Metric Inverted -An efficient inverted indexing

method for metric spaces

Benjamin SznajderJonathan MamouYosi MassMichal Shmueli-Scheuer

IBM Research - Haifa

Presented by: Shai Erera

Outline

Motivation Problem Definition Metric Inverted Index Retrieval Experiments Conclusions

Outline

Motivation Problem Definition Metric Inverted Index Retrieval Experiments Conclusions

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?

Outline

Motivation Problem Definition Metric Inverted Index Retrieval Experiments Conclusions

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]

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))

q

k=5

Outline

Motivation Problem Definition Metric Inverted Index Retrieval Experiments Conclusions

Metric Inverted Index

Assume a collection of objects each having m features – Object D = {F1:v1, F2:v2,…, Fm:vm}

– m metric spaces

Indexing steps– Lexicon creation (select candidates)– Invert objects (canonization to lexicon terms)

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

Metric inverted indexing – invert objects

Given object D = {F1:v1, F2:v2,…, Fm:vm}

Canonization – map features (Fi:vi) to lexicon entries– For each feature select the n nearest lexicon terms – D’ = {F1:v11, F1:v12, …F1:v1n,

F2:v21, F2:v22, …F2:v2n, …

Fm:vm1, Fm:vm2, …Fm:vmn}

Index D’ in the relevant posting-lists

Outline

Motivation Problem Definition Metric Inverted Index Retrieval Experiments Conclusions

Retrieval stage – term selection

Given Q = {F1:qv1, F2:qv2,…, Fm:qvm} Canonization

– For each feature select the n nearest lexicon terms

– Q’ = {F1:qv11, F1:qv12, …F1:qv1n, F2:qv21, F2:qv22, …F2:qv2n, … Fm:qvm1, Fm:qvm2, …Fm:qvmn}

Retrieval stage – Boolean Filtering

These m*n posting-lists will be queried via a Boolean Query

Two possible modes:– Strict-query-mode:

– Fuzzy-query-mode:

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))

Outline

Motivation Problem Definition Metric Inverted Index Retrieval Experiments Conclusions

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

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@K: MAP computed on relevant and retrieved lists of size k

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

Effectiveness

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

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

5 10 15 20 25 30

# nearest terms

MA

P

K=10

K=20

K=30

Effectiveness

MAP vs. lexicon size Number Nearest Terms =30

0.80.820.840.860.880.9

0.920.940.960.98

1

3000 12000 24000 48000

lexicon's size

MA

P

K=10

K=20

K=30

Effectiveness vs. Efficiency

MAP vs. number of comparisons Number Nearest Terms =30

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

0 50000 100000 150000 200000

#comparisons

MA

P

lexicon=3000

lexicon=12000

lexicon=24000

lexicon=48000

M-Tree vs. Metric Inverted

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

500000

5 10 20 30 40

top-k

# co

mp

aris

on

s

M-Tree

MII - lexicon=3000

MII - lexicon=12000

MII - lexicon=24000

MII - lexicon=48000

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

Outline

Motivation Problem Definition Metric Inverted Index Retrieval Experiments Conclusions

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