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Efficient and robust feature selection via joint l21norms minimization. NIPS
, 2010
"... Feature selection is an important component of many machine learning applications. Especially in many bioinformatics tasks, efficient and robust feature selection methods are desired to extract meaningful features and eliminate noisy ones. In this paper, we propose a new robust feature selection met ..."
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Cited by 69 (24 self)
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Feature selection is an important component of many machine learning applications. Especially in many bioinformatics tasks, efficient and robust feature selection methods are desired to extract meaningful features and eliminate noisy ones. In this paper, we propose a new robust feature selection method with emphasizing joint ℓ2,1norm minimization on both loss function and regularization. The ℓ2,1norm based loss function is robust to outliers in data points and the ℓ2,1norm regularization selects features across all data points with joint sparsity. An efficient algorithm is introduced with proved convergence. Our regression based objective makes the feature selection process more efficient. Our method has been applied into both genomic and proteomic biomarkers discovery. Extensive empirical studies are performed on six data sets to demonstrate the performance of our feature selection method. 1
Robust Principal Component Analysis with NonGreedy ℓ1Norm Maximization
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... Principal Component Analysis (PCA) is one of the most important methods to handle highdimensional data. However, the high computational complexity makes it hard to apply to the large scale data with high dimensionality, and the used ℓ2norm makes it sensitive to outliers. A recent work proposed prin ..."
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Cited by 11 (2 self)
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Principal Component Analysis (PCA) is one of the most important methods to handle highdimensional data. However, the high computational complexity makes it hard to apply to the large scale data with high dimensionality, and the used ℓ2norm makes it sensitive to outliers. A recent work proposed principal component analysis based on ℓ1norm maximization, which is efficient and robust to outliers. In that work, a greedy strategy was applied due to the difficulty of directly solving the ℓ1norm maximization problem, which is easy to get stuck in local solution. In this paper, we first propose an efficient optimization algorithm to solve a general ℓ1norm maximization problem, and then propose a robust principal component analysis with nongreedy ℓ1norm maximization. Experimental results on real world datasets show that the nongreedy method always obtains much better solution than that of the greedy method.
Signal Separation using Nonnegative Matrix Factorization Based on R1norm
"... Abstract: Nonnegative Matrix Factorization (NMF) based methods have found use in the context of blind source separation, semisupervised, and unsupervised learning. These techniques require the use of a suitable cost function to determine the optimal factorization, and most work has focused on the u ..."
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Abstract: Nonnegative Matrix Factorization (NMF) based methods have found use in the context of blind source separation, semisupervised, and unsupervised learning. These techniques require the use of a suitable cost function to determine the optimal factorization, and most work has focused on the use of least square formulation which is prone to large noise and outliers. In this paper we developed robust NMF algorithm using R1norm which exhibit stability and robustness w.r.t. large noises. This algorithm is as efficient as the algorithms for least square formulations, avoiding the significant computational complexities routinely associated with R1norm formulations. The experimental show that R1NMF can effectively separate the observed that contain outliers better than standard NMF. [ W. kider and M. E. Abd El Aziz. Signal Separation using Nonnegative Matrix Factorization Based on R1norm.
1Robust Bayesian Tensor Factorization for Incomplete Multiway Data
"... Abstract—We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying lowCPrank tensor capturing the global information and a sparse tensor capturing the local information (also considered as ou ..."
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Abstract—We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying lowCPrank tensor capturing the global information and a sparse tensor capturing the local information (also considered as outliers), thus providing the robust predictive distribution over missing entries. The lowCPrank tensor is modeled by multilinear interactions between multiple latent factors on which the column sparsity is enforced by a hierarchical prior, while the sparse tensor is modeled by a hierarchical view of Studentt distribution that associates an individual hyperparameter with each element independently. For model learning, we develop an efficient closedform variational inference under a fully Bayesian treatment, which can effectively prevent the overfitting problem and scales linearly with data size. In contrast to existing related works, our method can perform model selection automatically and implicitly without need of tuning parameters. More specifically, it can discover the groundtruth of CP rank and automatically adapt the sparsity inducing priors to various types of outliers. In addition, the tradeoff between the lowrank approximation and the sparse representation can be optimized in the sense of maximum model evidence. The extensive experiments and comparisons with many stateoftheart algorithms on both synthetic and realworld datasets demonstrate the superiorities of our method from several perspectives. Index Terms—Tensor factorization, tensor completion, robust factorization, rank determination, variational Bayesian inference, video background modeling F 1