SSVM swMATH ID: 12678 Software Authors: Lee, Yuh-Jye; Mangasarian, O.L. Description: SSVM: A smooth support vector machine for classification. Smoothing methods, extensively used for solving important mathematical programming problems and applications, are applied here to generate and solve an unconstrained smooth reformulation of the support vector machine for pattern classification using a completely arbitrary kernel. We term such reformulation a Smooth Support Vector Machine (SSVM). A fast Newton-Armijo algorithm for solving the SSVM converges globally and quadratically. Numerical results and comparisons are given to demonstrate the effectiveness and speed of the algorithm. On six publicly available datasets, tenfold cross validation correctness of SSVM was the highest compared with four other methods as well as the fastest. On larger problems, SSVM was comparable or faster than SVM light [T. Joachims, in: Advances in kernel methods – support vector learning, MIT Press: Cambridge, MA (1999)], SOR [O. L. Mangasarian and D. R. Musicant, IEEE Trans. Neural Networks 10, 1032-1037 (1999)] and SMO [J. Platt, in: Advances in kernel methods – support vector learning, MIT Press: Cambridge, MA (1999)]. SSVM can also generate a highly nonlinear separating surface, such as a checkerboard. Homepage: http://research.cs.wisc.edu/dmi/svm/ssvm/ Keywords: classification; support vector machines; smoothing; Newton-Armijo algorithm Related Software: UCI-ml; LIBSVM; RSVM; Pegasos; SVMlight; LIBLINEAR; Matlab; ElemStatLearn; GPDT; TPMSVM; bmrm; C4.5; CPLEX; PRMLT; TRON; SVMTorch; AdaBoost.MH; L-BFGS; CONV_QP; Kernel-Machines Cited in: 65 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year SSVM: A smooth support vector machine for classification. Zbl 1017.90105Lee, Yuh-Jye; Mangasarian, O. L. 2001 all top 5 Cited by 136 Authors 5 Lee, Yuh-Jye 5 Mangasarian, Olvi L. 4 Sciandrone, Marco 4 Yuan, Yubo 3 Ketabchi, Saeed 2 Che, Haitao 2 Gupta, Deepak Kumar 2 Lee, Yoonkyung 2 Lin, Yi 2 Moosaei, Hossein 2 Ni, Tie 2 Piccialli, Veronica 2 Shao, Yuanhai 2 Wang, Zhen 2 Zanghirati, Gaetano 1 Bai, Lan 1 Balasundaram, S. 1 Ballard, Dana H. 1 Bazikar, Fatemeh 1 Behboodi-Kahoo, Malihe 1 Bruni, Renato 1 Cao, Feilong 1 Carrizosa, Emilio 1 Cassioli, Andrea 1 Chandra, Suresh 1 Chang, Chien-Chung 1 Chapelle, Olivier 1 Chen, Jein-Shan 1 Chen, Wei-Po 1 Chiavaioli, A. 1 Chien, Li-Jen 1 Cocianu, Catalina-Lucia 1 Cui, Jiangtao 1 De Leone, Renato 1 De Nicolao, Giuseppe 1 Deng, Naiyang 1 Dinuzzo, Francesco 1 Faccini, Daniel 1 Fan, Weiguo 1 Feng, Jiashi 1 Feng, Yunlong 1 Ferguson, Stuart 1 Ferraro, Maria Brigida 1 Fletcher, Roger 1 Fung, Glenn Martin 1 Gaudioso, Manlio 1 Grigor’eva, Xeniya Vladimirovna 1 Gu, Weizhe 1 Guarracino, Mario Rosario 1 Günter, Simon 1 Han, Le 1 He, Lifang 1 Herty, Michael Matthias 1 Hien, Le Thi Khanh 1 Huang, Chien-Ming 1 Huang, Suyun 1 Huang, XiaoLin 1 Jiang, Wei 1 Jung, Yoonsuh 1 Kapil 1 Klar, Axel 1 Ko, Chun-Hsu 1 Lazzari, Cinzia 1 Li, Chunna 1 Li, Meixia 1 Li, Qingna 1 Li, Yan 1 Liang, Jinjin 1 Lin, Chih-Jen 1 Lin, Dennis Kon Jin 1 Liu, Hongwei 1 Liu, Liming 1 Lu, Canyi 1 Lucidi, Stefano 1 MacEachern, Steven N. 1 Maggioni, Francesca 1 Mehrkanoon, Siamak 1 Mircea, Marinela 1 Nguyen, Cuong Viet 1 Niu, Lingfeng 1 Palagi, Laura 1 Pardalos, Panos M. 1 Peng, Jian-Xun 1 Peng, Xinjun 1 Pham, Huy Nguyen Anh 1 Potra, Florian-Alexandru 1 Pu, Dongmei 1 Rafferty, Karen 1 Khemchandani Rastogi, Reshma 1 Razzaghi, Mohamad 1 Richhariya, Bharat 1 Risi, A. 1 Romero Morales, Dolores 1 Rosen, J. Ben 1 Rothkopf, Constantin A. 1 Saigal, Pooja 1 Schraudolph, Nicol N. 1 Serafini, Thomas 1 Shabanzadeh, Parvaneh 1 Shubham, K. ...and 36 more Authors all top 5 Cited in 38 Serials 7 Computational Optimization and Applications 5 Annals of Operations Research 4 Pattern Recognition 3 Journal of Optimization Theory and Applications 3 Computers & Operations Research 2 Information Sciences 2 Neural Networks 2 Machine Learning 2 Neural Computation 2 Filomat 2 Mathematical Problems in Engineering 2 Optimization Methods & Software 2 Journal of Applied Mathematics and Computing 2 Journal of Industrial and Management Optimization 1 Biological Cybernetics 1 IEEE Transactions on Information Theory 1 Applied Mathematics and Computation 1 Journal of the American Statistical Association 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Statistics & Probability Letters 1 Advances in Mathematics 1 Optimization 1 Statistical Science 1 Mathematical and Computer Modelling 1 Applied Mathematical Modelling 1 European Journal of Operational Research 1 Computational Statistics and Data Analysis 1 Annals of Mathematics and Artificial Intelligence 1 Abstract and Applied Analysis 1 Soft Computing 1 Journal of Inequalities and Applications 1 Journal of Applied Mathematics 1 Journal of Machine Learning Research (JMLR) 1 EURASIP Journal on Applied Signal Processing 1 4OR 1 Acta Numerica 1 Numerical Algebra, Control and Optimization 1 ISRN Applied Mathematics all top 5 Cited in 10 Fields 42 Computer science (68-XX) 38 Operations research, mathematical programming (90-XX) 23 Statistics (62-XX) 9 Numerical analysis (65-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Biology and other natural sciences (92-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year