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Nonnegative Matrix Factorization (NMF) is a promising relaxation technique for clustering analysis. However, conventional NMF methods that directly approximate the pairwise similarities using the least square error often yield mediocre performance for data in curved manifolds because they can capture only the immediate similarities between data samples. Here we propose a new NMF clustering method which replaces the approximated matrix with its smoothed version using random walk. Our method can thus accommodate farther relationships between data samples. Furthermore, we introduce a novel regularization in the proposed objective function in order to improve over spectral clustering. The new learning objective is optimized by a multiplicative Majorization-Minimization algorithm with a scalable implementation for learning the factorizing matrix. Extensive experimental results on real-world datasets show that our method has strong performance in terms of cluster purity.
Author Information
Zhirong Yang (Aalto University)
Tele Hao (Supercell Oy)
Onur Dikmen (University of Helsinki)
Xi Chen (NYU)
Xi Chen is an associate professor with tenure at Stern School of Business at New York University, who is also an affiliated professor to Computer Science and Center for Data Science. Before that, he was a Postdoc in the group of Prof. Michael Jordan at UC Berkeley. He obtained his Ph.D. from the Machine Learning Department at Carnegie Mellon University (CMU). He studies high-dimensional statistical learning, online learning, large-scale stochastic optimization, and applications to operations. He has published more than 20 journal articles in statistics, machine learning, and operations, and 30 top machine learning peer-reviewed conference proceedings. He received NSF Career Award, ICSA Outstanding Young Researcher Award, Faculty Research Awards from Google, Adobe, Alibaba, and Bloomberg, and was featured in Forbes list of “30 Under30 in Science”.
Erkki Oja (Aalto University)
More from the Same Authors
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2018 Poster: Near-Optimal Policies for Dynamic Multinomial Logit Assortment Selection Models »
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2016 Poster: On the Recursive Teaching Dimension of VC Classes »
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2016 Poster: InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets »
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2016 Poster: VIME: Variational Information Maximizing Exploration »
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2016 Poster: Improving Variational Autoencoders with Inverse Autoregressive Flow »
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2016 Poster: Improved Techniques for Training GANs »
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2014 Poster: Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing »
Yuchen Zhang · Xi Chen · Denny Zhou · Michael Jordan -
2014 Spotlight: Spectral Methods meet EM: A Provably Optimal Algorithm for Crowdsourcing »
Yuchen Zhang · Xi Chen · Denny Zhou · Michael Jordan -
2013 Workshop: Crowdsourcing: Theory, Algorithms and Applications »
Jennifer Wortman Vaughan · Greg Stoddard · Chien-Ju Ho · Adish Singla · Michael Bernstein · Devavrat Shah · Arpita Ghosh · Evgeniy Gabrilovich · Denny Zhou · Nikhil Devanur · Xi Chen · Alexander Ihler · Qiang Liu · Genevieve Patterson · Ashwinkumar Badanidiyuru Varadaraja · Hossein Azari Soufiani · Jacob Whitehill -
2013 Poster: Variance Reduction for Stochastic Gradient Optimization »
Chong Wang · Xi Chen · Alexander Smola · Eric Xing -
2012 Poster: Optimal Regularized Dual Averaging Methods for Stochastic Optimization »
Xi Chen · Qihang Lin · Javier Pena -
2011 Poster: Nonnegative dictionary learning in the exponential noise model for adaptive music signal representation »
Onur Dikmen · Cédric Févotte -
2010 Spotlight: Graph-Valued Regression »
Han Liu · Xi Chen · John Lafferty · Larry Wasserman -
2010 Poster: Multivariate Dyadic Regression Trees for Sparse Learning Problems »
Han Liu · Xi Chen -
2010 Poster: Graph-Valued Regression »
Han Liu · Xi Chen · John Lafferty · Larry Wasserman -
2009 Poster: Adaptive Regularization for Transductive Support Vector Machine »
Zenglin Xu · Rong Jin · Jianke Zhu · Irwin King · Michael R Lyu · Zhirong Yang -
2009 Spotlight: Adaptive Regularization for Transductive Support Vector Machine »
Zenglin Xu · Rong Jin · Jianke Zhu · Irwin King · Michael R Lyu · Zhirong Yang -
2009 Poster: Nonparametric Greedy Algorithms for the Sparse Learning Problem »
Han Liu · Xi Chen -
2009 Poster: Heavy-Tailed Symmetric Stochastic Neighbor Embedding »
Zhirong Yang · Irwin King · Zenglin Xu · Erkki Oja -
2009 Spotlight: Heavy-Tailed Symmetric Stochastic Neighbor Embedding »
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