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Discriminative Similarity for Clustering and Semi-Supervised Learning
Similarity-based clustering and semi-supervised learning methods separate the
data into clusters or classes according to the pairwise similarity between the
data, and the pairwise similarity is crucial for their performance. In this
paper, we propose a novel discriminative similarity learning framework which
learns discriminative similarity for either data clustering or semi-supervised
learning. The proposed framework learns classifier from each hypothetical
labeling, and searches for the optimal labeling by minimizing the
generalization error of the learned classifiers associated with the
hypothetical labeling. Kernel classifier is employed in our framework. By
generalization analysis via Rademacher complexity, the generalization error
bound for the kernel classifier learned from hypothetical labeling is expressed
as the sum of pairwise similarity between the data from different classes,
parameterized by the weights of the kernel classifier. Such pairwise similarity
serves as the discriminative similarity for the purpose of clustering and
semi-supervised learning, and discriminative similarity with similar form can
also be induced by the integrated squared error bound for kernel density
classification. Based on the discriminative similarity induced by the kernel
classifier, we propose new clustering and semi-supervised learning methods