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Spectral Clustering Oracles in Sublinear Time

Series: Theory Seminar

Speaker: Dr. Michael Kapralov Assistant Professor School of Computer and Communication Sciences EPFL, Switzerland

Date/Time: Jul 23 16:00:00

Location: Microsoft teams - ONLINE

Faculty Advisor:

Abstract:
Given an n-vertex graph G that can be partitioned into a few clusters with good inner conductance and ϵ-sparse boundary, i.e. admits a good clustering, can we quickly tell which cluster a given vertex belongs to? A clustering oracle is a small space data structure that provides query access to an approximate clustering of the input graph in sublinear time. In this talk I will describe a clustering oracle that provides query access to an O(ϵlogk) -approximate clustering in time about n1/2+O(ϵ), where k is the number of clusters, which is essentially optimal for constant k. Our main tool is a new way of obtaining dot product access to the spectral embedding of a clusterable graph in sublinear time using the distribution of a few short random walks started at uniformly random vertices in the graph. Microsoft teams link: https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZGE3NDg5NzktMWQ0Zi00MzFmLTg5OTgtMTMyYWM4MWQyYjI2%40thread.v2/0?context=%7b%22Tid%22%3a%226f15cd97-f6a7-41e3-b2c5-ad4193976476%22%2c%22Oid%22%3a%227c84465e-c38b-4d7a-9a9d-ff0dfa3638b3%22%7d

Speaker Bio:

Host Faculty: Dr. Anand Louis