Paper PDF: http://www.icmc.usp.br/pessoas/junio/PublishedPapers/RodriguesJr_et_al-IV2010.pdf

Institute of Mathematics and Computer SciencesUniversity of Sao Paulo (USP) - Brazil

London, UK - July/2010

Combining Visual Analytics and Content Based Data Retrieval Technology for Efficient Data Analysis

Jose F Rodrigues Jr – junio@icmc.usp.br

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Context and Context and problems:problems:

content-based content-based data retrieval data retrieval

and and visualizationvisualization

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Context: Content-based data retrieval

Metric spaces: de facto solution for non-orderable data domains Multivariate data Image Video Sound Text

Metric spaces Content-based Data Retrieval It demands three things:

1.Features extraction/annotation2.A distance function

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Context: Content-based data retrievalFeatures extraction/annotation

Features extraction transforms data objects into multivariate data

Features annotation translates real world objects into multivariate data

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Distance functions measure the distance in between features vectors

L2=Euclidiana

r

L0=LInfinity=Chebychev

L1=Manhatan

Context: Content-based data retrieval Distance functions

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Distance FunctionFeatures/Multivariate Data

Context: Content-based data retrieval

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Distance FunctionFeatures/Multivariate Data

Context: Content-based data retrieval

Similarity QueriesSimilarity Queries

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Context: Metric spaces

Metric Structure

Distance Function

Features ExtractionFeatures ExtractionContent-based data retrieval

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Context: Metric spaces

Metric Structure

Distance Function

Features ExtractionFeatures ExtractionContent-based data retrieval

Data retrieval

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Context: Metric spaces

Problem 1 - it is difficult to make sense of metric spaces:High dimensionalityToo many data itemsSimilarity queries work like a black box:

no opportunity to check the context of what was retrieved

nor what else could have been retrieved

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Context: Visualization

The goal of this conference

Important aid for data analysis

Interactive

Intuitive

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Context: Visualization

Visualization mantra:overview first, zoom & filter, then details on

demand

Hence: filtering is an essential part of visualization

The principal means for visual filtering is Interactive brushing

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Context: Visualization

Problem 2 - interactive brushing may be inefficient:Overlap of graphical elementsToo many data elements to select one at a timeSelection based on geometrical primitives (as

spheres and cubes) will brush more elements than what is desired

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Context: Visualization

Problem 3 - the user’s interests may yield filterings that cannot be accomplished with brushing:Semantical interests lead to data items that are:

Not equally importantNot visually adjacentNot at the same analytical context

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Methodology:Methodology:

Why not put Why not put together together

content-based content-based data retrieval data retrieval

and and visualization?visualization?

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Linking CBDR and visualization

Metric spaces are properly spatial

Visualizations use space as one of its main channels for data coding

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Linking CBDR and visualization

?

CBDR Visualization

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Linking CBDR and visualization

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Linking CBDR and visualization

Slim-Tree - Family of Metric Access Methods(Traina Jr. et al. 2000)

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Linking CBDR and visualization

Multidimensional Projection with Fastmap algorithm(Faloutsos and K.-I. Lin 1995)

Slim-Tree - Family of Metric Access Methods(Traina Jr. et al. 2000)

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Methodology:Methodology:

content-based content-based data retrieval viadata retrieval via

Slim-TreeSlim-Tree

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Slim-Tree Metric Access Method

Goal: performance in similarity queries Challenge: multidimensional data, and queries based on

similarity rather than equality Demands: a distance function satisfying triangular

inequality, symmetry and non-negativity Principle: use of progressively hierarchical (tree)

restricting radiuses around representative objects Engineer: clustering subtrees and use of trigonometry

for branch pruning during search Mechanism: dynamic, balanced, bottom-up, disk-

oriented Data: representatives at inner nodes, objects at the leaves

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Video: Metric-Tree-Example-faster.avi

Slim-Tree Metric Access Method

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Oq

• Example: Range Query

Query object Oq and a query radius rq

Slim-Tree Metric Access Method

Oj

Op

Okrepr0(O )p

repr1(O )p

obj(Op)

Oi

Ol Om

repr1(O )i

repr (O1 j)

obj(O m)obj(Ok)

obj(O i)obj(O l)

obj(O j)

...

......

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Methodology:Methodology:

visualization viavisualization via

FastMapFastMap

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FastMap

Projection of p-dimensional points in k mutually orthogonal directions; p > k

Imagine that the points are in a Euclidean space Select two pivot points xa and xb that are far apart Compute a pseudo-projection of the remaining points

along the “line” xaxb

“Project” the points to an orthogonal subspace and recurse

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FastMap: Selecting the Pivot Points

Find the two-furthest points O(n2) Use heuristic 2*(n-1) O(n)

Select any point x0

Let x1 be the furthest from x0

Let x2 be the furthest from x1

Return (x1, x2)x0

x2

x1

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FastMap: Selecting the Pivot Points

Find the two-furthest points O(n2) Use heuristic 2*(n-1) O(n)

Select any point x0

Let x1 be the furthest from x0

Let x2 be the furthest from x1

Return (x1, x2)x0

x2

x1

- 14th International Conference on Information Visualisation (IV 2010) -

FastMap: Selecting the Pivot Points

Find the two-furthest points O(n2) Use heuristic 2*(n-1) O(n)

Select any point x0

Let x1 be the furthest from x0

Let x2 be the furthest from x1

Return (x1, x2)x0

x2

x1

- 14th International Conference on Information Visualisation (IV 2010) -

FastMap: Selecting the Pivot Points

Find the two-furthest points O(n2) Use heuristic 2*(n-1) O(n)

Select any point x0

Let x1 be the furthest from x0

Let x2 be the furthest from x1

Return (x1, x2)x0

x2

x1

XaXb

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FastMap: Pseudo-Projections

Given pivots (xa , xb ), and any third point y

From the law of cosines, one can get to:

The pseudo-projection for y is

This is the first of k coordinates to compute

xa

xb

y

cy da,y

db,y

da,b 2 2 2 2by ay ab y abd d d c d

2 2 2

2ay ab by

yab

d d dc

d

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FastMap: “Project to orthogonal plane”

For orthogonality, the points are considered as if projected on a hyperplane perpendicular to XaXb;

hence p becomes p-1 The projection is not done properly

said, but the distance function for such configuration is determined

We can compute distances within the “orthogonal hyperplane” using the Pythagorean theorem

2 2'( ', ') ( , ) ( )z yd y z d y z c c

xb

xa

y

z

y’ z’dy’,z’

dy,z

cz-cy

Get back to the previous slide and use d ’ to calculate the next cy

coordinate; repeat until k coordinates are computed

- 14th International Conference on Information Visualisation (IV 2010) -

FastMap: “Project to orthogonal plane”

For orthogonality, the points are considered as if projected on a hyperplane perpendicular to XaXb;

hence p becomes p-1 The projection is not done properly

said, but the distance function for such configuration is determined

We can compute distances within the “orthogonal hyperplane” using the Pythagorean theorem

2 2'( ', ') ( , ) ( )z yd y z d y z c c

xb

xa

y

z

y’ z’dy’,z’

dy,z

cz-cy

Get back to the previous slide and use d ’ to calculate the next cy

coordinate; repeat until k coordinates are computed

More important than what it does, is how it does; and this step is the main engineer behind FastMap – it allows it to work recursively and fast.

- 14th International Conference on Information Visualisation (IV 2010) -

FastMap: “Project to orthogonal plane”

For orthogonality, the points are considered as if projected on a hyperplane perpendicular to XaXb;

hence p becomes p-1 The projection is not done properly

said, but the distance function for such configuration is determined

We can compute distances within the “orthogonal hyperplane” using the Pythagorean theorem

2 2'( ', ') ( , ) ( )z yd y z d y z c c

xb

xa

y

z

y’ z’dy’,z’

dy,z

cz-cy

Get back to the previous slide and use d ’ to calculate the next coordinate; repeat until k coordinates are computed

• Good point: overall complexity is k*n O(n), better than any other

• Bad point: original distances are not strictly maintained stress (like any other technique of its kind)

• All in all, FastMap is a top five multidimensional projection technique (along with MDS, PCA, LSP, FDP), but with the best performance

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Solving the stated Solving the stated problems:problems:

innovating withinnovating with

MetricSPlatMetricSPlat

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Breast Cancer Wisconsin (Diagnostic) Data Set• 9 descriptive attributes annotated from tissue biopsies:

1. ClumpThickness2. UniforSize3. UniforShape4. MargAdhes5. SingleEpithSize6. BareNuclei7. BlandChromatin8. NormalNucleoli9. Mitoses

• Breast Cancer classification:• benign (class 0) • malign (class 1)

Demonstration dataset

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Problem 1

Problem 1 - it is difficult to make sense of metric spaces

Choose a distance function, which will be the same for FastMap and SlimTree

Build a SlimTreeChoose an element of interest to be the center of the

projectionRetrieve the entire dataset out of the SlimTreeFastMap-project all the elements of the dataset in 3DUse central point for translation

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Video: Problem1-final.avi

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Problem 2

Problem 2 - interactive brushing may be inefficient Data selections may demand too many brushing steps Attribute by attribute selection may not correspond to

similarity as expected by the user In 3D projection, spheres and cubes do not apply for non-

regular regions of interest Due to stress, projection does not exactly correpond to

the original data configuration Approach:

Brush one element of interestPerform a KNN/Range query having this element as

the query center

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Video: Problem2-final.avi

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Problem 3

Problem 3 - the user’s interests may yield filterings that cannot be accomplished with brushingWeight attributes according to perception and

knowledge domainRedefine metric space and projectionPropagate data to multivariate visualization

techniques

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Video: Problem3-final.avi

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Without weighting of attributes 2 and 3 After weighting of attributes 2 and 3

KNN(15, 441) = <445, 444, 449, 433, 450, 448, 447, 446, 443, 442, 440, 439, 438, 437, 436> = R

KNN(15, 441) = <456, 454, 453, 452, 450, 449, 448, 447, 443, 441, 436, 433, 430, 425, 424> = R´

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Without weighting of attributes 2 and 3 After weighting of attributes 2 and 3

KNN(15, 441) = <445, 444, 449, 433, 450, 448, 447, 446, 443, 442, 440, 439, 438, 437, 436> = R

KNN(15, 441) = <456, 454, 453, 452, 450, 449, 448, 447, 443, 441, 436, 433, 430, 425, 424> = R´

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Without weighting of attributes 2 and 3 After weighting of attributes 2 and 3

KNN(15, 441) = <445, 444, 449, 433, 450, 448, 447, 446, 443, 442, 440, 439, 438, 437, 436> = R

KNN(15, 441) = <456, 454, 453, 452, 450, 449, 448, 447, 443, 441, 436, 433, 430, 425, 424> = R´

The query answer is 60% different:

R’ - R = {456, 454, 453, 452, 450, 441, 430, 425, 424}R ∩ R’ = {449, 448, 447, 443, 436, 433}

It retrieves elements whose attributes 2 and 3 are more similar to the query center 441 at attributes 2 and 3.

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References

C. Faloutsos and K.-I. Lin, “FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets”, Proc. ACM SIGMOD, 1995, 163-174

C. Traina Jr., A. Traina, B. Seeger, C. Faloutsos, “Slim-trees: High Performance Metric Trees Minimizing Overlap Between Nodes”, Int. Conference on Extending Database Technology (EDBT), 2000, 51--65

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Resources

D. Mount, “Feature Selection”, Presentation for CMSC 828K - University of Maryland - http://www.kanungo.com/teaching/cmsc828K/dave/feature.ppt- accessed 07/2010

Tomáš Skopal, Jaroslav Pokorný, Michal Krátký, Václav Snášel, “Revisiting M-tree Building Principles”, Presentation for Advances in Databases and Information Systems 2003

http://siret.ms.mff.cuni.cz/skopal/pres/mtree.ppt - accessed 07/2010

Clemens Marschner, “MTree Tester Applet”

http://www.cmarschner.net/mtree.html - accessed 07/2010

Texas A&M University, “Function Plotter”

http://www.math.tamu.edu/AppliedCalc/Classes/Plot2/CardPlot.html

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Thank youThank youhttp://www.icmc.usp.br/~junio

Link “MetricSPlat”

junio@icmc.usp.br