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1
Multi-dimensional Visualization
based on Bidimensional Mapping
Rosane Minghim
Instituto de Ciências Matemáticas e de
Computação
USP-São Carlos2
Projection Techniques
• : xi, xj R, xi,xj X
• d: yi, yj R, yi,yj Y
• f: X Y,|(xi,xj) – d(f(xi), f(xj))| 0, xi,xj X
X Rm Y Rp={1,2,3}f
3
Ex: Mapping to plane of patents
surgery, drugs, molecular bio
4
Problems PCA
390 dimensions
2
5
Problems PCA
6
Problems PCA
7
• Let X be the points in theoriginal space Rn, we apply adistance measure dij* betweenXi an Xj., and find Y, theprojected point, ex. R2 and dij
the Euclidean distancebetween them.
• Sammon’s method applies anerror function to measure thetarget.
Ex: Sammon Mapping
8
Force Based Point Placement
3
9
Force Scheme [Tejada et al.,
2003]
x'
q'
10
Force Based Point Placement
11
Force Scheme [Tejada et al.,
2003]
x'
q'
12
Force Scheme [Tejada et al.,
2003]
x'
q'
4
13
Force Scheme [Tejada et al.,
2003]
x'
q'
< 0
14
Force Scheme [Tejada et al.,
2003]
x'
< 0
< 0
< 0 > 0
> 0
15
• Let Vi = {pi1,…,piki} be a neighborhood of a point pi and
let ci be the coordinates of pi em Rp
• Each pi is the centroid of points in Vi
pi
pi1
pi2 pi3
pi4
pi5
ij Vp
ji cki
c 01
LSP: Laplacian Matrix
16
LSP: Laplacian Matrix
Lx1=0, Lx2=0, …, Lxp=0
Where x1, x2,…, xp are vectors containing
the coordinates of the points and L is the
matrix given by:
therwise o
V pki
ji
Lij ij
0
1
1 0
0
...
0
0
L
1
2
n
x
x
x
=
5
17
LSP: Adicionando os Pontos de
Controle
C
LA
therwise
pocontrolais pCij
j
o0
int1
ncninx
nib
icpi
0
0100
0010
L
1
2
n
x
x
x
1
2
0
0
0
c
c
18
LSP: Overview
Escolher os pontos de
controle
Determinar a
vizinhança dos pontos
Pontos
em Rm
Projetar os
pontos de controle
Resolver um
sistema linear esparso
Pontos em Rp
19
Choosing the Control Points
• In order to select the control points
• the space Rm is split into nc clusters
using k-medoids.
• the control points are the medoids of
each cluster
20
Choosing the Control Points
• Once the control points are chosen, these
points are projected onto Rd through a
fast dimensionality reduction method
• Fast Projection (Fastmap or NNP)
• Force Placement
6
21
Control points
in blue
22
Content – based by Projections
23
Example
24
Projection Example: IDH
7
25
Projection Example: voting in US
Senate
26
Point Placement by Phylogenetic Tree
Construction Algorithms (N-J Trees)
27
Point Placement by Phylogenetic Tree
Construction Algorithms (N-J Trees)
28
NJ similarity Tree
8
29
• Alternate view (N-J Tree)
30
31
Exploration
32
• Finding Relationships
Exploration
9
33 34
• Building a Surface
35
RSS News Flash
Bird and Flu 36Palestinian
10
37
Bush Iraq
38
Bush Iraq
39
Application 1: Visual Text
Mapping
• Approach 1: Relationship Based
(Metadata)
• Approach 2: Content based
40
Relationships :
Topic Bursts and co-word
(Mane and Borner)
2004
11
41
Relationships :
Citation and Co-citation
(Borner)
(2003)
42
Content-based Text Mapping
• Approach 1: Pre-clustering & View
• Approach 2: Dimension reduction
(Projections)
43
Content - based
(Skupin)
(2002)
(abstracts)
SOM
44
Content - based
(Dimensional
Reduction)
News flash
IN-SPIRE
(PNL)
12
45
Content - based
(Surface
View)
IN-SPIRE
46
• Self-Organization Maps (SOMs) cartográficos (ex.
Skurpin 2002)
SOM based
47
Mapeamento para o plano permitindo a
exploração.
Ex: Patents surgery, drugs, molecular bio
48
Exemplos de Mapas
13
49
Exemplos de Mapas
50
51
• Detailing topics
52
14
53
Time Series – Streamflow in Hidroelectrics
54
• Cattle performance data
• Translated to text from categorical
information, e.g.,
• Ranges of weight to words such as:
{weight_below_fifty_percent;
weight_between_fifty_seventy_five; etc..}
• 9135 individuals
Text from attributes
55
Cattle performance data
56
Cattle performance data
Colored
by word
‘top’
15
57
Cattle performance data
Colored
by
female
58
Cattle performance data
Colored
by farm
59
Images?
60
Pipeline
Image
Data Set
Feature
AcquisitionFeature
Selection
Similarity
CalculationVisualizationClassification
Interaction
16
61
PEx-Image – Sample Content
62
PEx-Image – Group Content
63
PEx-Image – Image as Visual
Mark
64
PEx-Image – Coordination
17
65
PEx-Image – Coordination
66
Comparison of Distance Metrics
Euclidean City Block Cosine
512 MRI medical images
12 classes
67
Comparison of Distance Metrics
Euclidean City Block Cosine
512 MRI medical images
12 classes
68
Comparison of Feature Space (1)
16 Gabor
Filters
Fourier, Mean
and Deviation
72 co-ocurrence
matrices All combined
512 MRI medical images
12 classes
18
69
Comparison of Feature Space (1)
16 Gabor
Filters
Fourier, Mean
and Deviation
72 co-ocurrence
matrices All combined
512 MRI medical images
12 classes
70
Comparison of Feature Space (2)
All combined
1000 X-Ray images from
ImageCLEF
116 classes
1024 Wavelet Features
71
Comparison of Feature Space (2)
All combined
1000 X-Ray images from
ImageCLEF
116 classes
1024 Wavelet Features
72
Detailed Inspection
19
73
Detailed Inspection
74
ImageCLEF Training Data Set (1)
9000 X-Ray
images
116 classes
75
ImageCLEF Training Data Set (2)Class 108 Class 111
76
• RSS Patent Data, recovered from the
Web http://www.freepatentsonline.com/
• Case 1:
• 170 files
• Graphics processing, printer, database,
document, ai
Further Examples on Text
20
77
Further Examples
78
Further Examples
79
Further Examples
80
(ink jet,
document)
21
81 82
83
Patents – case 2
• http://www.freepatentsonline.com/
• 172 files
• surgery (2), drugs(2), molecular biology
84
Patents surgery, drugs, molecular bio
22
85
Patents surgery, drugs, molecular bio
stopwords selection
86
Patents surgery, drugs, molecular bio
topics
87
Patents surgery, drugs, molecular bio
88
Patents surgery, drugs, molecular bio
23
89
Projection Explorer (PEx)
http://infoserver.lcad.icmc.usp.br/ 90
Alneu de Andrade Lopes – Mineração de textos
alneu@
Haim Levkowitz – Visualization
João E. S. Batista Neto – Imaging
jbatista@
Collaborators
91
Maria Cristina F. Oliveira
cristina@
Rosane Minghim
Visualization Group
Luis Gustavo
Nonato
malhas
Fernando Vieira
Paulovich
Visualização/Projeções
92
Doutorandos
Danilo Medeiros Eler
Aretha Barbosa
Kátia Felizardo
Mestrandos
Jorge Poco Medina
Christian
Tácito Neves
Renato Oliveira
Gabrial Andery
24
93
Other Partnerships
Sérgio Furuie (Poli – USP), Brazil
Lars Linsen (Jacobs University
Bremen), Germany
Charl Botha (TU Delft ); Anton Heijs
(Treparel Inc.), The Netherlands
94
Link
• infoserver.lcad.icmc.usp.br (Pex, Pex-WEB, Pex-Temporal, Pex-Image).
95
Referências
• Cuadros, A. M, Paulovich, F. V., Minghim, R., Telles, G. P - Point Placement by
Phylogenetic Trees and its Application to Visual Analysis of Document Collections
IEEE VAST 2007, Sacramento, CA, USA, IEEE CS Press, pp.99-106.
• Paulovih, F. V., Oliveira, M.C.F., Minghim, R. - The Projection Explorer: A Flexible
Tool for Projection-based Multidimensional Visualization, IEEE Sibgrapi 2007, IEEE
CS Press, Belo Horizonte, Brazil,pp. 27-34.
• Lopes, A. A., Minghim, R., Melo, V., Paulovich, F.V.; Mapping texts through
dimensionality reduction and visualization techniques for interactive exploration of
document collections, SPIE Conference on Visualization and Data Analysis, San
Jose, CA, USA Jan. 2006, 6060T-11.
• Minghim, R., Paulovich, F.V., Lopes, A. A.; Content-based text mapping using
multidimensional projections for exploration of document collections, SPIE
Conference on Visualization and Data Analysis, San Jose, CA, USA Jan. 2006,
6060T-11.
96
Referências
• Pinho, R. D. ; Oliveira, M. C. F. ; Minghim, R. ; Andrade, M. G. . Voromap: A Voronoi-based Tool
for Visual Exploration of Multidimensional Data. In: 10th International Conference on
Information Visualization, 2006, Londres. Proceedings of Information Visualisation 2006,
2006. v. 1. p. 39-44
• Paulovich, F. V. ; Minghim, R. . Text Map Explorer: a Tool to Create and Explore Document
Maps. In: Information Visualisation 2006 (IV06) 10th International Conference on Information
Visualisation, 2006, Londres. Proceedings of Information Visualisation 2006, 2006. v. 1. p. 245-
251.
• Paulovich, F. V. ; Nonato, L. G. ; MINGHIM, R. ; Levkowitz, H. . Least Square Projection: a fast
high precision multidimensional projection technique and its application to document mapping.
IEEE Transactions on Visualization and Computer Graphics, 2008.
• Minghim, R. ; Levkowitz, H. ; Nonato, L. G. ; Watanabe, L. S. ; Salvador, V. C. L. ; Lopes, H. ;
Pesco, S. ; Tavares, G. . Spider Cursor: A simple versatile interaction tool for data visualization
and exploration. In: ACM GRAPHITE'05 - 3rd International Conference on Computer Graphics
and Interactive Techniques in Australasia and Southeast Asia, 2005, Dunedin. Proceedings of
Graphite 2005, 2005. p. 307-314.