.879-approximation algorithms for MAX CUT and MAX 2SAT
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
A Min-max Cut Algorithm for Graph Partitioning and Data Clustering
ICDM '01 Proceedings of the 2001 IEEE International Conference on Data Mining
Kernel Matrix Completion by Semidefinite Programming
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Multiclass Spectral Clustering
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
IEEE Transactions on Information Theory
Clustering the normalized compression distance for influenza virus data
Algorithms and Applications
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Clustering algorithms based on a matrix of pairwise similarities (kernel matrix) for the data are widely known and used, a particularly popular class being spectral clustering algorithms. In contrast, algorithms working with the pairwise distance matrix have been studied rarely for clustering. This is surprising, as in many applications, distances are directly given, and computing similarities involves another step that is error-prone, since the kernel has to be chosen appropriately, albeit computationally cheap. This paper proposes a clustering algorithm based on the SDP relaxation of the max-k-cut of the graph of pairwise distances, based on the work of Frieze and Jerrum. We compare the algorithm with Yu and Shi's algorithm based on spectral relaxation of a norm-k-cut. Moreover, we propose a simple heuristic for dealing with missing data, i.e., the case where some of the pairwise distances or similarities are not known. We evaluate the algorithms on the task of clustering natural language terms with the Google distance, a semantic distance recently introduced by Cilibrasi and Vitányi, using relative frequency counts from WWW queries and based on the theory of Kolmogorov complexity.