1-norm Support Vector Machines

By Ji Zhu, Saharon Rosset, Trevor J. Hastie, Robert Tibshirani. 2003

1,029 citations recorded by the source corpus.

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Citations in the corpus

On Security and Sparsity of Linear Classifiers for Adversarial Settings (2016, methodology): “1, where we consider diﬀerent norms to model input data uncertainty against the corresponding SVMs; i.e. , the standard SVM [17], the Inﬁnity-norm SVM [18] and the 1-norm SVM [19] against (cid:96) 2 , (cid:96) 1 and (cid:96) ∞ -norm uncertainty models, respectively.”
Communication-efficient algorithms for decentralized and stochastic optimization (2017, positive): “For convex case, we study 1-norm SVM problem [7,67], i.”
A study in Rashomon curves and volumes: A new perspective on generalization and model simplicity in machine learning (2019, methodology): “Instead we propose a procedure that allows us to compute an L-1 ball that is contained within the Rashomon set for the SVM-1 (Cai et al., 2011; Zhu et al., 2004) learning algorithm.”
An Efficient Algorithm for Computing the HHSVM and Its Generalizations (2013, unknown): “However, because of the (cid:2) 2 penalty the SVM uses all variables in classiﬁcation, which could be a great disadvantage in high-dimensional classiﬁcation (Zhu et al. 2004).”
New Statistical Learning Methods for Estimating Optimal Dynamic Treatment Regimes (2015, methodology): “A possible solution under the proposed framework is to incorporate sparse penalties in the optimization procedure, for example, the l1 penalty (Bradley and Mangasarian, 1998; Zhu et al., 2003).”
A Feature Selection Newton Method for Support Vector Machine Classification (2004, methodology): “Our approach is based on a 1-norm SVM formulation that is known [3, 28] to generate very sparse solutions.”
Similarity Learning for Provably Accurate Sparse Linear Classification (2012, background): “As Balcan et al. Note that Problem (1) is essentially an L 1 -regularized linear SVM ( Zhu et al., 2003) with an empirical similarity map (Balcan et al., 2008), and can be eﬃciently solved.”
An Interior-Point Method for Large-Scale l1-Regularized Logistic Regression (2007, methodology): “The idea also comes up in signal processing (basis pursuit [11, 12] and wavelet thresholding [19]), portfolio optimization [34], control design [26], computer-aided design of integrated circuits [9, 56], and machine learning (sparse principal component analysis [15], maximum likelihood estimation of”
Supervised classification and mathematical optimization (2013, background): “In spite of the benefits of modeling distances to hyperplanes with the Euclidean distance, several authors have proposed the use of other distance measures [47, 48, 149, 163, 191, 247], mainly the `1 norm.”
Optimization Models for Machine Learning: A Survey (2019, background): “reduce the number of features that are involved in the classification model [43, 218].”
Emotion recognition using wireless signals (2016, methodology): “To do this, EQ-Radio uses l1-SVM [65] which selects a subset of relevant features while training an SVM classifier.”
Local Causal and Markov Blanket Induction for Causal Discovery and Feature Selection for Classification Part I: Algorithms and Empirical Evaluation (2010, methodology): “…on theL1-norm penalty (also known as lasso penalty), for example, feature selection via solution of theL1-norm formulation of SVM classification problem (Zhu et al., 2004; Fung and Mangasarian, 2004) and penalized least squares with lasso penalty on the regression coefficients(Tibshirani, 1996).”
A Comparison of Optimization Methods and Software for Large-scale L1-regularized Linear Classification (2010, methodology): “Readers interested in using L1-loss SVMs can refer to Bradley and Mangasarian (1998), Zhu et al. (2004), Fung and Mangasarian (2004), Mangasarian (2006), and references therein.”
SLEP: Sparse Learning with Efficient Projections (2011, methodology): “The use of the `1 norm regularization has led to sparse models for linear regression [69], principle component analysis [83], linear discriminant analysis [76], canonical correlation analysis [65, 75], partial least squares [28], support vector machines [82], and logistic regression [27, 35, 64, 68]”
Accelerated Mini-batch Randomized Block Coordinate Descent Method (2014, background): “In the past decade, researchers have developed a large family of sparse regularized M-estimators, such as Sparse Linear Regression [16, 23], Group Sparse Linear Regression [21], Sparse Logistic Regression [9], Sparse Support Vector Machine [22, 18], and etc.”