Nonnegative Lagrangian Relaxation of K-Means and Spectral Clustering
We show that K-means and spectral clustering objective functions can be written as a trace of quadratic forms. Instead of relaxation by eigenvectors, we propose a novel relaxation maintaining the nonnegativity of the cluster indicators and thus give the cluster posterior probabilities, therefore res...
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| creator | Ding, Chris He, Xiaofeng Simon, Horst D. |
| description | We show that K-means and spectral clustering objective functions can be written as a trace of quadratic forms. Instead of relaxation by eigenvectors, we propose a novel relaxation maintaining the nonnegativity of the cluster indicators and thus give the cluster posterior probabilities, therefore resolving cluster assignment difficulty in spectral relaxation. We derive a multiplicative updating algorithm to solve the nonnegative relaxation problem. The method is briefly extended to semi-supervised classification and semi-supervised clustering. |
| doi_str_mv | 10.1007/11564096_51 |
| format | Conference Proceeding |
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Instead of relaxation by eigenvectors, we propose a novel relaxation maintaining the nonnegativity of the cluster indicators and thus give the cluster posterior probabilities, therefore resolving cluster assignment difficulty in spectral relaxation. We derive a multiplicative updating algorithm to solve the nonnegative relaxation problem. 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| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Lecture notes in computer science, 2005, p.530-538 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_17324987 |
| source | Springer Books |
| subjects | Applied sciences Artificial intelligence Bipartite Graph Computer science control theory systems Exact sciences and technology Learning and adaptive systems Nonnegative Matrix Factorization Simultaneous Cluster Spectral Cluster Spectral Relaxation |
| title | Nonnegative Lagrangian Relaxation of K-Means and Spectral Clustering |
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