Relationship between PCA and K-means Clustering

• Spectral Relaxation for K-means Clustering,
  (Cluster indicators for K-means relax to principal components)
  Hongyuan Zha, Chris Ding, Ming Gu, Xiaofeng He and Horst Simon.
  Neural Information Processing Systems vol.14 (NIPS 2001). pp. 1057-1064, Vancouver, Canada. Dec. 2001.
  ( Postscript file)

• K-means Clustering via Principal Component Analysis.
  (Show that the solution of K-means are given by PCA. Follow-up work on NIPS'01 paper on Spectral Relaxation of K-means by Zha et al)
  Chris Ding and Xiaofeng He.
  Proc. of Int'l Conf. Machine Learning (ICML 2004), pp 225-232. July 2004. ( PDF file)

PCA and Extension

• R1-PCA: Rotational Invariant L1-norm Principal Component Analysis for Robust Subspace Factorization ( PDF file)
  Chris Ding, Ding Zhou, Xiaofeng He, Hongyuan Zha
  Proc. of Int'l Conf. Machine Learning (ICML 2006), June 2006.

• Two-dimensional Singular Value Decomposition (2DSVD) for 2D Maps and Images (PDF file, PS file)
  [PCA computes low-rank representation for a set of 1D vectors; 2DSVD (2DPCA or 2D factorization of 3D Tensor] computes low-dim representation for a set of 2D maps/matrices).
  Chris Ding and Jieping Ye.
  Proc. SIAM Int'l Conf. Data Mining (SDM'05), pp:32-43, April 2005.

Adaptive Dimension Reduction

• Adaptive Dimension Reduction for Clustering High Dimensional Data.
  (Recursive projection to cluster centroid subspace instead of PCA subspace)
  Chris Ding, Xiaofeng He, Hongyuan Zha, Horst Simon.
  Proc. 2nd IEEE Int'l Conf. Data Mining, pp.147-154, Dec. 2002. Maebashi, Japan.
  ( Postscript file)

Clustering and Ordering of bipartite graph (contingency table) --- Correspondence Analysis

• Bipartite Graph Partitioning and Data Clustering,
  (Simultaneous clustering of rows and columns of a rectangle data matrix with a coherent objective function. We show this two-way clustering is identical to Correspondence Analysis).
  Hongyuan Zha, Xiaofeng He, Chris Ding, Ming Gu and Horst Simon.
  Proc. of ACM 10th Int'l Conf. Information and Knowledge Management (CIKM 2001), pp.25-31, 2001, Atlanta, USA.
  ( Postscript file)

• Unsupervised feature selection via two-way ordering in gene expression analysis
  (Optimal two ordering and Correspondence Analysis)
  Chris Ding.
  Bioinformatics. v.19, pp.1259-1266, 2003.
  (Paper and supplimentary data)

From PCA to Scaled PCA, Self-Aggregation

• Document Retrieval and Clustering: from Principal Component Analysis to Self-aggregation Networks.
  (Refined objective functions for simultaneous clustering of rows and columns of a rectangle data matrix using connectivity networks)
  Chris Ding.
  Proc. Int'l Parallel and Distributed Processing Symposium Proceedings of 9th Int'l Workshop on Artificial Intelligence and Statistics, January 2003, Key West, Florida, Eds. C.M. Bishop and B.J. Frey (editors)
  ( ps file)

• Data Clustering: Principal Components, Hopfield and Self-Aggregation Networks.
  (Clustering objectives and solutions: evolution from the simple to the sophisticated)
  Chris Ding.
  Proc. Int'l Joint Conf on Artificial Intelligence (IJCAI 2003), pp.479-484. August 2003 ( Postscript file)