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Yes we can - simplex volume maximization for descriptive web-scale matrix factorization

 
: Thurau, C.; Kersting, K.; Bauckhage, C.

:
Postprint urn:nbn:de:0011-n-1486459 (767 KByte PDF)
MD5 Fingerprint: 445918142c1623d76cc65373ac2e1bcd
© ACM 2010 This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution.
Erstellt am: 22.12.2010


Huang, X.J.; Jones, Gareth; Koudas, Nick; Wu, Xindong; Collins-Thompson, Kevyn ; Association for Computing Machinery -ACM-, Special Interest Group on Information Retrieval -SIGIR-; Association for Computing Machinery -ACM-, Special Interest Group on Hypertext, Hypermedia, and Web; Association for Computing Machinery -ACM-, Special Interest Group on Knowledge Discovery and Data Mining -SIGKDD-:
CIKM 2010, 19th International Conference on Information & Knowledge Management and Co-located Workshops. CD-ROM : October 26-30, 2010, Toronto, Ontario, Canada, proceedings
New York: ACM, 2010
ISBN: 978-1-4503-0099-5
S.1785-1788
International Conference on Information and Knowledge Management (CIKM) <19, 2010, Toronto>
Englisch
Konferenzbeitrag, Elektronische Publikation
Fraunhofer IAIS ()

Abstract
Matrix factorization methods are among the most common techniques for detecting latent components in data. Popular examples include the Singular Value Decomposition or Non- negative Matrix Factorization. Unfortunately, most meth- ods su er from high computational complexity and therefore do not scale to massive data. In this paper, we present a lin- ear time algorithm for the factorization of gigantic matrices that iteratively yields latent components. We consider a constrained matrix factorization s.t. the latent components form a simplex that encloses most of the remaining data. The algorithm maximizes the volume of that simplex and thereby reduces the displacement of data from the space spanned by the latent components. Hence, it also lowers the Frobenius norm, a common criterion for matrix factorization quality. Our algorithm is e\'0ecient, well-grounded in distance geometry, and easily applicable to matrices with billions of entries. In addition, the resulting factors allow for an in- tuitive interpretation of data: every data point can now be expressed as a convex combination of the most extreme and thereby often most descriptive instances in a collection of data. Extensive experimental validations on web-scale data, including 80 million images and 1.5 million twitter tweets, demonstrate superior performance compared to related fac- torization or clustering techniques.

: http://publica.fraunhofer.de/dokumente/N-148645.html