Clustering, Hamming Embedding, Generalized LSH and the Max Norm

TL;DR

This paper explores the convex relaxation of clustering and Hamming embedding, analyzing their asymmetric variants, their connection to Locality-Sensitive Hashing (LSH), and their relation to the max-norm ball, highlighting differences between symmetric and asymmetric cases.

Contribution

It provides a comprehensive analysis of asymmetric clustering and Hamming embedding, linking them to LSH and max-norm, and clarifies differences between symmetric and asymmetric formulations.

Findings

Relationship between asymmetric clustering and LSH clarified

Connection between Hamming embedding and max-norm established

Differences between symmetric and asymmetric versions explained

Abstract

We study the convex relaxation of clustering and hamming embedding, focusing on the asymmetric case (co-clustering and asymmetric hamming embedding), understanding their relationship to LSH as studied by (Charikar 2002) and to the max-norm ball, and the differences between their symmetric and asymmetric versions.