Simultaneous Clustering and Optimization for Evolving Datasets

For any i such that 1 i 6, A i represents an instance of the dataset, X i represents the corresponding optimization variable, v i represents a vertex of graph G, and e ij represents the edge connecting v i and v j. heuristic rules used in traditional clustering methods. A formulation of convex clustering was proposed in [13] by relaxing the formulation of k-means clustering. Subsequently, [15] and [16] provided several sufficient conditions for recovering the clustering membership theoretically . Other studies, e.g., [8], [17], focus on improving the efficiency of convex clustering. Although those previous studies attained great improvement of convex clustering for static datasets, they are unsuitable for handling evolving datasets due to a high computational cost. The method proposed in the paper reduces such computational cost and makes a good tradeoff between efficiency and accuracy .