Metric Inverted - An efficient inverted indexing method for metric spaces

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Metric Inverted -An efficient inverted
indexingmethod for metric spaces

• Benjamin Sznajder
• Jonathan Mamou
• Yosi Mass
• Michal Shmueli-Scheuer
• IBM Research - Haifa

Presented by Shai Erera
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Outline

• Motivation
• Problem Definition
• Metric Inverted Index
• Retrieval
• Experiments
• Conclusions

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Outline

• Motivation
• Problem Definition
• Metric Inverted Index
• Retrieval
• Experiments
• Conclusions

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Motivation

• Web 2.0 enables mass multimedia productions
• Still, search is limited to manually added
  metadata
• State of the art solutions for CBIR (Content
  Based Image Retrieval) do not scale
• Reveal linear scalability in the collection size
  due to large number of distance computations
• Can we use textIR methods to scale up CBIR?

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Outline

• Motivation
• Problem Definition
• Metric Inverted Index
• Retrieval
• Experiments
• Conclusions

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Problem definition

• Low level image features can be generalized to
  Metric Spaces
• Metric Space An ordered pair (S,d) , where S is
  a domain and d a distance function d S x S ? R
  such that
• d satisfies non-negativity, reflexibility,
  symmetry and triangle inequality
• The best-k results for a query in a metric space
  are the k objects with the smallest distance to
  the query
• Convert distances to scores (small distance
  high score) between 0,1

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Problem definition

• Top-K Problem
• Assume m metric spaces, a Query Q, an aggregate
  function f and a score function sd()
• Retrieve the best k objects D with highest
  f(sd1(Q,D), sd2(Q,D)sdm(Q,D))

k5
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Outline

• Motivation
• Problem Definition
• Metric Inverted Index
• Retrieval
• Experiments
• Conclusions

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Metric Inverted Index

• Assume a collection of objects each having m
  features
• Object D F1v1, F2v2,, Fmvm
• m metric spaces
• Indexing steps
• Lexicon creation (select candidates)
• Invert objects (canonization to lexicon terms)

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Metric inverted indexing Lexicon creation

• Number of different features too large
• Need to select candidates
• Naïve solution
• Lexicon of fixed size l
• Select randomly l/m documents and extract their
  features
• These l features form our lexicon
• Improvement
• Replace the random choice by clustering (K-Means
  etc.)
• Keep the lexicon in an M-Tree structure

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Metric inverted indexing invert objects

• Given object D F1v1, F2v2,, Fmvm
• Canonization map features (Fivi) to lexicon
  entries
• For each feature select the n nearest lexicon
  terms
• D F1v11, F1v12, F1v1n, F2v21,
  F2v22, F2v2n, Fmvm1, Fmvm2,
  Fmvmn
• Index D in the relevant posting-lists

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Outline

• Motivation
• Problem Definition
• Metric Inverted Index
• Retrieval
• Experiments
• Conclusions

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Retrieval stage term selection

• Given Q F1qv1, F2qv2,, Fmqvm
• Canonization
• For each feature select the n nearest lexicon
  terms
• Q F1qv11, F1qv12, F1qv1n,
  F2qv21, F2qv22, F2qv2n,
  Fmqvm1, Fmqvm2, Fmqvmn

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Retrieval stage Boolean Filtering

• These mn posting-lists will be queried via a
  Boolean Query
• Two possible modes
• Strict-query-mode
• Fuzzy-query-mode

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Retrieval stage Scoring

• Documents retrieved by the Boolean Query are
  fully scored
• Return the best k objects with the highest
  aggregate score
• f(sd_1(Q,D),sd_2(Q,D), ,sd_m(Q,D))

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Outline

• Motivation
• Problem Definition
• Metric Inverted Index
• Retrieval
• Experiments
• Conclusions

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Experiments

• Focus on
• Efficiency
• Effectiveness
• Collection of 160,000 images from Flickr
• 3 features are extracted from each image
• EdgeHistogram, ScalableColor and ColorLayout
• 180 queries Fuzzy-Query-Mode
• Sampled from the collection of images
• Compared to M-tree data-structure

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Experiments Measures Used

• Effectiveness MAP is a natural candidate for
  measuring
• Problem In Image Retrieval, no document is
  irrelevant
• Solution we defined as relevant the k highest
  scored documents in the collection (according to
  the M-Tree computation)
• MAP_at_K MAP computed on relevant and retrieved
  lists of size k

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Experiments Measures Used contd.

• Efficiency we compute the number of computations
  per query
• A computation unit (cu) is a distance computation
  call between two feature values

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Effectiveness

• MAP vs. number of Nearest Terms
• size of the lexicon 12000

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Effectiveness

• MAP vs. lexicon size
• Number Nearest Terms 30

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Effectiveness vs. Efficiency

• MAP vs. number of comparisons
• Number Nearest Terms 30

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M-Tree vs. Metric Inverted

• Number of comparisons vs. top-k
• Number Nearest Terms 30

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Outline

• Motivation
• Problem Definition
• Metric Inverted Index
• Retrieval
• Experiments
• Conclusions

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Conclusions

• We reduce the gap between Text IR and Multimedia
  Retrieval
• Our method achieves very good approximation (MAP
  98)
• Our method improves drastically the efficiency
  (90) over state-of-the-art methods