Indexing and Data Mining in Multimedia Databases

Indexing and Data Mining in Multimedia Databases Christos Faloutsos CMU www.cs.cmu.edu/~christos

Outline
Goal: ‘Find similar / interesting things’
Problem - Applications
Indexing - similarity search
New tools for Data Mining: Fractals
Conclusions
Resources

Problem
Given a large collection of (multimedia) records, find similar/interesting things, ie:
Allow fast, approximate queries, and
Find rules/patterns

Sample queries
Similarity search
Find pairs of branches with similar sales patterns
find medical cases similar to Smith's
Find pairs of sensor series that move in sync
Find shapes like a spark-plug

Sample queries –cont’d
Rule discovery
Clusters (of branches; of sensor data; ...)
Forecasting (total sales for next year?)
Outliers (eg., unexpected part failures; fraud detection)

Outline
Conclusions
related projects @ CMU and resourses

Indexing - Multimedia
Problem:
given a set of (multimedia) objects,
find the ones similar to a desirable query object

distance function: by expert day $price 1 365 day $price 1 365 day $price 1 365

‘GEMINI’ - Pictorially day 1 365 day 1 365 S1 Sn F(S1) F(Sn) eg, avg eg,. std

Remaining issues
how to extract features automatically?
how to merge similarity scores from different media

Outline
Visualization: Fastmap
Relevance feedback: FALCON
Data Mining / Fractals
Conclusions

FastMap ?? 0 1 100 100 100 O5 1 0 100 100 100 O4 100 100 0 1 1 O3 100 100 1 0 1 O2 100 100 1 1 0 O1 O5 O4 O3 O2 O1 ~100 ~1

FastMap
Multi-dimensional scaling (MDS) can do that, but in O(N**2) time
We want a linear algorithm: FastMap [SIGMOD95]

Applications: time sequences
given n co-evolving time sequences
visualize them + find rules [ICDE00]
time rate HKD JPY DEM

Applications - financial
currency exchange rates [ICDE00]
USD(t) USD(t-5) FRF GBP JPY HKD

Applications - financial
currency exchange rates [ICDE00]
USD(t) USD(t-5) USD HKD JPY FRF DEM GBP

Application: VideoTrails
[ACM MM97]

VideoTrails - usage
scene-cut detection (about 10% errors)
scene classification (eg., dialogue vs action)

Outline
Visualization: Fastmap
Data Mining / Fractals
Conclusions

Merging similarity scores
eg., video: text, color, motion, audio
weights change with the query!
solution 1: user specifies weights
solution 2: user gives examples 
and we ‘learn’ what he/she wants: rel. feedback (Rocchio, MARS, MindReader)
but: how about disjunctive queries?

‘FALCON’ Inverted Vs Vs Trader wants only ‘unstable’ stocks

“Single query point” methods Rocchio + + + + + + x

“Single query point” methods Rocchio MindReader + + + + + + MARS The averaging affect in action... x x x + + + + + + + + + + + +

+ + + + + Main idea: FALCON Contours feature1 (eg., temperature) feature2 eg., frequency [Wu+, vldb2000]

Conclusions for indexing + visualization
GEMINI: fast indexing, exploiting off-the-shelf SAMs
FastMap: automatic feature extraction in O( N ) time
FALCON: relevance feedback for disjunctive queries

Outline
Conclusions
Resourses

Data mining & fractals – Road map
Motivation – problems / case study
Definition of fractals and power laws
Solutions to posed problems
More examples

Problem #1 - spatial d.m.
Galaxies (Sloan Digital Sky Survey w/ B. Nichol)
- ‘spiral’ and ‘ elliptical ’ galaxies
(stores & households ; mpg & MTBF...)
- patterns? ( not Gaussian; not uniform)
attraction/repulsion?
separability??

Problem#2: dim. reduction
given attributes x 1 , ... x n
possibly, non-linearly correlated
drop the useless ones
(Q: why?
A: to avoid the ‘dimensionality curse’)

Answer:
Fractals / self-similarities / power laws

What is a fractal?
= self-similar point set, e.g., Sierpinski triangle:
... zero area; infinite length!

Definitions (cont’d)
Paradox: Infinite perimeter ; Zero area!
‘dimensionality’: between 1 and 2
actually: Log(3)/Log(2) = 1.58… (long story)

Intrinsic (‘fractal’) dimension
Q: fractal dimension of a line?
Eg: #cylinders; miles / gallon 4 2 3 3 2 4 1 5 y x

A: nn ( <= r ) ~ r^ 1
(‘power law’: y=x^a)

A: nn ( <= r ) ~ r^ 1
(‘power law’: y=x^a)
Q: fd of a plane?
A: nn ( <= r ) ~ r^ 2
fd== slope of (log(nn) vs log(r) )

Sierpinsky triangle == ‘correlation integral’ log( r ) log(#pairs within <=r ) 1.58

Road map
Motivation – problems / case studies
More examples
Conclusions

Solution#1: spatial d.m.
Galaxies (Sloan Digital Sky Survey w/ B. Nichol - ‘BOPS’ plot - [sigmod2000])
clusters?
separable?
attraction/repulsion?
data ‘scrubbing’ – duplicates?

Solution#1: spatial d.m. log(r) log(#pairs within <=r ) spi-spi spi-ell ell-ell - 1.8 slope - plateau! - repulsion!

Solution#1: spatial d.m. log(r) log(#pairs within <=r ) spi-spi spi-ell ell-ell - 1.8 slope - plateau! - repulsion! [w/ Seeger, Traina, Traina, SIGMOD00]

spatial d.m. Heuristic on choosing # of clusters r1 r2 r1 r2

Solution#1: spatial d.m. log(r) log(#pairs within <=r ) spi-spi spi-ell ell-ell - 1.8 slope - plateau! - repulsion!

Solution#1: spatial d.m. log(r) log(#pairs within <=r ) spi-spi spi-ell ell-ell
- 1.8 slope
- plateau!
repulsion!!
- duplicates

Problem #2: Dim. reduction

Solution:
drop the attributes that don’t increase the ‘partial f.d.’ PFD
dfn: PFD of attribute set A is the f.d. of the projected cloud of points [w/ Traina, Traina, Wu, SBBD00]

Problem #2: dim. reduction PFD~1 PFD~1 global FD=1 PFD=1 PFD=0 PFD=1

Problem #2: dim. reduction PFD~1 PFD=1 global FD=1 PFD=1 PFD=0 PFD=1 Notice: ‘max variance’ would fail here

Problem #2: dim. reduction PFD~1 PFD~1 global FD=1 PFD=1 PFD=0 PFD=1 Notice: SVD would fail here

Road map
More examples
fractals
power laws
Conclusions

disk traffic
Not Poisson, not(?) iid - BUT: self-similar
How to model it?
time #bytes

traffic
disk traces (80-20 ‘law’ = ‘multifractal’ [ICDE’02])
time #bytes 20% 80%

Traffic
Many other time-sequences are bursty/clustered: (such as?)

Tape accesses # tapes needed, to retrieve n records? (# days down, due to failures / hurricanes / communication noise...) time Tape#1 Tape# N

Tape accesses # tapes retrieved # qual. records 50-50 = Poisson real time Tape#1 Tape# N

More apps: Brain scans
Oct-trees; brain-scans
octree levels Log(#octants) 2.63 = fd

GIS points
Cross-roads of Montgomery county:
any rules?

GIS
A: self-similarity:
intrinsic dim. = 1.51
avg#neighbors(<= r ) = r^D
log( r ) log(#pairs(within <= r)) 1.51

Examples:LB county
Long Beach county of CA (road end-points)

More fractals:
cardiovascular system: 3 (!)
stock prices (LYCOS) - random walks: 1.5
Coastlines: 1.2-1.58 (?)
1 year 2 years

Road map
More examples
fractals
power laws
Conclusions

Fractals <-> Power laws
self-similarity ->
<=> fractals
<=> scale-free
<=> power-laws (y=x^ a , F=C*r^(-2))
log( r ) log(#pairs within <=r ) 1.58

Zipf’s law Bible RANK-FREQUENCY plot: (in log-log scales) Zipf’s (first) Law: log(rank) log(freq) “ the” “ and” 

Zipf’s law
similarly for first names (slope ~-1)
last names (~ -0.7)
etc

More power laws
Energy of earthquakes (Gutenberg-Richter law) [simscience.org]
log(count) magnitude day amplitude

Clickstream data <url, u-id, ....> Web Site Traffic log(freq) log(count) Zipf

Lotka’s law
library science (Lotka’s law of publication count); and citation counts: ( citeseer.nj.nec.com 6/2001)
log(#citations) log(count) J. Ullman

Korcak’s law Scandinavian lakes area vs complementary cumulative count (log-log axes) log(count( >= area)) log(area)

More power laws: Korcak Japan islands; area vs cumulative count (log-log axes) log(area) log(count( >= area))

(Korcak’s law: Aegean islands)

Olympic medals: log rank log(# medals) USA China Russia

SALES data – store#96 # units sold count of products

TELCO data # of service units count of customers

More power laws on the Internet degree vs rank, for Internet domains (log-log) [sigcomm99] log(rank) log(degree) -0.82

Even more power laws:
Income distribution (Pareto’s law);
duration of UNIX jobs [Harchol-Balter]
Distribution of UNIX file sizes
Web graph [CLEVER-IBM; Barabasi]

Overall Conclusions:
‘ Find similar/interesting things’ in multimedia databases
Indexing: feature extraction (‘GEMINI’)
automatic feature extraction: FastMap

Conclusions - cont’d
New tools for Data Mining: Fractals/power laws:
appear everywhere
lead to skewed distributions (Gaussian, Poisson, uniformity, independence)
‘ correlation integral’ for separability/cluster detection
PFD for dimensionality reduction

Resources:
Software and papers:
www . cs . cmu .edu/~christos
Fractal dimension (FracDim)
Separability (sigmod 2000, kdd2001)
Relevance feedback for query by content (FALCON – vldb 2000)

Resources
Manfred Schroeder “ Chaos, Fractals and Power Laws ”

Indexing and Data Mining in Multimedia Databases

by Tommy96 on May 10, 2010

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Indexing and Data Mining in Multimedia Databases — Presentation Transcript