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

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U. of Alberta, 2001C. Faloutsos2 Outline Goal: ‘Find similar / interesting things’ Problem - Applications Indexing - similarity search New tools for Data Mining: Fractals Conclusions Resources

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U. of Alberta, 2001C. Faloutsos3 Problem Given a large collection of (multimedia) records, find similar/interesting things, ie: Allow fast, approximate queries, and Find rules/patterns

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U. of Alberta, 2001C. Faloutsos4 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

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U. of Alberta, 2001C. Faloutsos5 Sample queries –cont’d Rule discovery –Clusters (of patients; of customers;...) –Forecasting (total sales for next year?) –Outliers (eg., fraud detection)

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U. of Alberta, 2001C. Faloutsos6 Outline Goal: ‘Find similar / interesting things’ Problem - Applications Indexing - similarity search New tools for Data Mining: Fractals Conclusions Resourses

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U. of Alberta, 2001C. Faloutsos7 Indexing - Multimedia Problem: given a set of (multimedia) objects, find the ones similar to a desirable query object (quickly!)

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U. of Alberta, 2001C. Faloutsos8 day $price 1365 day $price 1365 day $price 1365 distance function: by expert

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U. of Alberta, 2001C. Faloutsos9 day 1365 day 1365 S1 Sn F(S1) F(Sn) ‘GEMINI’ - Pictorially eg, avg eg,. std off-the-shelf S.A.Ms (spatial Access Methods)

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U. of Alberta, 2001C. Faloutsos10 ‘GEMINI’ fast; ‘correct’ (=no false dismissals) used for –images (eg., QBIC) (2x, 10x faster) –shapes (27x faster) –video (eg., InforMedia) –time sequences ([Rafiei+Mendelzon], ++)

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U. of Alberta, 2001C. Faloutsos11 Remaining issues how to extract features automatically? how to merge similarity scores from different media

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U. of Alberta, 2001C. Faloutsos12 Outline Goal: ‘Find similar / interesting things’ Problem - Applications Indexing - similarity search –Visualization: Fastmap –Relevance feedback: FALCON Data Mining / Fractals Conclusions

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U. of Alberta, 2001C. Faloutsos13 FastMap O1O2O3O4O5 O1011100 O2101100 O3110100 O4100 01 O5100 10 ~100 ~1 ??

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U. of Alberta, 2001C. Faloutsos14 FastMap Multi-dimensional scaling (MDS) can do that, but in O(N**2) time We want a linear algorithm: FastMap [SIGMOD95]

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U. of Alberta, 2001C. Faloutsos15 Applications: time sequences given n co-evolving time sequences visualize them + find rules [ICDE00] time rate HKD JPY DEM

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U. of Alberta, 2001C. Faloutsos16 Applications - financial currency exchange rates [ICDE00] USD(t) USD(t-5) FRF GBP JPY HKD

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U. of Alberta, 2001C. Faloutsos17 Applications - financial currency exchange rates [ICDE00] USD HKD JPY FRF DEM GBP USD(t) USD(t-5)

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U. of Alberta, 2001C. Faloutsos18 Application: VideoTrails [ACM MM97]

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U. of Alberta, 2001C. Faloutsos19 VideoTrails - usage scene-cut detection (about 10% errors) scene classification (eg., dialogue vs action)

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U. of Alberta, 2001C. Faloutsos20 Outline Goal: ‘Find similar / interesting things’ Problem - Applications Indexing - similarity search –Visualization: Fastmap –Relevance feedback: FALCON Data Mining / Fractals Conclusions

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U. of Alberta, 2001C. Faloutsos21 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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U. of Alberta, 2001C. Faloutsos22 DEMO server demo

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U. of Alberta, 2001C. Faloutsos23 ‘FALCON’ Inverted VsVs Trader wants only ‘unstable’ stocks

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U. of Alberta, 2001C. Faloutsos24 ‘FALCON’ Inverted VsVs average: is flat!

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U. of Alberta, 2001C. Faloutsos25 “Single query point” methods Rocchio + + + + + + x avg std

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U. of Alberta, 2001C. Faloutsos26 “Single query point” methods RocchioMindReader + + + + + + + + + + + + + + + + + + MARS The averaging affect in action... xx x

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U. of Alberta, 2001C. Faloutsos27 + + + + + Main idea: FALCON Contours feature1 (eg., avg) feature2 eg., std [Wu+, vldb2000]

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U. of Alberta, 2001C. Faloutsos28 A: Aggregate Dissimilarity : parameter (~ -5 ~ ‘soft OR’) + + + + + g1 g2 x

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U. of Alberta, 2001C. Faloutsos29 converges quickly (~5 iterations) good precision/recall is fast (can use off-the-shelf ‘spatial/metric access methods’) FALCON

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U. of Alberta, 2001C. Faloutsos30 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

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U. of Alberta, 2001C. Faloutsos31 Outline Goal: ‘Find similar / interesting things’ Problem - Applications Indexing - similarity search New tools for Data Mining: Fractals Conclusions Resourses

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U. of Alberta, 2001C. Faloutsos32 Data mining & fractals – Road map Motivation – problems / case study Definition of fractals and power laws Solutions to posed problems More examples

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U. of Alberta, 2001C. Faloutsos33 Problem #1 - spatial d.m. Galaxies (Sloan Digital Sky Survey w/ B. Nichol) - ‘spiral’ and ‘elliptical’ galaxies (stores & households; healthy & ill subjects) - patterns? (not Gaussian; not uniform) -attraction/repulsion? - separability??

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U. of Alberta, 2001C. Faloutsos34 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’) engine size mpg

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U. of Alberta, 2001C. Faloutsos35 Answer: Fractals / self-similarities / power laws

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U. of Alberta, 2001C. Faloutsos36 What is a fractal? = self-similar point set, e.g., Sierpinski triangle:... zero area; infinite length!

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U. of Alberta, 2001C. Faloutsos37 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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U. of Alberta, 2001C. Faloutsos38 Intrinsic (‘fractal’) dimension Q: fractal dimension of a line? xy 51 42 33 24 Eg: #cylinders; miles / gallon

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U. of Alberta, 2001C. Faloutsos39 Intrinsic (‘fractal’) dimension Q: fractal dimension of a line? A: nn ( <= r ) ~ r^1

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U. of Alberta, 2001C. Faloutsos40 Intrinsic (‘fractal’) dimension Q: fractal dimension of a line? A: nn ( <= r ) ~ r^1 Q: fd of a plane? A: nn ( <= r ) ~ r^2 fd== slope of (log(nn) vs log(r) )

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U. of Alberta, 2001C. Faloutsos41 Sierpinsky triangle log( r ) log(#pairs within <=r ) 1.58 == ‘correlation integral’

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U. of Alberta, 2001C. Faloutsos42 Observations self-similarity -> fractals scale-free power-laws (y=x^a, F=C*r^(-2)) log( r ) log(#pairs within <=r ) 1.58

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U. of Alberta, 2001C. Faloutsos43 Road map Motivation – problems / case studies Definition of fractals and power laws Solutions to posed problems More examples Conclusions

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U. of Alberta, 2001C. Faloutsos44 Solution#1: spatial d.m. Galaxies (Sloan Digital Sky Survey w/ B. Nichol - ‘BOPS’ plot - [sigmod2000]) clusters? separable? attraction/repulsion? data ‘scrubbing’ – duplicates?

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U. of Alberta, 2001C. Faloutsos45 Solution#1: spatial d.m. log(r) log(#pairs within <=r ) spi-spi spi-ell ell-ell - 1.8 slope - plateau! - repulsion!

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U. of Alberta, 2001C. Faloutsos46 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]

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U. of Alberta, 2001C. Faloutsos47 spatial d.m. r1r2 r1 r2 Heuristic on choosing # of clusters

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U. of Alberta, 2001C. Faloutsos48 Solution#1: spatial d.m. log(r) log(#pairs within <=r ) spi-spi spi-ell ell-ell - 1.8 slope - plateau! - repulsion!

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U. of Alberta, 2001C. Faloutsos49 Solution#1: spatial d.m. log(r) log(#pairs within <=r ) spi-spi spi-ell ell-ell - 1.8 slope - plateau! -repulsion!! -duplicates

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U. of Alberta, 2001C. Faloutsos50 Problem #2: Dim. reduction

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U. of Alberta, 2001C. Faloutsos51 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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U. of Alberta, 2001C. Faloutsos52 Problem #2: dim. reduction PFD~1 global FD=1 PFD=1 PFD=0 PFD=1

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U. of Alberta, 2001C. Faloutsos53 Problem #2: dim. reduction PFD~1 PFD=1 global FD=1 PFD=1 PFD=0 PFD=1 Notice: ‘max variance’ would fail here

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U. of Alberta, 2001C. Faloutsos54 Problem #2: dim. reduction PFD~1 global FD=1 PFD=1 PFD=0 PFD=1 Notice: SVD would fail here

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U. of Alberta, 2001C. Faloutsos55 Currency dataset

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U. of Alberta, 2001C. Faloutsos56 self-similar? fd=1.98 fd=4.25 currency eigenfaces

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U. of Alberta, 2001C. Faloutsos57 FDR on the ‘currency’ dataset if unif + indep.

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U. of Alberta, 2001C. Faloutsos58 FDR on the ‘currency’ dataset if unif + indep. HKD: “useless” >1.98 axis are needed

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U. of Alberta, 2001C. Faloutsos59 Road map Motivation – problems / case studies Definition of fractals and power laws Solutions to posed problems More examples Conclusions

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U. of Alberta, 2001C. Faloutsos60 App. : traffic disk traces: self-similar (also: web traffic; comm. errors; etc) time #bytes

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U. of Alberta, 2001C. Faloutsos61 More apps: Brain scans Oct-trees; brain-scans octree levels Log(#octants) 2.63 = fd

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U. of Alberta, 2001C. Faloutsos62 More fractals: stock prices (LYCOS) - random walks: 1.5 1 year2 years

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U. of Alberta, 2001C. Faloutsos63 More fractals: coast-lines: 1.1-1.2 (up to 1.58)

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U. of Alberta, 2001C. Faloutsos64

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U. of Alberta, 2001C. Faloutsos65 Examples:MG county Montgomery County of MD (road end- points)

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U. of Alberta, 2001C. Faloutsos66 Examples:LB county Long Beach county of CA (road end-points)

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U. of Alberta, 2001C. Faloutsos67 More power laws: Zipf’s law Bible - rank vs frequency (log-log) log(rank) log(freq) “a” “the”

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U. of Alberta, 2001C. Faloutsos68 More power laws Freq. distr. of first names; last names (Mandelbrot)

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U. of Alberta, 2001C. Faloutsos69 Internet Internet routers: how many neighbors within h hops? U of Alberta

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U. of Alberta, 2001C. Faloutsos70 Internet topology Internet routers: how many neighbors within h hops? [SIGCOMM 99] Reachability function: number of neighbors within r hops, vs r (log- log). Mbone routers, 1995 log(hops) log(#pairs) 2.8

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U. of Alberta, 2001C. Faloutsos71 More power laws: areas – Korcak’s law Scandinavian lakes ([icde99], w/ Proietti)

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U. of Alberta, 2001C. Faloutsos72 More power laws: areas – Korcak’s law Scandinavian lakes area vs complementary cumulative count (log-log axes) log(count( >= area)) log(area)

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U. of Alberta, 2001C. Faloutsos73 Olympic medals: log rank log(# medals)

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U. of Alberta, 2001C. Faloutsos74 More power laws Energy of earthquakes (Gutenberg-Richter law) [simscience.org] log(count) magnitudeday amplitude

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U. of Alberta, 2001C. Faloutsos75 Even more power laws: Income distribution (Pareto’s law); sales distributions; duration of UNIX jobs Distribution of UNIX file sizes publication counts (Lotka’s law)

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U. of Alberta, 2001C. Faloutsos76 Even more power laws: web hit frequencies ([Huberman]) hyper-link distribution [Barabasi], ++

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U. of Alberta, 2001C. Faloutsos77 Overall Conclusions: ‘Find similar/interesting things’ in multimedia databases Indexing: feature extraction (‘GEMINI’) –automatic feature extraction: FastMap –Relevance feedback: FALCON

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U. of Alberta, 2001C. Faloutsos78 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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U. of Alberta, 2001C. Faloutsos79 Conclusions - cont’d –can model bursty time sequences (buffering/prefetching) –selectivity estimation (‘how many neighbors within x km?) –dim. curse diagnosis (it’s the fractal dim. that matters! [ICDE2000])

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U. of Alberta, 2001C. Faloutsos80 Resources: Software and papers: –http://www.cs.cmu.edu/~christoshttp://www.cs.cmu.edu/~christos –Fractal dimension (FracDim) –Separability (sigmod 2000) –Relevance feedback for query by content (FALCON – vldb 2000)

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