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Clustering, Hamming Embedding, Generalized LSH and the Max Norm

  • Behnam Neyshabur
  • Yury Makarychev
  • Nathan Srebro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8776)

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.

Keywords

Clustering Hamming Embedding LSH Max Norm 

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References

  1. Alon, N., Naor, A.: Approximating the cut-norm via grothendieck’s inequality. SIAM Journal on Computing 35(4), 787–803 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Andoni, A., Indyk, P.: Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. In: FOCS, pp. 459–468 (2006)Google Scholar
  3. Arora, S., Berger, E., Hazan, E., Kindler, G., Safra, M.: On non-approximability for quadratic programs. In: FOCS, pp. 206–215 (2005)Google Scholar
  4. Banerjee, A., Dhillon, I., Ghosh, J., Merugu, S., Modha, D.S.: A generalized maximum entropy approach to bregman co-clustering and matrix approximation. In: SIGKDD, pp. 509–514 (2004)Google Scholar
  5. Buchok, L.V.: Two new approaches to obtaining estimates in the danzer-grunbaum problem. Mathematical Notes 87(4), 489–496 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. Charikar, M., Wirth, A.: Maximizing quadratic programs: Extending grothendieck’s inequality. In: FOCS, pp. 54–60 (2004)Google Scholar
  7. Charikar, M.S.: Similarity estimation techniques from rounding algorithms. In: STOC (2002)Google Scholar
  8. Danzer, L., Grünbaum, B.: Über zwei probleme bezüglich konvexer körper von p. erdös und von vl klee. Mathematische Zeitschrift 79(1), 95–99 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  9. Dhillon, I., Subramanyam, M., Dharmendra, S.M.: Information-theoretic co-clustering. In: SIGKDD (2003)Google Scholar
  10. Gionis, A., Indyk, P., Motwani, R.: Similarity search in high dimensions via hashing. VLDB 99, 518–529 (1999)Google Scholar
  11. Indyk, P., Motwani, R.: Approximate nearest neighbors: towards removing the curse of dimensionality. In: STOC, pp. 604–613 (1998)Google Scholar
  12. Jalali, A., Chen, Y., Sanghavi, S., Xuo, H.: Clustering partially observed graphs via convex optimization. In: ICML (2011)Google Scholar
  13. Jalali, A., Srebro, N.: Clustering using max-norm constrained optimization. In: ICML (2012)Google Scholar
  14. Krivine, J.L.: Sur la constante de grothendieck. C. R. Acad. Sci. Paris Ser. A-B 284, 445–446 (1977)MathSciNetzbMATHGoogle Scholar
  15. Neyshabur, B., Yadollahpour, P., Makarychev, Y., Salakhutdinov, R., Srebro, N.: The power of asymmetry in binary hashing. In: NIPS (2013)Google Scholar
  16. Srebro, N., Rennie, J., Jaakkola, T.: Maximum margin matrix factorization. In: NIPS (2005)Google Scholar
  17. Srebro, N., Shraibman, A.: Rank, trace-norm and max-norm. In: Auer, P., Meir, R. (eds.) COLT 2005. LNCS (LNAI), vol. 3559, pp. 545–560. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. Thompson, A.C.: Minkowski Geometry. Cambridge University Press (1996)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Behnam Neyshabur
    • 1
  • Yury Makarychev
    • 1
  • Nathan Srebro
    • 1
  1. 1.Toyota Technological Institute at ChicagoJapan

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