1. Indexing and Data Mining in Multimedia Databases
Christos Faloutsos
CMU

2. Outline Goal: ‘Find similar / interesting things’
Problem - Applications
Indexing - similarity search
New tools for Data Mining: Fractals
Conclusions
Resources
USC 2001
C. Faloutsos

3. Problem
Given a large collection of (multimedia) records, find similar/interesting things, ie:
Allow fast, approximate queries, and
Find rules/patterns
USC 2001
C. Faloutsos

4. 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
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5. 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)
USC 2001
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6. Outline Goal: ‘Find similar / interesting things’
Problem - Applications
Indexing - similarity search
New tools for Data Mining: Fractals
Conclusions
related CMU and resourses
USC 2001
C. Faloutsos

7. Indexing - Multimedia Problem: given a set of (multimedia) objects,
find the ones similar to a desirable query object
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8. distance function: by expert
day
$price 1
365
day
$price 1
365
day
$price 1
365
distance function: by expert
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9. ‘GEMINI’ - Pictorially
eg,. std S1
F(S1) 1
365
day
F(Sn) Sn
eg, avg 1
365
day
USC 2001
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10. Remaining issues how to extract features automatically?
how to merge similarity scores from different media
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11. Outline Goal: ‘Find similar / interesting things’
Problem - Applications
Indexing - similarity search
Visualization: Fastmap
Relevance feedback: FALCON
Data Mining / Fractals
Conclusions
USC 2001
C. Faloutsos

12. FastMap
~100 O1 O2 O3 O4 O5 1
100 ?? ~1
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13. FastMap
Multi-dimensional scaling (MDS) can do that, but in O(N**2) time
We want a linear algorithm: FastMap [SIGMOD95]
USC 2001
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14. Applications: time sequences
given n co-evolving time sequences
visualize them + find rules [ICDE00]
DEM
rate
JPY
HKD
time
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15. Applications - financial
currency exchange rates [ICDE00]
FRF
GBP
JPY
HKD
USD(t)
USD(t-5)
USC 2001
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16. Applications - financial
currency exchange rates [ICDE00]
USD
HKD
JPY
FRF
DEM
GBP
USD(t)
USD(t-5)
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17. Application: VideoTrails
[ACM MM97]
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18. VideoTrails - usage scene-cut detection (about 10% errors)
scene classification (eg., dialogue vs action)
USC 2001
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19. Outline Goal: ‘Find similar / interesting things’
Problem - Applications
Indexing - similarity search
Visualization: Fastmap
Relevance feedback: FALCON
Data Mining / Fractals
Conclusions
USC 2001
C. Faloutsos

20. 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?
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21. ‘FALCON’ Vs Inverted Vs Trader wants only ‘unstable’ stocks USC 2001
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22. “Single query point” methods+ + + x + + +
Rocchio
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23. “Single query point” methods+ + + + + x x x + + +
Rocchio
MindReader
MARS
The averaging affect in action...
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24. Main idea: FALCON Contours
[Wu+, vldb2000] + +
feature2
eg., frequency + + +
feature1 (eg., temperature)
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25. 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
USC 2001
C. Faloutsos

26. Outline Goal: ‘Find similar / interesting things’
Problem - Applications
Indexing - similarity search
New tools for Data Mining: Fractals
Conclusions
Resourses
USC 2001
C. Faloutsos

27. Data mining & fractals – Road map
Motivation – problems / case study
Definition of fractals and power laws
Solutions to posed problems
More examples
USC 2001
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28. 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??
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29. Problem#2: dim. reduction
given attributes x1, ... xn
possibly, non-linearly correlated
drop the useless ones
(Q: why?
A: to avoid the ‘dimensionality curse’)
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30. Answer: Fractals / self-similarities / power laws USC 2001
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31. What is a fractal?
= self-similar point set, e.g., Sierpinski triangle:
zero area;
infinite length!
...
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32. Definitions (cont’d) Paradox: Infinite perimeter ; Zero area!
‘dimensionality’: between 1 and 2
actually: Log(3)/Log(2) = 1.58… (long story)
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33. Intrinsic (‘fractal’) dimension
Eg:
#cylinders; miles / gallon
Q: fractal dimension of a line? x y 5 1 4 2 3
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34. Intrinsic (‘fractal’) dimension
Q: fractal dimension of a line?
A: nn ( <= r ) ~ r^1
(‘power law’: y=x^a)
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35. Intrinsic (‘fractal’) dimension
Q: fractal dimension of a line?
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) )
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36. Sierpinsky triangle == ‘correlation integral’ log(#pairs
log( r )
log(#pairs
within <=r )
1.58
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37. Road map Motivation – problems / case studies
Definition of fractals and power laws
Solutions to posed problems
More examples
Conclusions
USC 2001
C. Faloutsos

38. Solution#1: spatial d.m.
Galaxies (Sloan Digital Sky Survey w/ B. Nichol - ‘BOPS’ plot - [sigmod2000])
clusters?
separable?
attraction/repulsion?
data ‘scrubbing’ – duplicates?
USC 2001
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39. Solution#1: spatial d.m. log(#pairs within <=r ) - 1.8 slope
- plateau!
- repulsion!
ell-ell
spi-spi
spi-ell
log(r)
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40. [w/ Seeger, Traina, Traina, SIGMOD00]
Solution#1: spatial d.m.
[w/ Seeger, Traina, Traina, SIGMOD00]
log(#pairs within <=r )
- 1.8 slope
- plateau!
- repulsion!
ell-ell
spi-spi
spi-ell
log(r)
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41. spatial d.m. r1 r2 r2 r1 Heuristic on choosing # of clusters USC 2001
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42. Solution#1: spatial d.m. log(#pairs within <=r ) - 1.8 slope
- plateau!
- repulsion!
ell-ell
spi-spi
spi-ell
log(r)
USC 2001
C. Faloutsos

43. Solution#1: spatial d.m. log(#pairs within <=r ) - 1.8 slope
- plateau!
repulsion!!
ell-ell
spi-spi
-duplicates
spi-ell
log(r)
USC 2001
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44. Problem #2: Dim. reduction
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45. 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]
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46. Problem #2: dim. reduction
global FD=1
PFD=1
PFD~1
PFD=0
PFD=1
PFD~1
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47. Problem #2: dim. reduction
global FD=1
PFD=1
PFD=1
Notice: ‘max variance’ would fail here
PFD=0
PFD=1
PFD~1
USC 2001
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48. Problem #2: dim. reduction
global FD=1
PFD=1
PFD~1
Notice: SVD would fail here
PFD=0
PFD=1
PFD~1
USC 2001
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49. Road map Motivation – problems / case studies
Definition of fractals and power laws
Solutions to posed problems
More examples
fractals
power laws
Conclusions
USC 2001
C. Faloutsos

50. disk traffic Not Poisson, not(?) iid - BUT: self-similar
How to model it?
time
#bytes
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51. traffic disk traces (80-20 ‘law’ = ‘multifractal’ [ICDE’02]) 20% 80%
#bytes
time
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52. Traffic Many other time-sequences are bursty/clustered: (such as?)
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53. Tape accesses # tapes needed, to retrieve n records?
(# days down, due to failures / hurricanes / communication noise...)
time
Tape#1
Tape# N
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54. Tape accesses 50-50 = Poisson # tapes retrieved Tape#1 Tape# N real
time
Tape#1
Tape# N
real
# qual. records
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55. More apps: Brain scans Oct-trees; brain-scans Log(#octants) 2.63 = fd
octree levels
Log(#octants)
2.63 = fd
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56. GIS points Cross-roads of Montgomery county: any rules? USC 2001
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57. GIS A: self-similarity: intrinsic dim. = 1.51
avg#neighbors(<= r ) = r^D
log(#pairs(within <= r))
1.51
log( r )
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58. Examples:LB county Long Beach county of CA (road end-points) USC 2001
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59. More fractals: cardiovascular system: 3 (!)
stock prices (LYCOS) - random walks: 1.5
Coastlines: (?)
1 year
2 years
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60. USC 2001
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61. Road map Motivation – problems / case studies
Definition of fractals and power laws
Solutions to posed problems
More examples
fractals
power laws
Conclusions
USC 2001
C. Faloutsos

62. Fractals <-> Power laws
self-similarity ->
<=> fractals
<=> scale-free
<=> power-laws (y=x^a, F=C*r^(-2))
log(#pairs
within <=r )
1.58
log( r )
USC 2001
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63. Zipf’s law “the” log(freq) “and” Bible
RANK-FREQUENCY plot: (in log-log scales)
log(rank)
Zipf’s (first) Law:
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64. Zipf’s law similarly for first names (slope ~-1) last names (~ -0.7)
etc
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65. More power laws
Energy of earthquakes (Gutenberg-Richter law) [simscience.org]
log(count)
amplitude
day
magnitude
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66. Clickstream data <url, u-id, ....> Web Site Traffic log(count)
log(freq)
log(count)
Zipf
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67. Lotka’s law
library science (Lotka’s law of publication count); and citation counts: (citeseer.nj.nec.com 6/2001)
log(count)
J. Ullman
log(#citations)
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68. Korcak’s law log(count( >= area))
Scandinavian lakes area vs complementary cumulative count (log-log axes)
log(area)
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69. More power laws: Korcak
log(count( >= area))
Japan islands;
area vs cumulative count (log-log axes)
log(area)
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70. (Korcak’s law: Aegean islands)
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71. Olympic medals: log(# medals) Russia China USA log rank USC 2001
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72. SALES data – store#96 count of products # units sold USC 2001
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73. TELCO data
count of
customers
# of service units
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74. More power laws on the Internet
log(degree)
-0.82
log(rank)
degree vs rank, for Internet domains (log-log) [sigcomm99]
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75. 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]
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76. Overall Conclusions:
‘Find similar/interesting things’ in multimedia databases
Indexing: feature extraction (‘GEMINI’)
automatic feature extraction: FastMap
Relevance feedback: FALCON
USC 2001
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77. 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
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78. 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)
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79. Resources Manfred Schroeder “Chaos, Fractals and Power Laws” USC 2001
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