Minimal Loss Hashing for Compact Binary Codes

1. Minimal Loss Hashing for Compact Binary Codes Mohammad Norouzi David Fleet University of Toronto

2. Near Neighbor Search

3. Near Neighbor Search

4. Near Neighbor Search

5. Similarity-Preserving Binary Hashing • Why binary codes? • Sub-linear search using hash indexing(even exhaustive linear search is fast) • Binary codes are storage-efficient

6. binary quantization parameter matrix input vector Similarity-Preserving Binary Hashing Hash function kth row of W Random projections used by locality-sensitive hashing (LSH) and related techniques [Indyk & Motwani ‘98; Charikar ’02; Raginsky & Lazebnik ’09]

7. Learning Binary Hash Functions • Reasons to learn hash functions: • to find more compact binary codes • to preserve general similarity measures • Previous work • boosting [Shakhnarovich et al ’03] • neural nets [Salakhutdinov & Hinton 07; Torralba et al 07] • spectral methods [Weiss et al ’08] • loss-based methods [Kulis & Darrel ‘09] • …

8. Formulation Input data: Similarity labels: Hash function: Binary codes:

9. Hash code quality measured by a loss function: : code for item 1 : code for item 2 : similarity label Loss Function measures consistency binary codes similarity label cost Similar items should map to nearby hash codes Dissimilar items should map to very different codes

10. Dissimilar items should map to codes no closer than bits Hinge Loss Similar items should map to codes within a radius of bits

11. Given training pairs with similarity labels Empirical Loss • Good: • incorporates quantization and Hamming distance • Not so good: • discontinuous, non-convex objective function

12. We minimize an upper bound on empirical loss, inspired by structural SVM formulations [Taskar et al ‘03; Tsochantaridis et al ‘04; Yu & Joachims ‘09]

13. Bound on loss LHS = RHS

14. Bound on loss • Remarks: • piecewise linear in W • convex-concave in W • relates to structural SVM with latent variables [Yu & Joachims ‘09]

15. Bound on Empirical Loss • Loss-adjusted inference • Exact • Efficient

16. Perceptron-like Learning • Initialize with LSH • Iterate over pairs • Compute , the codes given by • Solve loss-adjusted inference • Update [McAllester et al.., 2010]

17. Experiment: Euclidean ANN Similarity based on Euclidean distance • Datasets • LabelMe (GIST) • MNIST (pixels) • PhotoTourism (SIFT) • Peekaboom (GIST) • Nursery (8D attributes) • 10D Uniform

18. Experiment: Euclidean ANN 22K LabelMe • 512 GIST • 20K training • 2K testing • ~1% of pairs are similar Evaluation • Precision: #hits / number of items retrieved • Recall: #hits / number of similar items

19. Techniques of interest • MLH – minimal loss hashing (This work) • LSH – locality-sensitive hashing (Charikar ‘02) • SH – spectral hashing (Weiss, Torralba & Fergus ‘09) • SIKH – shift-Invariant kernel hashing (Raginsky & Lazebnik ‘09) • BRE – Binary reconstructive embedding (Kulis & Darrel ‘09)

20. Euclidean Labelme – 32 bits

21. Euclidean Labelme – 32 bits

22. Euclidean Labelme – 32 bits

23. Euclidean Labelme – 64 bits

24. Euclidean Labelme – 64 bits

25. Euclidean Labelme – 128 bits

26. Euclidean Labelme – 256 bits

27. Experiment: Semantic ANN • Semantic similarity measure based on annotations(object labels) from LabelMe database: • 512D GIST, 20K training, 2K testing Techniques of interest • MLH – minimal loss hashing • NN – nearest neighbor in GIST space • NNCA – multilayer network with RBM pre-training and nonlinear NCA fine tuning [Torralba, et al. ’09; Salakhutdinov & Hinton ’07]

28. Semantic LabelMe

29. Semantic LabelMe

33. Summary A formulation for learning binary hash functionsbased on • structured prediction with latent variables • hinge-like loss function for similarity search Experiments show that with minimal loss hashing • binary codes can be made more compact • semantic similarity based on human labels can be preserved

34. Thank you! • Questions?