SEMI-SUPERVISED CLUSTERING BASED ON SIGNED TOTAL VARIATION

We consider the problem of semi-supervised clustering on signed graphs that model similarity and dissimilarity relations between nodes. We introduce a signed version of total variation and use it to formulate a convex optimization problem for the cluster labels. This optimization problem includes a 1-norm regularization to cover cases where only few cluster labels are known. We propose an ADMM-based algorithm to solve the optimization problem. The complexity of this algorithm scales linearly with the number of edges of the graph. Our scheme is suitable for distributed implementation and can therefore efficiently handle large-dimensional applications. Numerical experiments confirm that our clustering scheme is superior to existing methods.

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