Minimal Loss Hashing for Compact Binary Codes

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Minimal Loss Hashing for Compact Binary Codes

• Mohammad Norouzi
• David Fleet
• University of Toronto

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Near Neighbor Search
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Near Neighbor Search
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Near Neighbor Search
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Similarity-Preserving Binary Hashing

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

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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
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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

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Formulation
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Loss Function
Similar items should map to nearby hash
codes Dissimilar items should map to very
different codes
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Hinge Loss
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Empirical Loss

• Good
• incorporates quantization and Hamming distance

• Not so good
• discontinuous, non-convex objective function

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We minimize an upper bound on empirical loss,
inspired by structural SVM formulations
Taskar et al 03 Tsochantaridis et al 04 Yu
Joachims 09
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Bound on loss
LHS RHS
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Bound on loss

• Remarks
• piecewise linear in W
• convex-concave in W
• relates to structural SVM with latent variables
  Yu Joachims 09

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Bound on Empirical Loss

• Loss-adjusted inference
• Exact
• Efficient

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Perceptron-like Learning
McAllester et al.., 2010
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Experiment Euclidean ANN
Similarity based on Euclidean distance

• Datasets
• LabelMe (GIST)
• MNIST (pixels)
• PhotoTourism (SIFT)
• Peekaboom (GIST)
• Nursery (8D attributes)
• 10D Uniform

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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

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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)

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Euclidean Labelme 32 bits
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Euclidean Labelme 32 bits
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Euclidean Labelme 32 bits
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Euclidean Labelme 64 bits
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Euclidean Labelme 64 bits
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Euclidean Labelme 128 bits
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Euclidean Labelme 256 bits
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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

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Semantic LabelMe
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Semantic LabelMe
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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

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• Thank you!
• Questions?