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. Near Neighbor Search. Near Neighbor Search. Near Neighbor Search. Similarity-Preserving Binary Hashing. Why binary codes? - PowerPoint PPT PresentationTRANSCRIPT
Minimal Loss Hashing for Compact Binary Codes
Mohammad Norouzi
David Fleet
University of Toronto
Near Neighbor Search
Near Neighbor Search
Near Neighbor Search
Similarity-Preserving Binary Hashing
Why binary codes?
Sub-linear search using hash indexing
(even exhaustive linear search is fast)
Binary codes are storage-efficient
input vector
parametermatrix
binaryquantization
Random projections used by locality-sensitive hashing
(LSH) and related techniques [Indyk & Motwani ‘98;
Charikar ’02; Raginsky & Lazebnik ’09]
Similarity-Preserving Binary Hashing
Hash function
kth row of W
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]
…
Formulation
Input data:
Similarity labels:
Hash function:
Binary codes:
Loss Function
Hash code quality measured by a loss function:
similarity label
binarycodes : code for item 1
: code for item 2
: similarity label
cost
measures consistency
Similar items should map to nearby hash codes
Dissimilar items should map to very different codes
Hinge Loss
Similar items should map to codes within a radius of bits
Dissimilar items should map to codes no closer than bits
Empirical Loss
Good:
incorporates quantization and Hamming distance
Not so good:
discontinuous, non-convex objective function
Given training pairs with similarity labels
We minimize an upper bound on empirical loss,
inspired by structural SVM formulations
[Taskar et al ‘03; Tsochantaridis et al ‘04; Yu &
Joachims ‘09]
Bound on loss
LHS = RHS
Bound on loss
Remarks: piecewise linear in W convex-concave in W relates to structural SVM with latent variables
[Yu & Joachims ‘09]
Bound on Empirical Loss
Loss-adjusted inference
Exact
Efficient
Perceptron-like Learning
Initialize with LSH
Iterate over pairs
• Compute , the codes given by
• Solve loss-adjusted inference
• Update
[McAllester et al.., 2010]
Experiment: Euclidean ANN
Similarity based on Euclidean distance
Datasets LabelMe (GIST) MNIST (pixels) PhotoTourism (SIFT) Peekaboom (GIST) Nursery (8D attributes) 10D Uniform
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
Techniques of interest
MLHMLH – minimal loss hashing (This work)
LSHLSH – locality-sensitive hashing (Charikar ‘02)
SHSH – spectral hashing (Weiss, Torralba & Fergus ‘09)
SIKHSIKH – shift-Invariant kernel hashing (Raginsky & Lazebnik ‘09)
BRE BRE – Binary reconstructive embedding (Kulis & Darrel ‘09)
Euclidean Labelme – 32 bits
Euclidean Labelme – 32 bits
Euclidean Labelme – 32 bits
Euclidean Labelme – 64 bits
Euclidean Labelme – 64 bits
Euclidean Labelme – 128 bits
Euclidean Labelme – 256 bits
Experiment: Semantic ANN
Semantic similarity measure based on annotations(object labels) from LabelMe database:
512D GIST, 20K training, 2K testing
Techniques of interest
MLHMLH – minimal loss hashing
NNNN – nearest neighbor in GIST space
NNCA NNCA – multilayer network with RBM pre-training and nonlinear NCA fine tuning [Torralba, et al. ’09; Salakhutdinov & Hinton ’07]
Semantic LabelMe
Semantic LabelMe
Summary
A formulation for learning binary hash functions
based 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
Thank you!
Questions?