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Unsupervised Learning:
Low-dimensional Embedding and Data Clustering are Equivalent

Chris H. Q. DING

School of Computer Science
Anhui University, Hefei, China and
University of Texas, Arlington, TX 76019 USA


Low-dimensional representation (LDR) of high-dimensional objects such as images can significantly improve their clustering performance. In this work, we show that the widely used LDR methods such as principal component analysis (PCA), Laplacian Embedding, and tensor decomposition are in fact mathematically equivalent to k-means clustering and graph spectral clustering that minimize cross-cutting edges. This provides a theoretical understanding of why these LDR techniques work well in practice. It also provides a solid foundation to build more complicated models to tackle more complex problems. On cognitive point of view, does human brain process high-dimensional images as low-dimensional objects?

Short Bio

Chris Hong-Qiang Ding obtained Ph.D. from Columbia University, did research at California Institute of Technology, Jet Propulsion Laboratory, and Lawrence Berkeley National Laboratory. He joined University of Texas at Arlington as a professor in 2007. His research areas are data mining, bioinformatics, high performance computing, focusing on matrix/ tensor approaches. He served on several top data mining conference committees, and reviewed research grants for National Science Foundations of USA, Israel, Ireland, and Hong Kong. He gave invited seminars at UC Berkeley, Stanford, Carnegie Mellon, University of Waterloo, University of Alberta, Google Research, IBM Research, Microsoft Research. He published 200 research papers with 12000 citations.

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Last updated: December 19, 2013