NDLI: Approximate Kernel Clustering

Content Provider	IEEE Xplore Digital Library
Author	Khot, S. Naor, A.
Copyright Year	2008
Description	Author affiliation: Courant Inst. of Math. Sci., New York, NY (Khot, S.; Naor, A.)
Abstract	In the kernel clustering problem we are given a large ntimesn positive semi-definite matrix $A=(a_{ij})$ with $Sigma_{i,j}$ $^{n}=1$ $a_{ij}=0$ and a small ktimesk positivesemi-definite matrix $B=b_{ij}.$ The goal is to find a partition $S_{1},..S_{k}$ of {1,...n} which maximizes the quantity $Sigma_{i,j=1}$ $^{k}(Sigma_{(i,j)isinS}$ $_{i}$ $_{timesS}$ $_{j}).$ We study the computational complexity of this generic clustering problem which originates in the theory of machine learning. We design a constant factor polynomial time approximation algorithm forthis problem, answering a question posed by Song, Smola, Gretton and Borgwardt. In some cases we manage to compute the sharp approximation threshold for this problem assuming the unique games conjecture (UGC). In particular, when B is the 3times3 identity matrix the UGC hardness threshold of this problem is exactly 16pi/27. We present and study a geometricconjecture of independent interest which we show would imply thatthe UGC threshold when B is the ktimesk identity matrix is 8pi/9(1-1/k) for every kges3.
Starting Page	561
Ending Page	570
File Size	334506
Page Count	10
File Format	PDF
ISBN	9780769534367
ISSN	02725428
DOI	10.1109/FOCS.2008.33
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-10-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Kernel User-generated content Machine learning Polynomials Computer science Computational complexity Algorithm design and analysis Approximation algorithms Clustering algorithms Machine learning algorithms inapproximability Approximation algorithm clustering
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in