Multiple kernel learning, conic duality, and the SMO algorithm
Abstract
While classical kernel-based classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimization of the coefficients of such a combination reduces to a convex optimization problem known as a quadratically-constrained quadratic program (QCQP). Unfortunately, current convex optimization toolboxes can solve this problem only for a small number of kernels and a small number of data points; moreover, the sequential minimal optimization (SMO) techniques that are essential in large-scale implementations of the SVM cannot be applied because the cost function is non-differentiable. We propose a novel dual formulation of the QCQP as a second-order cone programming problem, and show how to exploit the technique of Moreau-Yosida regularization to yield a formulation to which SMO techniques can be applied. We present experimental results that show that our SMO-based algorithm is significantly more efficient than the general-purpose interior point methods available in current optimization toolboxes.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
With a frozen value extraction function psi, training can make each memory unit statistically more efficient by tuning the key extraction function phi, i.e., learning a similarity metric (kernel).
“Let us first assume that each memory unit has a frozen value extraction function ψ.The training procedure can still make each memory unit statistically more efficient by tuning the parameters of the key extraction function φ, that is, by learning how to compare the current prediction context (x T , x T -1 , x T -2 . . . ) with past prediction contexts (x t , x t-1 , x t-2 . . . ) for t < T .”
From Memory Mosaics (2024) · cites this paper as Bach et al., 2004
Cites
Bertsekas, D. P. (1997) · Journal of the Operational Research Society · doi:10.1038/sj.jors.2600425 · Cited by 11,969 · see citing works
Fast Training of Support Vector Machines Using Sequential Minimal Optimization
Platt, J. C. (1998) · The MIT Press eBooks · doi:10.7551/mitpress/1130.003.0016 · Cited by 5,501 · see citing works
Algorithms for Minimization Without Derivatives
G., D., & Brent, R. P. (1974) · Mathematics of Computation · doi:10.2307/2005713 · Cited by 2,914 · see citing works
Applications of second-order cone programming
Lobo, M. S., Vandenberghe, L., Boyd, S., & Lebret, H. (1998) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(98)10032-0 · Cited by 2,405 · see citing works
Choosing Multiple Parameters for Support Vector Machines
Chapelle, O., Vapnik, V. N., Bousquet, O., & Mukherjee, S. (2002) · Machine Learning · doi:10.1023/a:1012450327387 · Cited by 2,215 · see citing works
Improvements to Platt's SMO Algorithm for SVM Classifier Design
Keerthi, S. S., Shevade, S., Bhattacharyya, C., & Murthy, K. R. K. (2001) · Neural Computation · doi:10.1162/089976601300014493 · Cited by 1,791 · see citing works
Making Large-Scale Support Vector Machine Learning Practical
Joachims, T. (1998) · The MIT Press eBooks · doi:10.7551/mitpress/1130.003.0015 · Cited by 1,623 · see citing works
Feature Selection via Concave Minimization and Support Vector Machines
Bradley, P. S., & Mangasarian, O. L. (1998) · Cited by 988 · see citing works
Andersen, E. D., & Andersen, K. D. (2000) · Applied Optimization · doi:10.1007/978-1-4757-3216-0_8 · Cited by 766 · see citing works
Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries
Lemaréchal, C., & Sagastizábal, C. A. (1997) · SIAM Journal on Optimization · doi:10.1137/s1052623494267127 · Cited by 242 · see citing works
Adaptive Scaling for Feature Selection in SVMs
Grandvalet, Y., & Canu, S. (2002) · Cited by 160 · see citing works
Ong, C. S., Williamson, R. C., & Smola, A. J. (2002) · neural information processing systems · Cited by 3 · see citing works
Flagged first, then by citations
1 of the 13 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer-Wise Relevance Propagation
Bach, S., Binder, A., Montavon, G., Klauschen, F., Müller, K.-R., & Samek, W. (2015) · PLOS ONE · doi:10.1371/journal.pone.0130140 · Cited by 4,524 · see citing works
Chapelle, O., Schölkopf, B., & Zien, A. (2006) · The MIT Press eBooks · doi:10.7551/mitpress/9780262033589.001.0001 · Cited by 4,560 · see citing works
Automated Flower Classification over a Large Number of Classes
Nilsback, M.-E., & Zisserman, A. (2008) · 2008 Sixth Indian Conference on Computer Vision, Graphics & Image Processing · doi:10.1109/icvgip.2008.47 · Cited by 3,442 · see citing works
Multiple Kernel Learning Algorithms
Gönen, M., & Alpaydın, E. (2011) · Cited by 1,651 · see citing works
Representing shape with a spatial pyramid kernel
Bosch, A., Zisserman, A., & Muñoz, X. (2007) · ACM International Conference on Image and Video Retrieval (CIVR) · doi:10.1145/1282280.1282340 · Cited by 1,407 · see citing works
Large Scale Multiple Kernel Learning
Sonnenburg, S., Rätsch, G., Schäfer, C., & Schölkopf, B. (2006) · MPG.PuRe (Max Planck Society) · Cited by 1,212 · see citing works
A Survey on Multi-view LearningPreprint
Xu, C., Tao, D., & Xu, C. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1304.5634 · Cited by 983 · see citing works
Cuingnet, R., Gérardin, E., Tessieras, J., Auzias, G., Lehéricy, S., Habert, M., Marie Chupin, A., Benali, H., & Olivier Colliot, A. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2010.06.013 · Cited by 962 · see citing works
Optimization for Machine Learning
Sra, S., Nowozin, S., & Wright, S. J. (2011) · The MIT Press eBooks · doi:10.7551/mitpress/8996.001.0001 · Cited by 909 · see citing works
Memory Fusion Network for Multi-view Sequential Learning
Zadeh, A., Liang, P. P., Mazumder, N., Poria, S., Cambria, E., & Morency, L.-P. (2018) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v32i1.12021 · Cited by 855 · see citing works
Multiple kernels for object detection
Vedaldi, A., Gulshan, V., Varma, M., & Zisserman, A. (2009) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2009.5459183 · Cited by 770 · see citing works
Optimization with Sparsity-Inducing Penalties
Bach, F., Jenatton, R., Mairal, J., & Obozinski, G. (2012) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000015 · Cited by 757 · see citing works
Self-citationVisualization and analysis of single-cell RNA-seq data by kernel-based similarity learning
Wang, B., Zhu, J., Pierson, E., Ramazzotti, D., & Batzoglou, S. (2017) · Nature Methods · doi:10.1038/nmeth.4207 · Cited by 706 · see citing works
Ren, Y., Zhang, L., & Suganthan, P. N. (2016) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2015.2471235 · Cited by 681 · see citing works
Consistency of the group Lasso and multiple kernel learningPreprint
Bach, F. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0707.3390 · Cited by 680 · see citing works
Self-citationMachine Learning Methods for Attack Detection in the Smart Grid
Özay, M., Esnaola, I., Vural, F. T. Y., Kulkarni, S. R., & Poor, H. V. (2015) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2015.2404803 · Cited by 645 · see citing works
Optimization with Sparsity-Inducing Penalties
Bach, F. (2011) · now publishers, Inc. eBooks · doi:10.1561/9781601985118 · Cited by 605 · see citing works
Self-citationDomain Transfer Multiple Kernel Learning
Duan, L., Tsang, I. W.-H., & Xu, D. (2011) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2011.114 · Cited by 548 · see citing works
On feature combination for multiclass object classification
Gehler, P., & Nowozin, S. (2009) · 2009 IEEE 12th International Conference on Computer Vision · doi:10.1109/iccv.2009.5459169 · Cited by 797 · see citing works
Learning The Discriminative Power-Invariance Trade-Off
Varma, M., & Ray, D. (2007) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2007.4408875 · Cited by 516 · see citing works
Modeling Spatial-Temporal Clues in a Hybrid Deep Learning Framework for Video Classification
Wu, Z., Wang, X., Jiang, Y., Ye, H., & Xue, X. (2015) · ACM International Conference on Multimedia (ACM MM) · doi:10.1145/2733373.2806222 · Cited by 483 · see citing works
Generalized Composite Kernel Framework for Hyperspectral Image Classification
Li, J., Marpu, P., Plaza, A., et al. (2013) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2012.2230268 · Cited by 484 · see citing works
Joint covariate selection and joint subspace selection for multiple classification problems
Obozinski, G., Taskar, B., & Jordan, M. I. (2009) · Statistics and Computing · doi:10.1007/s11222-008-9111-x · Cited by 456 · see citing works
Self-citationNeighborhood Repulsed Metric Learning for Kinship Verification
Lu, J., Zhou, X., Tan, Y.-P., Shang, Y., & Zhou, J. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.134 · Cited by 442 · see citing works
A Survey on Multiview Clustering
Chao, G., Sun, S., & Bi, J. (2021) · IEEE Transactions on Artificial Intelligence · doi:10.1109/tai.2021.3065894 · Cited by 438 · see citing works
lp-Norm Multiple Kernel Learning
Kloft, M. (2011) · DepositOnce · doi:10.14279/depositonce-2978 · Cited by 423 · see citing works
ModDrop: Adaptive Multi-Modal Gesture Recognition
Neverova, N., Wolf, C., Taylor, G., & Nebout, F. (2016) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2015.2461544 · Cited by 420 · see citing works
Multiple Kernel Fuzzy Clustering
Huang, H.-C., Chuang, Y., & Chen, C. (2011) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2011.2170175 · Cited by 408 · see citing works
More generality in efficient multiple kernel learning
Varma, M., & Babu, B. R. (2009) · International Conference on Machine Learning · doi:10.1145/1553374.1553510 · Cited by 400 · see citing works
3D skeleton-based human action classification: A survey
Presti, L. L., & Cascia, M. L. (2015) · Pattern Recognition · doi:10.1016/j.patcog.2015.11.019 · Cited by 393 · see citing works
Multi-View Intact Space Learning
Xu, C., Tao, D., & Xu, C. (2015) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2015.2417578 · Cited by 395 · see citing works
Boccard, J., & Rutledge, D. N. (2013) · Analytica Chimica Acta · doi:10.1016/j.aca.2013.01.022 · Cited by 392 · see citing works
Learning the Kernel Function via Regularization
Micchelli, C. A., & Pontil, M. (2005) · doi:10.5555/1046920.1088710 · Cited by 390 · see citing works
Discriminative Semi-Supervised Feature Selection Via Manifold Regularization
Xu, Z., King, I., Lyu, M. R.-T., & Jin, R. (2010) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2010.2047114 · Cited by 387 · see citing works
Jiang, Y., Wu, Z., Wang, J., Xue, X., & Chang, S. (2017) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2017.2670560 · Cited by 401 · see citing works
Micchelli, C. A., Xu, Y., & Zhang, H. (2006) · Syracuse University Libraries (Syracuse University) · Cited by 379 · see citing works
Support union recovery in high-dimensional multivariate regression
Obozinski, G., Wainwright, M. J., & Jordan, M. I. (2010) · The Annals of Statistics · doi:10.1214/09-aos776 · Cited by 353 · see citing works
Self-citationSalient object detection via bootstrap learning
Tong, N., Lu, H., Ruan, X., & Yang, M. (2015) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2015.7298798 · Cited by 309 · see citing works
Graph-based malware detection using dynamic analysis
Anderson, B., Quist, D., Neil, J., et al. (2011) · Journal of Computer Virology and Hacking Techniques · doi:10.1007/s11416-011-0152-x · Cited by 296 · see citing works
More efficiency in multiple kernel learning
Rakotomamonjy, A., Bach, F., Canu, S., et al. (2007) · International Conference on Machine Learning · doi:10.1145/1273496.1273594 · Cited by 282 · see citing works
Self-citationLocalized multiple kernel learning
Gönen, M., & Alpaydın, E. (2008) · International Conference on Machine Learning · doi:10.1145/1390156.1390201 · Cited by 277 · see citing works
Multi-View Clustering and Feature Learning via Structured Sparsity
Wang, H., Nie, F., & Huang, H. (2013) · Cited by 274 · see citing works
Multiple Kernel Learning for Visual Object Recognition: A Review
Bucak, S. S., Jin, R., & Jain, A. K. (2014) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.212 · Cited by 274 · see citing works
Multiclass multiple kernel learning
Zien, A., & Ong, C. S. (2007) · International Conference on Machine Learning · doi:10.1145/1273496.1273646 · Cited by 269 · see citing works
Multi-View Learning With Incomplete Views
Xu, C., Tao, D., & Xu, C. (2015) · IEEE Transactions on Image Processing · doi:10.1109/tip.2015.2490539 · Cited by 264 · see citing works
A multiple-kernel support vector regression approach for stock market price forecasting
Yeh, C.-Y., Huang, C.-W., & Lee, S.-J. (2010) · Expert Systems with Applications · doi:10.1016/j.eswa.2010.08.004 · Cited by 255 · see citing works
Multiview Hessian Regularization for Image Annotation
Liu, W., & Tao, D. (2013) · IEEE Transactions on Image Processing · doi:10.1109/tip.2013.2255302 · Cited by 254 · see citing works
Li, C., Yu, X., Huang, T., & He, X. (2017) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2017.2691760 · Cited by 257 · see citing works
Young, J., Modat, M., Cardoso, M. J., Mendelson, A., Cash, D., & Ourselin, S. (2013) · NeuroImage Clinical · doi:10.1016/j.nicl.2013.05.004 · Cited by 249 · see citing works
A Multiple-Kernel Fuzzy C-Means Algorithm for Image Segmentation
Chen, L., Chen, C. L. P., & Lu, M. (2011) · IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics) · doi:10.1109/tsmcb.2011.2124455 · Cited by 250 · see citing works
Combined SVM-Based Feature Selection and Classification
Neumann, J. K., Schnörr, C., & Steidl, G. (2005) · Machine Learning · doi:10.1007/s10994-005-1505-9 · Cited by 248 · see citing works
Multiple Kernel Learning for Dimensionality Reduction
Lin, Y., Liu, T.-L., & Fuh, C. (2010) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2010.183 · Cited by 245 · see citing works
Image Classification with Segmentation Graph Kernels
Harchaoui, Z., & Bach, F. (2007) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2007.383049 · Cited by 244 · see citing works
Self-citationLearning with Support Vector Machines
Campbell, C., & Ying, Y. (2011) · Synthesis lectures on artificial intelligence and machine learning · doi:10.2200/s00324ed1v01y201102aim010 · Cited by 242 · see citing works
Anomaly detection in aircraft data using Recurrent Neural Networks (RNN)
Nanduri, A., & Sherry, L. (2016) · Integrated Communications, Navigation and Surveillance Conference (ICNS) · doi:10.1109/icnsurv.2016.7486356 · Cited by 242 · see citing works
Dai, W., Yang, Q., Xue, G.-R., & Yu, Y. H. (2008) · International Conference on Machine Learning · doi:10.1145/1390156.1390182 · Cited by 227 · see citing works
Simple and Efficient Multiple Kernel Learning by Group Lasso
Xu, Z., Jin, R., Yang, H., et al. (2010) · Cited by 225 · see citing works
“Who are you?” - Learning person specific classifiers from video
Šivic, J., Everingham, M., & Zisserman, A. (2009) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2009.5206513 · Cited by 223 · see citing works
Learning Relevant Image Features With Multiple-Kernel Classification
Tuia, D., Camps‐Valls, G., Matasci, G., & Kanevski, M. (2010) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2010.2049496 · Cited by 218 · see citing works
Fast protein classification with multiple networks
Tsuda, K., Shin, H., & Schölkopf, B. (2005) · Bioinformatics · doi:10.1093/bioinformatics/bti1110 · Cited by 217 · see citing works
Audio-Visual Instance Discrimination with Cross-Modal Agreement
Morgado, P. M., Vasconcelos, N. M., & Misra, I. (2021) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr46437.2021.01229 · Cited by 218 · see citing works
Data Fusion by Matrix Factorization
Žitnik, M., & Zupan, B. (2014) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2014.2343973 · Cited by 207 · see citing works
Exploring Large Feature Spaces with Hierarchical Multiple Kernel LearningPreprint
Bach, F. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0809.1493 · Cited by 206 · see citing works
Self-citationEfficient Structure Learning of Markov Networks using L1-Regularization
Lee, S., Ganapathi, V., & Koller, D. (2007) · The MIT Press eBooks · doi:10.7551/mitpress/7503.003.0107 · Cited by 197 · see citing works
How far can you get with a modern face recognition test set using only simple features?
Pinto, N., DiCarlo, J. J., & Cox, D. (2009) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2009.5206605 · Cited by 197 · see citing works
Robust late fusion with rank minimization
Ye, G., Liu, D., Jhuo, I., & Chang, S.-F. (2012) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2012.6248032 · Cited by 193 · see citing works
MFAS: Multimodal Fusion Architecture Search
Perez-Rua, J.-M., Vielzeuf, V., Pateux, S., Baccouche, M., & Jurie, F. (2019) · 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2019.00713 · Cited by 193 · see citing works
Sparse distance learning for object recognition combining RGB and depth information
Lai, K., Bo, L., Ren, X., & Fox, D. (2011) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2011.5980377 · Cited by 191 · see citing works
Exclusive Lasso for Multi-task Feature Selection
Zhou, Y., Jin, R., & Hoi, S. C. H. (2010) · Cited by 190 · see citing works
Multiple kernel learning for heterogeneous anomaly detection
Das, S., Matthews, B. L., Srivastava, A. N., et al. (2010) · ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/1835804.1835813 · Cited by 189 · see citing works
Representative Multiple Kernel Learning for Classification in Hyperspectral Imagery
Gu, Y., Wang, C., You, D., et al. (2012) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/tgrs.2011.2176341 · Cited by 189 · see citing works
Factorized Latent Spaces with Structured Sparsity
Jia, Y., Salzmann, M., & Darrell, T. J. (2010) · Cited by 181 · see citing works
Bio-inspired Dynamic 3D Discriminative Skeletal Features for Human Action Recognition
Chaudhry, R., Ofli, F., Kurillo, G., et al. (2013) · IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) · doi:10.1109/cvprw.2013.153 · Cited by 179 · see citing works
Multimodal Similarity-Preserving Hashing
Masci, J., Bronstein, M. M., Bronstein, A. M., & Schmidhuber, J. (2014) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2013.225 · Cited by 182 · see citing works
Leave-One-Out Kernel Optimization for Shadow Detection and Removal
Vicente, T. F. Y., Hoai, M., & Samaras, D. (2017) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2017.2691703 · Cited by 179 · see citing works
Neural Multimodal Cooperative Learning Toward Micro-Video Understanding
Wei, Y., Wang, X., Guan, W., Nie, L., Lin, Z., & Chen, B. (2019) · IEEE Transactions on Image Processing · doi:10.1109/tip.2019.2923608 · Cited by 177 · see citing works
Automatic Construction and Natural-Language Description of Nonparametric Regression Models
Lloyd, J. R., Duvenaud, D., Grosse, R., Tenenbaum, J. B., & Zoubin Ghahramani, A. (2014) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v28i1.8904 · Cited by 172 · see citing works
Conditional Similarity Networks
Veit, A., Belongie, S., & Karaletsos, T. (2017) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2017.193 · Cited by 170 · see citing works
Chen, T., Andersen, M. S., Lennart Ljung, A., Chiuso, A., & Pillonetto, G. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2351851 · Cited by 169 · see citing works
Assessing and mapping language, attention and executive multidimensional deficits in stroke aphasia
Schumacher, R., Halai, A. D., & Ralph, M. A. L. (2019) · Brain · doi:10.1093/brain/awz258 · Cited by 169 · see citing works
Learning to Score Figure Skating Sport Videos
Xu, C., Fu, Y., Zhang, B., Chen, Z., Jiang, Y., & Xue, X. (2019) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2019.2927118 · Cited by 173 · see citing works
Pattern recognition of number gestures based on a wireless surface EMG system
Chen, X., & Wang, Z. J. (2012) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2012.08.005 · Cited by 167 · see citing works
Zhao, B. L., Kwok, J. T.-Y., & Zhang, C. (2009) · SIAM International Conference on Data Mining · doi:10.1137/1.9781611972795.55 · Cited by 163 · see citing works
Moreau-Yosida Regularization for Grouped Tree Structure Learning
Liu, J., & Ye, J. (2010) · Cited by 159 · see citing works
Multiple Kernel Learning-Based Transfer Regression for Electric Load Forecasting
Wu, D., Wang, B., Precup, D., & Boulet, B. (2019) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2019.2933413 · Cited by 159 · see citing works
Wang, H., Nie, F., Huang, H., Risacher, S. L., Saykin, A. J., Shen, L., & Initiative, A. D. N. (2012) · Bioinformatics · doi:10.1093/bioinformatics/bts228 · Cited by 159 · see citing works
Robust Visual Knowledge Transfer via Extreme Learning Machine-Based Domain Adaptation
Zhang, L., & Zhang, D. D. (2016) · IEEE Transactions on Image Processing · doi:10.1109/tip.2016.2598679 · Cited by 156 · see citing works
Wu, Z., Jiang, Y., Wang, J., Pu, J., & Xue, X. (2014) · ACM International Conference on Multimedia (ACM MM) · doi:10.1145/2647868.2654931 · Cited by 156 · see citing works
Lu, J., Wang, G., & Moulin, P. (2013) · IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2013.48 · Cited by 155 · see citing works
Introduction to Statistical Machine Learning
杉山, 将. (2016) · Elsevier eBooks · doi:10.1016/c2014-0-01992-2 · Cited by 162 · see citing works
Characterizing structural relationships in scenes using graph kernels
Fisher, M., Savva, M., & Hanrahan, P. (2011) · ACM SIGGRAPH Conference (SIGGRAPH) · doi:10.1145/1964921.1964929 · Cited by 154 · see citing works
Multiple Kernel Learning and the SMO Algorithm
Sun, Z., Theera-Ampornpunt, N., Varma, M., et al. (2010) · neural information processing systems · Cited by 154 · see citing works
An Extended Level Method for Efficient Multiple Kernel Learning
Xu, Z., Jin, R., King, I., et al. (2008) · Cited by 152 · see citing works
Supervised classification and mathematical optimization
Carrizosa, E., & Morales, D. R. (2012) · Computers & Operations Research · doi:10.1016/j.cor.2012.05.015 · Cited by 150 · see citing works
Group-sensitive multiple kernel learning for object categorization
Yang, J., Li, Y., Tian, Y., Duan, L., & Gao, W. (2009) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2009.5459172 · Cited by 150 · see citing works
Supervised patient similarity measure of heterogeneous patient records
Sun, J., Wang, F., Hu, J., & Edabollahi, S. (2012) · ACM SIGKDD Explorations Newsletter · doi:10.1145/2408736.2408740 · Cited by 149 · see citing works
Multikernel Adaptive Filtering
Yukawa, M. (2012) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2012.2200889 · Cited by 146 · see citing works
Chen, Z.-Y., Fan, Z., & Sun, M. (2012) · European Journal of Operational Research · doi:10.1016/j.ejor.2012.06.040 · Cited by 146 · see citing works
A general and efficient multiple kernel learning algorithm
Sonnenburg, S., Rätsch, G., & Schäfer, C. (2005) · Max Planck Institute for Plasma Physics · Cited by 146 · see citing works
Optimal kernel selection in Kernel Fisher discriminant analysis
Kim, S.-J., Magnani, A., & Boyd, S. (2006) · International Conference on Machine Learning · doi:10.1145/1143844.1143903 · Cited by 146 · see citing works
- Authors
- Bach, F. R., Lanckriet, G. R. G., & Jordan, M. I.
- Affiliations
- University of California, Berkeley (US)
- Venue
- Twenty-first international conference on Machine learning - ICML '04
- Publisher
- ACM Press
- Published
- 2004
- Pages
- 6
- OpenAlex
- W2031823405
- Semantic Scholar
- 141e6c1dd532504611266d08458dbe2a0dbb4e98
- Cited by
- 1,453
- References
- 13
- Citations by year
- 2026: 7 · 2025: 4 · 2024: 19 · 2023: 20 · 2022: 22 · 2021: 36 · 2020: 52 · 2019: 84 · 2018: 89 · 2017: 86 · 2016: 84 · 2015: 116 · 2014: 136 · 2013: 123 · 2012: 132
- Type
- conference abstract
- Language
- en
- Open access
- closed
- Locations
- International Conference on Machine Learning (publishedVersion)
- Funders
- Intel Corporation
- Microsoft Research
- Topics
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Physical Sciences › Computer Science › Artificial Intelligence › Stochastic Gradient Optimization Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Keywords
- multiple kernel learning, support vector machine, sequential minimal optimization, second-order cone programming, Moreau-Yosida regularization, quadratically constrained quadratic programming, non-differentiable cost functions
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
