Spectral Relaxation of K-means Clustering --- Equivalence to PCA

• 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.
  (Equivalence of K-means and PCA)
  Chris Ding and Xiaofeng He. Proc. of Int'l Conf. Machine Learning (ICML 2004), pp 225-232. July 2004. ( PDF file, PS file)

Graph Laplacian Based Spectral Clustering

• A Min-Max Cut for Graph Partitioning and Data Clustering,
  (Spectral clustering that minimizes between-cluster similarities and maximizes within-cluster similarities)
  Chris Ding, Xiaofeng He, Hongyuan Zha, Ming Gu and Horst Simon.
  Proc. of 1st IEEE Int'l Conf. Data Mining. San Jose, CA, 2001. pp.107-114.
  ( Conference paper PS file, Journal version PS file)

• A Spectral Method to Separate Disconnected and Nearly-disconnected Web Graph Components.
  (Perturbation analysis of the Laplacian matrix and spectral clustering objective functions)
  Chris Ding, Xiaofeng He and Hongyuan Zha.
  Proc 7th Int'l Conf. on Knowledge Discovery and Data Mining (KDD 2001) pp.275-280, August 2001.
  ( Postscript file)

• Spectral Relaxation Models and Structure Analysis for K-way Graph Clustering and Bi-clustering.
  (Spectral relaxation of Multi-way Normalized Cut and MinMaxCut)
  Ming Gu, Hongyuan Zha, Chris Ding, Xiaofeng He and Horst Simon. Technical Report, 2001.
  ( Postscript file)

• Unsupervised Learning: Self-aggregation in Scaled Principal Component Space.
  (Self-aggregation in Laplacian eigenspace and connectivity networks for cluster structure identification)
  C. Ding, X. He, Hongyuan Zha, and H. Simon. 6th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD 2002), T. Elomaa, H. Mannila, H. Toivonen (Eds.), Lecture Notes in Artificial Intelligence, Vol. 2431, pp. 112-124.
  ( PDF file)

• Linearized Cluster Assignment via Spectral Ordering
  (Reduce multi-way spectral clustering to 1-D clustering)
  Chris Ding and Xiaofeng He. Proc. of Int'l Conf. Machine Learning (ICML 2004), pp.233-240. July 2004. ( PDF file, PS file)

Spectral Clustering of Bipartite Graphs

• Bipartite Graph Partitioning and Data Clustering,
  (Simultaneous clustering of rows and columns of a rectangle data matrix with a coherent objective function)
  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)

• 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. 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)
  ( PDF 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)