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Xindong Wu - One of the best experts on this subject based on the ideXlab platform.

  • Manifold elastic net: a unified framework for sparse dimension reduction
    Data Mining and Knowledge Discovery, 2011
    Co-Authors: Tianyi Zhou, Xindong Wu
    Abstract:

    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.

  • Manifold elastic net: A unified framework for sparse dimension reduction
    Data Mining and Knowledge Discovery, 2011
    Co-Authors: Tianyi Zhou, Dacheng Tao, Xindong Wu
    Abstract:

    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.

Tianyi Zhou - One of the best experts on this subject based on the ideXlab platform.

  • Manifold elastic net: a unified framework for sparse dimension reduction
    Data Mining and Knowledge Discovery, 2011
    Co-Authors: Tianyi Zhou, Xindong Wu
    Abstract:

    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.

  • Manifold elastic net: A unified framework for sparse dimension reduction
    Data Mining and Knowledge Discovery, 2011
    Co-Authors: Tianyi Zhou, Dacheng Tao, Xindong Wu
    Abstract:

    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.

Hamid S Mousavi - One of the best experts on this subject based on the ideXlab platform.

  • a novel one layer recurrent neural network for the l1 regularized Least Square Problem
    Neurocomputing, 2018
    Co-Authors: Mohammad Mohammadi, Wout Hofman, Yaohua Tan, Hamid S Mousavi
    Abstract:

    The l1-regularized Least Square Problem has been considered in diverse fields. However, finding its solution is exacting as its objective function is not differentiable. In this paper, we propose a new one-layer neural network to find the optimal solution of the l1-regularized Least Squares Problem. To solve the Problem, we first convert it into a smooth quadratic minimization by splitting the desired variable into its positive and negative parts. Accordingly, a novel neural network is proposed to solve the resulting Problem, which is guaranteed to converge to the solution of the Problem. Furthermore, the rate of the convergence is dependent on a scaling parameter, not to the size of datasets. The proposed neural network is further adjusted to encompass the total variation regularization. Extensive experiments on the l1 and total variation regularized Problems illustrate the reasonable performance of the proposed neural network. © 2018 Elsevier B.V.

  • solving the l1 regularized Least Square Problem via a box constrained smooth minimization
    arXiv: Optimization and Control, 2017
    Co-Authors: Mohammad Mohammadi, Wout Hofman, Yaohua Tan, Hamid S Mousavi
    Abstract:

    In this paper, an equivalent smooth minimization for the L1 regularized Least Square Problem is proposed. The proposed Problem is a convex box-constrained smooth minimization which allows applying fast optimization methods to find its solution. Further, it is investigated that the property "the dual of dual is primal" holds for the L1 regularized Least Square Problem. A solver for the smooth Problem is proposed, and its affinity to the proximal gradient is shown. Finally, the experiments on L1 and total variation regularized Problems are performed, and the corresponding results are reported.

Mohammad Mohammadi - One of the best experts on this subject based on the ideXlab platform.

  • a novel one layer recurrent neural network for the l1 regularized Least Square Problem
    Neurocomputing, 2018
    Co-Authors: Mohammad Mohammadi, Wout Hofman, Yaohua Tan, Hamid S Mousavi
    Abstract:

    The l1-regularized Least Square Problem has been considered in diverse fields. However, finding its solution is exacting as its objective function is not differentiable. In this paper, we propose a new one-layer neural network to find the optimal solution of the l1-regularized Least Squares Problem. To solve the Problem, we first convert it into a smooth quadratic minimization by splitting the desired variable into its positive and negative parts. Accordingly, a novel neural network is proposed to solve the resulting Problem, which is guaranteed to converge to the solution of the Problem. Furthermore, the rate of the convergence is dependent on a scaling parameter, not to the size of datasets. The proposed neural network is further adjusted to encompass the total variation regularization. Extensive experiments on the l1 and total variation regularized Problems illustrate the reasonable performance of the proposed neural network. © 2018 Elsevier B.V.

  • solving the l1 regularized Least Square Problem via a box constrained smooth minimization
    arXiv: Optimization and Control, 2017
    Co-Authors: Mohammad Mohammadi, Wout Hofman, Yaohua Tan, Hamid S Mousavi
    Abstract:

    In this paper, an equivalent smooth minimization for the L1 regularized Least Square Problem is proposed. The proposed Problem is a convex box-constrained smooth minimization which allows applying fast optimization methods to find its solution. Further, it is investigated that the property "the dual of dual is primal" holds for the L1 regularized Least Square Problem. A solver for the smooth Problem is proposed, and its affinity to the proximal gradient is shown. Finally, the experiments on L1 and total variation regularized Problems are performed, and the corresponding results are reported.

Dacheng Tao - One of the best experts on this subject based on the ideXlab platform.

  • Manifold elastic net: A unified framework for sparse dimension reduction
    Data Mining and Knowledge Discovery, 2011
    Co-Authors: Tianyi Zhou, Dacheng Tao, Xindong Wu
    Abstract:

    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.