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Constrained Spectral Clustering: Incorporating Prior Knowledge for Document Analysis

Presented at SIGIR 2006, this paper introduces a semi-supervised document clustering method, CNC, that leverages user-provided prior knowledge to guide the clustering process. The model incorporates constraints in the form of document pairs that should be grouped together, enhancing cluster quality. Evaluation on Reuters-21578 and 20 Newsgroups datasets showcases CNC's effectiveness in generating accurate clusters with minimal training data.

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Constrained Spectral Clustering: Incorporating Prior Knowledge for Document Analysis

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  1. Document Clustering with Prior Knowledge Xiang Ji et al. Document Clustering with Prior Knowledge. SIGIR 2006 Presenter: Suhan Yu

  2. Traditional Clustering Methods • Methods • K-Means • Ratio Cut • Average Association • Normalized Cut • Min-Max Cut • Important question: • For each given data set, there are always many possible ways of partitioning the data set.

  3. Traditional Clustering Methods • Related Work on Semi-Supervised Learning: • Wagstaff et al. introduced two types of constraints: “must link” , “cannot link” • Basu, et al. developed a semi-supervised K-means that make use of labeled data to generate initial seed cluster, and to guide the clustering process.

  4. Normalized Cut • J. Shi and J. Malik. Normalized cuts and image segmentation. IEEE Transaction on Pattern Analysis and Machine Intelligence, 2000. • Model the given document set using a undirected graph G(V,E,W) • V: vertex set, represents a document vector • E: edge set, assigned a weight to reflect the similarity between the two documents. • W: graph affinity matrix

  5. Normalized Cut Measures how tightly the cluster S is connected with the rest of the data set. Measures how compact the entire data set is.

  6. Normalized Cut • Let be the indicator vector of the cluster ,and each element takes a binary value {1,0} • Then we get: D=diagonal matrix 1 2 3

  7. Normalized Cut 1 2 3 4 4 1 2 3 Minimize the cost function

  8. Normalized Cut

  9. Normalized Cut

  10. Incorporating Prior Knowledge • The prior knowledge is provided in the form of indicating several pairs of documents which the user whishes to be grouped into the same cluster. • Constraint vector:

  11. The flow path of CNC • Create the graph affinity matrix in which each element represents the similarity between the two documents. • Compute the diagonal matrix D • Form the constraint matrix U by the user • Form the matrix and compute its K smallest eigenvalues and the corresponding eigenvectors. • Project each document into the eigen-space spanned by the K eigenvectors. Apply K-means algorithm to find the K document clusters within this eigen-space

  12. Data description • This paper evaluated the performance of their document clustering model using two data set: Reuters-21578 and 20 Newsgroups document corpora. • Newsgroups data set contains 20000 documents that were collected from 20 newsgroups in the public domain.

  13. Evaluation • Given the two set of document clusters C, C’, their mutual information metric is defined as: 0: two sets are independent 1: two sets are identical

  14. Result

  15. Result

  16. Result

  17. Conclusion • This paper proposed a constrained spectral clustering method (CNC) to incorporate user’s prior knowledge during the document cluster analysis. • CNC model is a very effective semi-supervised document clustering tool, especially with very low amount of training samples. • CNC model did not form constraints for prior knowledge related to cannot-link constraint.

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