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Mikhail Belkin

  • Professor, Statistics
  • Professor, Computer Science & Engineering
  • 597 Dreese Laboratories
    2015 Neil Ave
    Columbus, OH 43210
  • 614-292-5841

Honors

  • 20110101

    2011 Lumley Research Award.

Chapters

2013

  • 2013. "Semi-Supervised Learning." In Academic Press Library in Signal Processing: Signal Processing Theory and Machine Learning,

2006

  • 2006. "The Geometric Basis of Semi-supervised Learning." In Semi-supervised Learning, edited by Chapelle, O., B. Schölkopf and A. Zien,

Journal Articles

2011

  • Melacci, S; Belkin, M, 2011, "Laplacian Support Vector Machines Trained in the Primal." JOURNAL OF MACHINE LEARNING RESEARCH 12, 1149-1184 - 1149-1184.

2010

  • Rosasco, L.; Belkin, M.; De Vito, E., 2010, "On Learning with Integral Operators." JOURNAL OF MACHINE LEARNING RESEARCH 11, 905-934 - 905-934.
  • S. Melacci, M. Belkin, 2010, "Laplacian Support Vector Machines Trained in the Primal." The Journal of Machine Learning Research

2006

  • M. Belkin, P. Niyogi, V. Sindhwani, 2006, "Manifold Regularization: a Geometric Framework for Learning from Examples." Journal of Machine Learning Research 7, 2399-2434 - 2399-2434.

2004

  • M. Belkin, P. Niyogi, 2004, "Semi-supervised Learning on Riemannian Manifolds." Machine Learning 56, no. 56, 209-239 - 209-239.

2003

  • Belkin, M.; Niyogi, P., 2003, "Laplacian eigenmaps for dimensionality reduction and data representation." NEURAL COMPUTATION 15, no. 6, 1373-1396 - 1373-1396.

Presentations

  • ""Learning a Basis from Imperfect measurements: Why and how.." 2015, Presented at Conference on Geometry and Data Analysis, University of Chicago,,
  • "Basis learning and spectral clustering." 2015, Presented at Penn State Statistics Colloquium,
  • "Geometric Aspects of Optimization and Applications to Spectral Clustering." 2016, Presented at Shape Analysis and Learning by Geometry and Machine,
  • "Machine learning: an introduction." 2016, Presented at Workshop on Computational Brain Research at IIT Madras,
  • "Back to the future: Radial Basis Function networks revisited." 2016, Presented at Information Theory and Application Workshop,
  • "Learning Mixture of Gaussians using Spectral Methods." 2007, Presented at Workshop on Geometric and Topological Approaches to Data Analysis,
  • "Learning from labeled and unlabeled data." 2007, Presented at The North Carolina State University, EECS Seminar,
  • "Geometry and Learning." 2007, Presented at 56th Session of the International Statistical Institute,
  • "Aspects of Manifold and Statistical Learning." 2007, Presented at Conference on Applied Inverse Problems (AIP) 2007,
  • "Aspects of Manifold and Statistical Learning." 2007, Presented at Information Theory and Applications Workshop,
  • "Aspects of Manifold and Statistical Learning." 2007, Presented at PASCAL Workshop on Graph Theory and Machine Learning,
  • "Aspects of Manifold and Statistical Learning." 2007, Presented at 6th International Congress on Industrial & Applied Mathematics,
  • "Aspects of Manifold and Statistical Learning." 2007, Presented at SIAM Conference on Applications of Dynamical Systems,
  • "New developments in Gaussian mixture modelling." 2010, Presented at Oregon State University joint Mathematics/Computer Science Colloquium,
  • "Mixture Learning and Eigenfunctions of Convolution Operators." 2010, Presented at 13th International Conference on Approximation Theory,
  • "Learning Gaussian Mixture Distributions." 2010, Presented at UCSD Information Theory and Applications Workshop,
  • "Clustering, Gaussian Mixture Models, and Sparse Eigenfunction Bases for Semi-Supervised Learning." 2010, Presented at Purdue Computer Science & Machine Learning Colloquium,
  • "Learning Mixtures of Gaussians in High Dimension." 2011, Presented at The Fourth International Conference on computational Harmonic Analysis,
  • "Learning Gaussian Mixture Models." 2011, Presented at Dagstuhl Workshop on Mathematical and Computational Foundations of Learning Theory,
  • "Supervised and Unsupervised Learning in High Dimension." 2010, Presented at OSU Center for Cognitive Science Cogfest 2010,
  • "Geometrical Methods and Data Analysis." 2010, Presented at Laboratoire J.-V. Poncelet,
  • "Spectral Methods in Statistical Learning." 2008, Presented at BIRS workshop on Understanding the New Statistics: Expanding Core Statistical Theory,
  • "Spectral Methods in Learning." 2008, Presented at 2008 Beijing International Conference on Machine Learning and Data Mining,
  • "Manifold Learning." 2008, Presented at 2nd LANL/OSU Workshop,
  • "Manifold Laplacians and Machine Learning." 2008, Presented at OSU Department of Mathematics, geometry seminar,
  • "Manifold and Geometric Learning." 2008, Presented at IMA workshop on Multi-Manifold Data Modeling and Applications,
  • "Learning Mixtures of Gaussians using Spectral Methods." 2008, Presented at FOCM Workshop on Learning Theory,
  • "Geometric View of Machine Learning." 2008, Presented at OSU Center for Cognitive Science Seminar Series,
  • "Geometric and spectral methods in learning." 2008, Presented at Carnegie-Mellon University Statistics Colloquium,
  • "Understanding Hidden Structure: Manifold Learning from Labeled and Unlabeled Data." 2011, Presented at Ohio State ECE IPS Seminar,
  • "Manifold learning, the heat equation and spectral clustering." 2011, Presented at Statistical Learning Theory and Applications (MIT CBCL course),
  • "Learning Mixtures of Gaussians in High Dimension." 2011, Presented at MIT Brains & Machines Seminar,
  • "Tutorial on Manifold and Semi-supervised Learning." 2009, Presented at Summer School on Manifold Learning in Image and Signal Analysis,
  • "Tutorial on Machine Learning." 2009, Presented at Summer School an Neuroinformatics,
  • "Towards Understanding Mixtures of Gaussians: Spectral Methods and Polynomial Time Learning with No Separation." 2009, Presented at Forum on Geometric Aspects of Machine Learning and Visual Analytics: Recent Developments and Future Challenges,
  • "Statistical Aspects og High-dimensional data." 2009, Presented at Peking University Statistics Department Colloquium,
  • "Statistical Aspects og High-dimensional data." 2009, Presented at Zhijiang University Computer Science,
  • "Semi-supervised Learning using Sparse Eigenfunction Bases and Gaussian Mixture Models." 2009, Presented at Center for Imaging Science Colloquium, John Hopkins University,
  • "Manifold and Semi-supervised Learning and Applications." 2009, Presented at 1st Sino-USA Summer School in Vision, Learning and Pattern Recognition,
  • "Manifold and Semi-supervised Learning." 2009, Presented at Microsoft Research Asia,
  • "Manifold and Semi-supervised Learning." 2009, Presented at Los Alamos Seminar,
  • "Learning mixtures of Gaussians using Convolution Operators." 2009, Presented at Information Theory and Applications Workshop, ITA 2009,
  • "Learning Gaussian Mixture Distributions in Hign Dimension." 2009, Presented at Seoul National University Statistics Colloquium,
  • "Geometry and Learning." 2009, Presented at Duke University, Computer Science Algorithms Seminar,
  • "Clustering, sparsity and semi-supervised learning." 2009, Presented at NIPS Workshop on Manifolds, Sparsity, and Structured models,
  • "Introduction to Machine Learning and Manifold Methods." 2010, Presented at Summer School in Neuroinformatics,
  • "An introduction to machine learning." 2011, Presented at Summer School an Neuroinformatics,
  • "Eigenvectors of orthogonally decomposble functions: theory and applications." 2016, Presented at ICML 2016 Workshop on Geometry in Machine Learning,
  • "Spectral Clustering and Semi-supervised Learning." 2006, Presented at WNAR/IMS meeting,
  • "Semi-supervised Learning." 2006, Presented at 21st European Conference on Operational Research 2006,
  • "Geometry and Manifold Structures in Statistical Learning." 2006, Presented at Workshop on New Perspectives in Geometric Analysis,
  • "Geometric View of Machine Learning." 2006, Presented at OSU Statistics Colloquium,
  • "Estimating Surface Volumes of Convex Bodies." 2006, Presented at American Mathematical Society Sectional Meeting,
  • "Aspects of Manifold and Statistical Learning." 2006, Presented at Institute of Mathematical Statistics Annual Meeting,
  • "Aspects of Manifold and Statistical Learning." 2006, Presented at Joint Statistical Meeting,
  • "Learning Mixtures of Gaussians and Other Distributions." 2012, Presented at Colloquium at Inria, Saclay,
  • "Algebraic-Geometric Methods for Learning Gaussian Mixture Models." 2012, Presented at Workshop on Algebraic Statistics, IST Austria,
  • "Inverse Density as an Inverse Problem." 2013, Presented at Seminar at Johann Radon Institute for Computational and Applied Mathematics,
  • "Inverse Density as an Inverse Problem via Fredholm Machines." 2013, Presented at Colloquium at the Italian Institute of Technology, Genova,
  • "Dealing with Singular Manifolds:Theory and Applications." 2012, Presented at Oberwolfach workshop on Learning Theory and Approximation,,
  • "Machine Learning and Differential Geometry of the Data." 2012, Presented at Colloquium at the Mathematical Sciences Center, Tsinghua University,
  • "Inverse Density as an Inverse Problem." 2013, Presented at International Conference on Approximation Theory and Applications,
  • "Understanding geometry of the data." 2010, Presented at International Conference on Geometry/Imaging,
  • "Machine Learning and Differential Geometry of the Data." 2012, Presented at Yaroslavl International Conference on Discrete Geometry,
  • "Inverse Density as an Inverse Problem." 2013, Presented at MPI for Biological Cybernetics, Tubingen,
  • "Inverse Density Estimation using Fredholm Machines." 2013, Presented at Spectral Learning Workshop, ICML 2013,
  • "Spectal Clustering Revisited." 2013, Presented at Workshop on Modern Applications of Homology and Cohomolog,
  • "Features and Representations." 2013, Presented at Workshop on Learning Data Representation: Hierarchies and Invarianc,
  • "Manifold and Semi-supervised Learning." 2013, Presented at Case Western CS Colloquium,
  • "Computing the Surface Area of a Convex Body using Heat Flows." 2013, Presented at International conference on Geometry, Topology, and Applications,,
  • "The Hidden Convexity of Spectral Clustering." 2013, Presented at NIPS 2013 Spectral Learning Workshop,
  • "Machine Learning and the Differential Geometry of the Data." 2014, Presented at Conference on Numerical Analysis and Scientific Computing,
  • "The Hidden Convexity of Spectral Clustering." 2014, Presented at Information Theory and Applications,
  • "The Hidden Convexity of Spectral Clustering." 2014, Presented at SAMSI Program on Low-dimensional Structure in High-dimensional Systems (LDHD) Transition Workshop,
  • "Independent Component Analysis, Spectral Clustering and the Blessing of Dimensionality." 2014, Presented at Duke CS Seminar,
  • "Statistical Machine Learning and Kernel Methods." 2014, Presented at MADALGO Summer School on Learning at Scale,
  • "Learning with Fredholm Kernels." 2015, Presented at Information Theory and Aplication,
  • "Gaussian Mixture Learning in High and Low Dimension." 2015, Presented at Neymann Seminar (Dept. of Statistics),
  • "Learning a Basis from Imperfect measurements: Why and how." 2014, Presented at Meeting on Mathematical Statistics, CIRM,
  • "Learning a Basis from Imperfect measurements: Why and how." 2014, Presented at Foundations of Computation Mathematics,
  • "Learning a Basis from Imperfect measurements: Why and how." 2015, Presented at Information Theory, Learning and Big Data,
  • "Learning a Basis from Imperfect measurements: Why and how." 2015, Presented at Groups and interactions in data, networks and biology,
  • "Learning from Labeled and Unlabeled Data." 2007, Presented at Industrial and Systems Engineering Seminar series,
  • "Eigenvectors of orthogonally decomposable functions: theory and applications." 2016, Presented at Simons Institute Seminar,
  • "Learning a Basis from Imperfect measurements: Why and how." 2016, Presented at Wilks Statistics Seminar, Princeton University,
  • "Toward understanding complex spaces: graph Laplacians on manifolds with singularities and boundaries." 2012, Presented at AMS Sectional Meeting, Special Session on Applied Topology,
  • "Algebraic-Geometric Methods for Learning Mixtures of Gaussians and Other Distributions." 2012, Presented at BIRS Workshop on Topological Data Analysis and Machine Learning Theory,
  • "Algebraic geometry for learning high-dimensional mixtures of Gaussians and other distributions." 2012, Presented at Nonparametric and high-dimensional statistics,
  • "Radial basis function networks unshackled." 2016, Presented at Boston University Data Science Initiative (DSI) Colloquium,
  • "Eigenvectors of orthogonally decomposable functions and applications." 2016, Presented at MIT Data Science Colloquium,
  • "Machine Learning: Shallow Architectures." 2017, Presented at Workshop on Computational Brain Research at IIT Madras,
  • "Smoothness and learning from data." 2017, Presented at UCLA CS Colloquium,
  • "Making shallow learning great again." 2017, Presented at Information Theory and Application Workshop,
  • "Subtle but not malicious? The (high) computational cost of non-smoothness in learning from big data." 2017, Presented at UC Berkeley Neymann Statistics Colloquium,

Papers in Proceedings

2016

  • James Voss, Mikhail Belkin, Luis Rademacher "The Hidden Convexity of Spectral Clustering." in AAAI 2016. (2 2016).
  • Justin Eldridge, Mikhail Belkin, Yusu Wang "Graphons, mergeons, and so on!." in Neural Information Processing (NIPS). (12 2016).
  • Qichao Que, Mikhail Belkin "Back to the future: Radial Basis Function networks revisited." in AI&Statistics 2016. (5 2016).
  • Mikhail Belkin, Luis Rademacher, James Voss "Learning a Hidden Basis Through Imperfect Measurements: An Algorithmic Primitive." in COLT 2016. (6 2016).
  • Jihun Hamm, Paul Cao, Mikhail Belkin "Learning Privately from Multiparty Data." in ICML 2016. (6 2016).
  • Mikhail Belkin, Luis Rademacher, James Voss "Learning a Hidden Basis Through Imperfect Measurements: An Algorithmic Primitive." in COLT 2016. (6 2016).
  • Chaoyue Liu, Mikhail Belkin "Clustering with Bregman Divergence." in Neural Inormation Processing Systems (NIPS). (12 2016).

2015

  • J. Hamm, A. Champion, G. Chen, M. Belkin, and D. Xuan "Crowd-ML: A Privacy-Preserving Learning Framework for a Crowd of Smart Devices." in ICDCS 2015. (6 2015).
  • James Voss, Mikhail Belkin, Luis Rademacher "A Pseudo-Euclidean Iteration for Optimal Recovery in Noisy ICA." in NIPS 2015. (12 2015).
  • Hamm, J.; Champion, A.C.; Chen, G.; Belkin, M. et al. "Crowd-ML: A Privacy-Preserving Learning Framework for a Crowd of Smart Devices." (1 2015).
  • Justin Eldridge, Mikhail Belkin, Yusu Wang "Beyond Hartigan Consistency: Merge Distortion Metric for Hierarchical Clustering." in COLT 2015. (6 2015).
  • Hamm, J.; Champion, A.C.; Chen, G.; Belkin, M. et al. "Crowd-ML: A Privacy-Preserving Learning Framework for a Crowd of Smart Devices." in 2015 IEEE 35th International Conference on Distributed Computing Systems. (1 2015).

2014

  • Joseph Anderson, Mikhail Belkin, Navin Goyal, Luis Rademacher, James Voss "The More, the Merrier: the Blessing of Dimensionality for Learning Large Gaussian Mixtures,." in 27th Annual Conference on Learning Theory (COLT 2014). (6 2014).

2013

  • M. Belkin, L. Rademacher, J. Voss "Blind signal separation in the presence of Gaussian noise." in The 26th Annual Conference on Learning Theory (COLT 2013). (6 2013).

2012

  • Mikhail Belkin, Qichao Que, Yusu Wang, Xueyuan Zhou "Toward Understanding Complex Spaces: Graph Laplacians on Manifolds with Singularities and Boundaries." in COLT 2012. (6 2012).

2011

  • X. Ge, I. Safa, M. Belkin, Y. Wang "Data Skeletonization via Reeb Graphs." in Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS 2011). (12 2011).

2010

  • M. Belkin, K. Sinha "Polynomial Learning of Distribution Families." in 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS 2010). (10 2010).

2009

  • M. Belkin, J. Sun, Y. Wang "Constructing Laplace Operator from Point Clouds in R^d." in Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2009. (1 2009).
  • L. Rosasco, M.Belkin, E. De Vito, "A Note on Perturbation Results for Learning Empirical Operators." in 22nd Annual Conference on Learning Theory (COLT 2009). (1 2009).
  • M. Belkin, J. Sun, Y. Wang "Discrete Laplace Operator for Meshed Surfaces." in 24th Annual Symposium on Computational Geometry (SOCG 2008). (1 2009).

2008

  • L. Ding, M. Belkin "Probabilistic Mixtures of Differential Profiles for Shape Recognition." in 19th International Conference on Pattern Recognition (ICPR 2008). (1 2008).

2006

  • Belkin, M.; Narayanan, H.; Niyogi, P.; SOC, I.C. "Heat flow and a faster algorithm to compute the surface area of a convex body." (1 2006).

2005

  • V. Sindhwani, P. Niyogi, M. Belkin "A Co-Regularization Approach to Semi-supervised Learning with Multiple Views." in ICML Workshop on Learning with Multiple Views, 2005. (1 2005).
  • V. Sindhwani, P. Niyogi, M. Belkin, S. Keerthi "Linear Manifold Regularization for Large Scale Semi-supervised Learning." in ICML Workshop on Learning with Partially Classified Training Data, 2005. (1 2005).
  • Belkin, M.; Niyogi, P. "Towards a theoretical foundation for Laplacian-based manifold methods." (1 2005).

2004

  • M. Belkin, I. Matveeva, P. Niyogi "Regularization and Semi-supervised Learning on Large Graphs." in 17th Annual Conference on Learning Theory, COLT 2004. (1 2004).
  • M. Belkin, I. Matveeva, P. Niyogi "Tikhonov Regularization and Semi-supervised Learning on Large Graphs." in International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2004, Special Session: Manifolds and Geometry in Signal Processing. (1 2004).

2002

  • M. Belkin, J. Goldsmith "Using Eigenvectors of the Bigram Graph to Infer Morpheme Identity." in Morphological and Phonological Learning: Proceedings of the 6th Workshop of the ACL Special Interest Group in Computational Phonology (SIGPHON 2002). (1 2002).

2001

  • M. Belkin, P. Niyogi "Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering." in Neural Information Processing Systems, (NIPS 2001).. (1 2001).