Feature Selection via Concave Minimization and Support Vector Machines

By Paul S. Bradley, Olvi L. Mangasarian. 1998

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Citations in the corpus

Communication-efficient algorithms for decentralized and stochastic optimization (2017, positive): “For convex case, we study 1-norm SVM problem [7,67], i.”
1-norm Support Vector Machines (2003, methodology): “It has also been used in [1] and [9] for classi£cation problems under the framework of SVMs. Similar to the ridge penalty, the lasso penalty also shrinks the £tted coef£cientsˆβ 's towards zero, hence (5) also bene£ts from the reduction in £tted coef£cients' variances.”
Use of the Zero-Norm with Linear Models and Kernel Methods (2003, methodology): “Bradley et al. (1995) and Bradley and Mangasarian (1998) propose an approximation method called FSV, which is used for variable selection and, later, by Fung et al. (2000), for finding sparse kernel expansions.”
On the Convergence of the Concave-Convex Procedure (2009, methodology): “For example, [3] proposed a successive linear approximation (SLA) algorithm for feature selection in support vector machines, which can be seen as a special case of CCCP.”
Feature selection for high-dimensional class-imbalanced data sets using Support Vector Machines (2014, background): “Note that, unlike the l 1 norm, k (cid:4) k 0 is not a norm because the triangle inequality does not hold [6].”
Feature Selection Based on Structured Sparsity: A Comprehensive Study (2017, background): “However, a major limitation is that the SVM cannot perform automatic feature selection [129], [130].”
Feature Selection for SVMs (2000, background): “Note, some previous work on feature selection for SVMs does exist, however results have been limited to linear kernels [3, 7] or linear probabilistic models [8].”
A Proof of Convergence of the Concave-Convex Procedure Using Zangwill's Theory (2012, methodology): “For example, Bradley and Mangasarian ( 1998 ) proposed a successive linear approximation (SLA) algorithm for feature selection in support vector machines, which can be seen as a special case of CCCP.”
Estimating Individualized Treatment Rules Using Outcome Weighted Learning (2012, methodology): “For standard SVM, the l 1 penalty has been shown to be effective in selecting relevant variables via shrinking small coefﬁcients to zero (Bradley and Mangasarian 1998; Zhu et al. 2003).”
Discriminative Semi-Supervised Feature Selection Via Manifold Regularization (2009, methodology): “In [8], the authors proposed feature selection concave method that uses an approximate”
Deep Feature Selection: Theory and Application to Identify Enhancers and Promoters (2015, methodology): “Commonly used sparse regularization terms include l1-norm (LASSO) [24], non-negativity [16], and SCAD [5].”
SSVM: A Smooth Support Vector Machine for Classification (2001, methodology): “For moderate sized datasets, SSVM gave the highest tenfold cross validation correctness on six publicly available datasets as well as the fastest times when compared with four other methods given in [2, 4].”
A review of feature selection methods with applications (2015, methodology): “The proposed approach was compared with distance-based and entropybased feature selection, and with SVM and neural network wrappers.”
Relief-Based Feature Selection: Introduction and Review (2017, methodology): “ic feature subset selection (Van Laarhoven and Aarts, 1987; Holland, 1992). Examples include wrappers for Na¨ıve Bayes (Cortizo and Giraldez, 3 Urbanowicz et al. 2006), Support Vector Machines (SVM) (Bradley and Mangasarian, 1998), and most any modeling algorithm combined with a feature subset gener”
Distributed nonconvex constrained optimization over time-varying digraphs (2018, background): “Moreover, a vast class of nonconvex surrogates can also be considered, including the SCAD [17], the “transformed” 1 [53], the logarithmic [47], and the exponential [7]; see Table 2.”