Projection Techniques. Problems PCA. Y R p={1,2,3} X R m. Multi-dimensional Visualization based on Bidimensional Mapping
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1 Projection Techniques Multi-dimensional Visualization based on Bidimensional Mapping X R m f Y R p={1,2,3} Rosane Minghim Instituto de Ciências Matemáticas e de Computação USP-São Carlos 1 : x i, x j R, x i,x j X d: y i, y j R, y i,y j Y f: X Y, (x i,x j ) d(f(x i ), f(x j )) 0, x i,x j X 2 Ex: Mapping to plane of patents surgery, drugs, molecular bio Problems PCA 390 dimensions 3 4 1
2 Problems PCA Problems PCA 5 6 Ex: Sammon Mapping Force Based Point Placement Let X be the points in the original space R n, we apply a distance measure d ij * between Xi an Xj., and find Y, the projected point, ex. R 2 and d ij the Euclidean distance between them. Sammon s method applies an error function to measure the target
3 Force Scheme [Tejada et al., 2003] Force Based Point Placement q' x' 9 10 Force Scheme [Tejada et al., 2003] q' Force Scheme [Tejada et al., 2003] q' x' x'
4 Force Scheme [Tejada et al., 2003] Force Scheme [Tejada et al., 2003] < 0 q' < 0 < 0 x' x' > 0 < 0 > LSP: Laplacian Matrix Let V i = {p i1,,p iki } be a neighborhood of a point p i and let c i be the coordinates of p i em R p 1 c 0 i c j ki p j V i Each p i is the centroid of points in V i p i4 p i5 p i p i3 p i1 p i2 LSP: Laplacian Matrix Lx 1 =0, Lx 2 =0,, Lx p =0 Where x 1, x 2,, x p are vectors containing the coordinates of the points and L is the matrix given by: x 1 1 i j 0 x2 1 Lij p j Vi L = ki 0 otherwise x n
5 LSP: Adicionando os Pontos de Controle L 1 A Cij C 0 p j is otherwise a control point LSP: Overview Escolher os Pontos pontos de em R m controle 0 bi x p c i i n n i n nc L x1 x2 x n c1 c 2 Projetar os pontos de controle Determinar a vizinhança dos pontos Resolver um sistema linear esparso Pontos em R p Choosing the Control Points In order to select the control points the space R m is split into nc clusters using k-medoids. the control points are the medoids of each cluster Choosing the Control Points Once the control points are chosen, these points are projected onto R d through a fast dimensionality reduction method Fast Projection (Fastmap or NNP) Force Placement
6 Content based by Projections Control points in blue Example Projection Example: IDH
7 Projection Example: voting in US Senate Point Placement by Phylogenetic Tree Construction Algorithms (N-J Trees) Point Placement by Phylogenetic Tree Construction Algorithms (N-J Trees) NJ similarity Tree
8 Alternate view (N-J Tree) Exploration Exploration Finding Relationships
9 Building a Surface RSS News Flash Palestinian Bird and Flu
10 Bush Iraq Bush Iraq Application 1: Visual Text Mapping Relationships : Topic Bursts and co-word Approach 1: Relationship Based (Metadata) (Mane and Borner) 2004 Approach 2: Content based
11 Relationships : Citation and Co-citation Content-based Text Mapping Approach 1: Pre-clustering & View (Borner) (2003) Approach 2: Dimension reduction (Projections) Content - based Content - based (Skupin) (2002) (abstracts) SOM (Dimensional Reduction) News flash IN-SPIRE (PNL)
12 Content - based SOM based Self-Organization Maps (SOMs) cartográficos (ex. Skurpin 2002) (Surface View) IN-SPIRE Mapeamento para o plano permitindo a exploração. Ex: Patents surgery, drugs, molecular bio Exemplos de Mapas
13 Exemplos de Mapas Detailing topics
14 Time Series Streamflow in Hidroelectrics Text from attributes 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 Cattle performance data Cattle performance data Colored by word top
15 Cattle performance data Cattle performance data Colored by female Colored by farm Images? Pipeline Image Data Set Feature Acquisition Feature Selection Interaction Classification Visualization Similarity Calculation
16 PEx-Image Sample Content PEx-Image Group Content PEx-Image Image as Visual Mark PEx-Image Coordination
17 PEx-Image Coordination Comparison of Distance Metrics Euclidean City Block Cosine 512 MRI medical images 12 classes Comparison of Distance Metrics Euclidean City Block Cosine Comparison of Feature Space (1) 16 Gabor Filters Fourier, Mean and Deviation 72 co-ocurrence matrices All combined 512 MRI medical images 12 classes 512 MRI medical images 12 classes
18 Comparison of Feature Space (1) 16 Gabor Filters Fourier, Mean and Deviation 72 co-ocurrence matrices All combined Comparison of Feature Space (2) All combined 1024 Wavelet Features 512 MRI medical images 12 classes X-Ray images from ImageCLEF 116 classes 70 Comparison of Feature Space (2) Detailed Inspection All combined 1024 Wavelet Features 1000 X-Ray images from ImageCLEF 116 classes
19 Detailed Inspection ImageCLEF Training Data Set (1) X-Ray images 116 classes 74 ImageCLEF Training Data Set (2) Class 108 Class 111 Further Examples on Text RSS Patent Data, recovered from the Web Case 1: 170 files Graphics processing, printer, database, document, ai
20 Further Examples Further Examples Further Examples (ink jet, document)
21 81 82 Patents case 2 Patents surgery, drugs, molecular bio files surgery (2), drugs(2), molecular biology
22 Patents surgery, drugs, molecular bio stopwords selection Patents surgery, drugs, molecular bio topics Patents surgery, drugs, molecular bio Patents surgery, drugs, molecular bio
23 Projection Explorer (PEx) Collaborators Alneu de Andrade Lopes Mineração de textos Haim Levkowitz Visualization João E. S. Batista Neto Imaging Visualization Group Maria Cristina F. Oliveira Fernando Vieira Paulovich Visualização/Projeções Rosane Minghim Luis Gustavo Nonato malhas Doutorandos Danilo Medeiros Eler Aretha Barbosa Kátia Felizardo Mestrandos Jorge Poco Medina Christian Tácito Neves Renato Oliveira Gabrial Andery
24 Other Partnerships Link Sérgio Furuie (Poli USP), Brazil infoserver.lcad.icmc.usp.br (Pex, Pex-WEB, Pex-Temporal, Pex-Image). Lars Linsen (Jacobs University Bremen), Germany Charl Botha (TU Delft ); Anton Heijs (Treparel Inc.), The Netherlands 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 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 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. 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, v. 1. p 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, v. 1. p 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, 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, p
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