k-Median Clustering via Metric Embedding: Towards Better Initialization with Differential Privacy

In clustering algorithms, the choice of initial centers is crucial for the quality of the learned clusters. We propose a new initialization scheme for the k -median problem in the general metric space (e.g., discrete space induced by graphs), based on the construction of metric embedding tree structure of the data. We propose a novel and efficient search algorithm, for good initial centers that can be used subsequently for the local search algorithm. The so-called HST initialization method can produce initial centers achieving lower error than those from another popular method k -median, also with higher efficiency when k is not too small. Our HST initialization can also be easily extended to the setting of differential privacy (DP) to generate private initial centers.