on the YALE B, COIL-100, and MNIST datasets demonstrate the effectiveness of the proposed method.
Xindong Wu - One of the best experts on this subject based on the ideXlab platform.
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Manifold elastic net: a unified framework for sparse dimension reduction
Data Mining and Knowledge Discovery, 2011Co-Authors: Tianyi Zhou, Xindong WuAbstract: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., Ann Stat 32(2):407–499, 2004), 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.
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Manifold elastic net: A unified framework for sparse dimension reduction
Data Mining and Knowledge Discovery, 2011Co-Authors: Tianyi Zhou, Dacheng Tao, Xindong WuAbstract: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.
Weishi Zheng - One of the best experts on this subject based on the ideXlab platform.
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Image to Video Person Re-Identification by Learning Heterogeneous Dictionary Pair With Feature Projection Matrix
IEEE Transactions on Information Forensics and Security, 2018Co-Authors: Xiaoyuan Jing, Shiguang Shan, Weishi ZhengAbstract:Person re-identification plays an important role in video surveillance and forensics applications. In many cases, person re-identification needs to be conducted between image and video clip, e.g., re-identifying a suspect from large quantities of pedestrian videos given a single image of the suspect. We call re-identification in this scenario as image to video person reidentification (IVPR). In practice, image and video are usually represented with different features, and there usually exist large variations between frames within each video. These factors make matching between image and video become a very challenging task. In this paper, we propose a joint feature Projection Matrix and heterogeneous dictionary pair learning (PHDL) approach for IVPR. Specifically, the PHDL jointly learns an intra-video Projection Matrix and a pair of heterogeneous image and video dictionaries. With the learned Projection Matrix, the influence caused by the variations within each video on the matching can be reduced. With the learned dictionary pair, the heterogeneous image and video features can be transformed into coding coefficients with the same dimension, such that the matching can be conducted by using the coding coefficients. Furthermore, to ensure that the obtained coding coefficients own favorable discriminability, the PHDL designs a point-to-set coefficient discriminant term. To make better use of the complementary spatial-temporal and visual appearance information contained in pedestrian video data, we further propose a multi-view PHDL approach, which can fuse different video information effectively in the dictionary learning process. Experiments on four publicly available person sequence data sets demonstrate the effectiveness of the proposed approaches.
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learning heterogeneous dictionary pair with feature Projection Matrix for pedestrian video retrieval via single query image
National Conference on Artificial Intelligence, 2017Co-Authors: Xiaoyuan Jing, Fei Wu, Yunhong Wang, Weishi ZhengAbstract:Person re-identification (re-id) plays an important role in video surveillance and forensics applications. In many cases, person re-id needs to be conducted between image and video clip, e.g., re-identifying a suspect from large quantities of pedestrian videos given a single image of him. We call re-id in this scenario as image to video person re-id (IVPR). In practice, image and video are usually represented with different features, and there usually exist large variations between frames within each video. These factors make matching between image and video become a very challenging task. In this paper, we propose a joint feature Projection Matrix and heterogeneous dictionary pair learning (PHDL) approach for IVPR. Specifically, PHDL jointly learns an intra-video Projection Matrix and a pair of heterogeneous image and video dictionaries. With the learned Projection Matrix, the influence of variations within each video to the matching can be reduced. With the learned dictionary pair, the heterogeneous image and video features can be transformed into coding coefficients with the same dimension, such that the matching can be conducted using coding coefficients. Furthermore, to ensure that the obtained coding coefficients have favorable discriminability, PHDL designs a point-to-set coefficient discriminant term. Experiments on the public iLIDS-VID and PRID 2011 datasets demonstrate the effectiveness of the proposed approach.
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learning heterogeneous dictionary pair with feature Projection Matrix for pedestrian video retrieval via single query image
National Conference on Artificial Intelligence, 2017Co-Authors: Xiaoke Zhu, Xiaoyuan Jing, Yunhong Wang, Wangmeng Zuo, Weishi ZhengAbstract:Person re-identification (re-id) plays an important role in video surveillance and forensics applications. In many cases, person re-id needs to be conducted between image and video clip, e.g., re-identifying a suspect from large quantities of pedestrian videos given a single image of him. We call re-id in this scenario as image to video person re-id (IVPR). In practice, image and video are usually represented with different features, and there usually exist large variations between frames within each video. These factors make matching between image and video become a very challenging task. In this paper, we propose a joint feature Projection Matrix and heterogeneous dictionary pair learning (PHDL) approach for IVPR. Specifically, PHDL jointly learns an intra-video Projection Matrix and a pair of heterogeneous image and video dictionaries. With the learned Projection Matrix, the influence of variations within each video to the matching can be reduced. With the learned dictionary pair, the heterogeneous image and video features can be transformed into coding coefficients with the same dimension, such that the matching can be conducted using coding coefficients. Furthermore, to ensure that the obtained coding coefficients have favorable discriminability, PHDL designs a point-to-set coefficient discriminant term. Experiments on the public iLIDS-VID and PRID 2011 datasets demonstrate the effectiveness of the proposed approach.
Huang Bai - One of the best experts on this subject based on the ideXlab platform.
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an efficient algorithm for designing Projection Matrix in compressive sensing based on alternating optimization
Signal Processing, 2016Co-Authors: Tao Hong, Huang Bai, Zhihui ZhuAbstract:This paper considers the problem of optimally designing the Projection Matrix ? for a certain class of signals which can be sparsely represented by a specified dictionary Ψ . The optimal Projection Matrix is proposed to minimize the distance between the Gram Matrix of the equivalent dictionary ? Ψ and a set of relaxed Equiangular Tight Frames (ETFs). An efficient method is derived for the optimal Projection Matrix design with a given Gram Matrix. In addition, an extension of Projection Matrix design is derived for the scenarios where the signals cannot be represented exactly sparse in a specified dictionary. Simulations with synthetic data and real images demonstrate that the obtained Projection Matrix significantly improves the signal recovery accuracy of a system and outperforms those obtained by the existing algorithms. HighlightsAn efficient method is derived for the optimal Projection Matrix with a target Gram Matrix.An innovated approach is developed to design the Projection Matrix when the signal is not exactly sparse.The simulations for natural images demonstrate the innovated approach can lead to a high PSNR.
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joint rank and positive semidefinite constrained optimization for Projection Matrix
Conference on Industrial Electronics and Applications, 2014Co-Authors: Huang Bai, Liping ChangAbstract:Sparse signals can be sensed with a reduced number of Projections and then reconstructed if compressive sensing is employed. Traditionally, the Projection Matrix is chosen as a random Matrix, but a Projection sensing Matrix that is optimally designed for a certain class of signals can further improve the reconstruction accuracy. This paper considers the problem of designing the Projection Matrix Φ for a compressive sensing system in which the dictionary Ψ is assumed to be given. A novel algorithm based on joint rank and positive semidefinite constrained optimization for optimal Projection Matrix searching is proposed. Simulation results reveal that the signal recovery performance of sensing Matrix obtained by proposed algorithm surpasses that of other standard sensing Matrix designs.
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on Projection Matrix optimization for compressive sensing systems
IEEE Transactions on Signal Processing, 2013Co-Authors: Zhihui Zhu, Liping Chang, Dehui Yang, Huang BaiAbstract:This paper considers the problem of designing the Projection Matrix $\Phi $ for a compressive sensing (CS) system in which the dictionary $\Psi $ is assumed to be given. The optimal Projection Matrix design is formulated in terms of finding those $\Phi $ such that the Frobenius norm of the difference between the Gram Matrix of the equivalent dictionary $\Phi \Psi $ and the identity Matrix is minimized. A class of the solutions is derived in a closed-form, which is a generalization of the existing results. More interestingly, it is revealed that this solution set is characterized by an arbitrary orthonormal Matrix. This freedom is then used to further enhance the performance of the CS system by minimizing the coherence between the atoms of the equivalent dictionary. An alternating minimization-based algorithm is proposed for solving the corresponding minimization problem. Experiments are carried out and simulations show that the Projection Matrix obtained by the proposed approach significantly improves the signal recovery accuracy of the CS system and outperforms those by existing algorithms.
Zhihui Zhu - One of the best experts on this subject based on the ideXlab platform.
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an efficient method for robust Projection Matrix design
arXiv: Learning, 2016Co-Authors: Tao Hong, Zhihui ZhuAbstract:Our objective is to efficiently design a robust Projection Matrix $\Phi$ for the Compressive Sensing (CS) systems when applied to the signals that are not exactly sparse. The optimal Projection Matrix is obtained by mainly minimizing the average coherence of the equivalent dictionary. In order to drop the requirement of the sparse representation error (SRE) for a set of training data as in [15] [16], we introduce a novel penalty function independent of a particular SRE Matrix. Without requiring of training data, we can efficiently design the robust Projection Matrix and apply it for most of CS systems, like a CS system for image processing with a conventional wavelet dictionary in which the SRE Matrix is generally not available. Simulation results demonstrate the efficiency and effectiveness of the proposed approach compared with the state-of-the-art methods. In addition, we experimentally demonstrate with natural images that under similar compression rate, a CS system with a learned dictionary in high dimensions outperforms the one in low dimensions in terms of reconstruction accuracy. This together with the fact that our proposed method can efficiently work in high dimension suggests that a CS system can be potentially implemented beyond the small patches in sparsity-based image processing.
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an efficient algorithm for designing Projection Matrix in compressive sensing based on alternating optimization
Signal Processing, 2016Co-Authors: Tao Hong, Huang Bai, Zhihui ZhuAbstract:This paper considers the problem of optimally designing the Projection Matrix ? for a certain class of signals which can be sparsely represented by a specified dictionary Ψ . The optimal Projection Matrix is proposed to minimize the distance between the Gram Matrix of the equivalent dictionary ? Ψ and a set of relaxed Equiangular Tight Frames (ETFs). An efficient method is derived for the optimal Projection Matrix design with a given Gram Matrix. In addition, an extension of Projection Matrix design is derived for the scenarios where the signals cannot be represented exactly sparse in a specified dictionary. Simulations with synthetic data and real images demonstrate that the obtained Projection Matrix significantly improves the signal recovery accuracy of a system and outperforms those obtained by the existing algorithms. HighlightsAn efficient method is derived for the optimal Projection Matrix with a target Gram Matrix.An innovated approach is developed to design the Projection Matrix when the signal is not exactly sparse.The simulations for natural images demonstrate the innovated approach can lead to a high PSNR.
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on Projection Matrix optimization for compressive sensing systems
IEEE Transactions on Signal Processing, 2013Co-Authors: Zhihui Zhu, Liping Chang, Dehui Yang, Huang BaiAbstract:This paper considers the problem of designing the Projection Matrix $\Phi $ for a compressive sensing (CS) system in which the dictionary $\Psi $ is assumed to be given. The optimal Projection Matrix design is formulated in terms of finding those $\Phi $ such that the Frobenius norm of the difference between the Gram Matrix of the equivalent dictionary $\Phi \Psi $ and the identity Matrix is minimized. A class of the solutions is derived in a closed-form, which is a generalization of the existing results. More interestingly, it is revealed that this solution set is characterized by an arbitrary orthonormal Matrix. This freedom is then used to further enhance the performance of the CS system by minimizing the coherence between the atoms of the equivalent dictionary. An alternating minimization-based algorithm is proposed for solving the corresponding minimization problem. Experiments are carried out and simulations show that the Projection Matrix obtained by the proposed approach significantly improves the signal recovery accuracy of the CS system and outperforms those by existing algorithms.
