A finite algorithm for finding the projection of a point onto the Canonical simplex of Rn
Journal of Optimization Theory and Applications
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Nonnegative matrix factorization via rank-one downdate
Proceedings of the 25th international conference on Machine learning
3D Face Recognition using Euclidean Integral Invariants Signature
SSP '07 Proceedings of the 2007 IEEE/SP 14th Workshop on Statistical Signal Processing
Learning kernels from indefinite similarities
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Similarity-based Classification: Concepts and Algorithms
The Journal of Machine Learning Research
Convex and Semi-Nonnegative Matrix Factorizations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Group theoretical methods in signal processing: learning similarities, transformations and invariants
An Efficient and Stable Algorithm for Learning Rotations
ICPR '10 Proceedings of the 2010 20th International Conference on Pattern Recognition
K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust perron cluster analysis for various applications in computational life science
CompLife'05 Proceedings of the First international conference on Computational Life Sciences
Classification with scattering operators
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Multi-spectral SIFT for scene category recognition
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
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For similarity-based clustering, we propose modeling the entries of a given similarity matrix as the inner products of the unknown cluster probabilities. To estimate the cluster probabilities from the given similarity matrix, we introduce a left-stochastic non-negative matrix factorization problem. A rotation-based algorithm is proposed for the matrix factorization. Conditions for unique matrix factorizations and clusterings are given, and an error bound is provided. The algorithm is particularly efficient for the case of two clusters, which motivates a hierarchical variant for cases where the number of desired clusters is large. Experiments show that the proposed left-stochastic decomposition clustering model produces relatively high within-cluster similarity on most data sets and can match given class labels, and that the efficient hierarchical variant performs surprisingly well.