Readings Covered Further Reading Parallel Coordinates only 2 - PowerPoint PPT Presentation

Readings Covered Further Reading Parallel Coordinates ◮ only 2 orthogonal axes in the plane Lecture 10: High Hyperdimensional Data Analysis Using Parallel Coordinates. Edward ◮ instead, use parallel axes! J. Wegman. Journal of the American Statistical Association, Vol. 85, Dimensionality No. 411. (Sep., 1990), pp. 664-675. Visualizing the non-visual: spatial analysis and interaction with Visualizing Proximity Data. Rich DeJordy, Stephen P . Borgatti, Chris information from text documents. James A. Wise et al, Proc. InfoVis Information Visualization Roussin and Daniel S. Halgin. Field Methods, 19(3):239-263, 2007. 1995 CPSC 533C, Fall 2007 Fast Multidimensional Scaling through Sampling, Springs and Hierarchical Parallel Coordinates for Visualizing Large Multivariate Interpolation. Alistair Morrison, Greg Ross, Matthew Chalmers, Data Sets Ying-Huey Fua, Matthew O. Ward, and Elke A. Information Visualization 2(1) March 2003, pp. 68-77. Rundensteiner, IEEE Visualization ’99. Tamara Munzner Cluster Stability and the Use of Noise in Interpretation of Clustering. Parallel Coordinates: A Tool for Visualizing Multi-Dimensional George S. Davidson, Brian N. Wylie, Kevin W. Boyack, Proc InfoVis Geometry. Alfred Inselberg and Bernard Dimsdale, IEEE UBC Computer Science 2001. Visualization ’90. Interactive Hierarchical Dimension Ordering, Spacing and Filtering for 15 October 2007 Exploration Of High Dimensional Datasets. Jing Yang, Wei Peng, Matthew O. Ward and Elke A. Rundensteiner. Proc. InfoVis 2003. [Hyperdimensional Data Analysis Using Parallel Coordinates. Edward J. Wegman. Journal of the American Statistical Association, 85(411), Sep 1990, p 664-675.] PC: Correllation PC: Duality PC: Axis Ordering Hierarchical Parallel Coords: LOD ◮ geometric interpretations ◮ rotate-translate ◮ hyperplane, hypersphere ◮ point-line ◮ points do have intrinsic order ◮ pencil: set of lines coincident at one point ◮ infovis ◮ no intrinsic order, what to do? ◮ indeterminate/arbitrary order ◮ weakness of many techniques ◮ downside: human-powered search ◮ upside: powerful interaction technique ◮ most implementations ◮ user can interactively swap axes ◮ Automated Multidimensional Detective [Parallel Coordinates: A Tool for Visualizing Multi-Dimensional Geometry. Alfred ◮ Inselberg 99 Inselberg and Bernard Dimsdale, IEEE Visualization ’90.] ◮ machine learning approach [Hierarchical Parallel Coordinates for Visualizing Large Multivariate Data Sets. Fua, [Hyperdimensional Data Analysis Using Parallel Coordinates. Edward J. Wegman. Ward, and Rundensteiner, IEEE Visualization 99.] Journal of the American Statistical Association, 85(411), Sep 1990, p 664-675.] Hierarchical Clustering Dimensionality Reduction Dimensionality Reduction: Isomap Visualizing Proximity Data ◮ 4096 D: pixels in image ◮ characterizing MDS vs. graph layout ◮ proximity-based coloring ◮ MDS ◮ 2D: wrist rotation, fingers extension ◮ interaction lecture later: ◮ nonmetric: ordering preserved, not exact ◮ mapping multidimensional space into distances ◮ structure-based brushing ◮ space of fewer dimensions ◮ general clusters meaningful, specific local ◮ extent scaling ◮ typically 2D for infovis distances less so ◮ keep/explain as much variance as possible metric (stress=.269) nonmetric (stress=.171) ◮ show underlying dataset structure ◮ multidimensional scaling (MDS) ◮ MDS: minimize differences between interpoint distances in high and low dimensions [Hierarchical Parallel Coordinates for Visualizing Large Multivariate Data Sets. Fua, [A Global Geometric Framework for Nonlinear Dimensionality Reduction. J. B. Ward, and Rundensteiner, IEEE Visualization 99.] Tenenbaum, V. de Silva, and J. C. Langford. Science 290(5500), pp 2319–2323, Dec [Visualizing Proximity Data. DeJordy, Borgatti, Roussin and Halgin. Field Methods, 22 2000] 19(3):239-263, 2007. ] From Matrix To Graph MDS vs GLA: Dimensionality MDS vs GLA: Outliers MDS vs GLA ◮ outliers distort with MDS ◮ intransitivity (triangle inequality doesn’t ◮ outliers automatically handled with GLA hold): GLA better ◮ MDS better when dim = 2D/3D ◮ data asymmetric: GLA better MDS (stress=.207) GLA (filter=.5) ◮ low stress ◮ interactive exploration (changing filter): ◮ GLA better when dim > 2D GLA allows ◮ 2D MDS shows MLK intermediate ◮ manual node repositioning: GLA allows ◮ GLA shows MLK part of patriotic group ◮ 3D MDS also shows MLK part of patritioc ◮ existence/absence of relationships at precise levels: GLA ◮ overview of all relationships at once: MDS [Visualizing Proximity Data. DeJordy, Borgatti, Roussin and Halgin. Field Methods, 19(3):239-263, 2007. ] [Visualizing Proximity Data. DeJordy, Borgatti, Roussin and Halgin. Field Methods, 19(3):239-263, 2007. ]

Critique Critique Spring-Based MDS: Naive Faster Spring Model [Chalmers 96] ◮ repeat for all points ◮ compute spring force to all other points ◮ compare distances only with a few points ◮ difference between high dim, low dim distance ◮ maintain small local neighborhood set ◮ move to better location using computed forces ◮ somewhat evangelical pro-graph stance ◮ compute distances between all points ◮ but we could use more such ◮ O ( n 2 ) iteration, O ( n 3 ) algorithm characterizations Faster Spring Model [Chalmers 96] Faster Spring Model [Chalmers 96] Faster Spring Model [Chalmers 96] Parent Finding [Morrison 02, 03] ◮ lay out a √ n subset with [Chalmers 96] ◮ compare distances only with a few points ◮ compare distances only with a few points ◮ compare distances only with a few points ◮ for all remaining points ◮ maintain small local neighborhood set ◮ maintain small local neighborhood set ◮ maintain small local neighborhood set ◮ each time pick some randoms, swap in if closer ◮ find ”parent”: laid-out point closest in high D ◮ each time pick some randoms, swap in if closer ◮ each time pick some randoms, swap in if closer ◮ small constant: 6 locals, 3 randoms typical ◮ place point close to this parent ◮ O ( n ) iteration, O ( n 2 ) algorithm ◮ O ( n 5 / 4 ) algorithm Issues True Dimensionality: Linear True Dimensionality: Nonlinear MDS Beyond Points ◮ how many dimensions is enough? ◮ nonlinear MDS: 10-15 ◮ galaxies: aggregation ◮ could be more than 2 or 3 ◮ all intermediate points possible ◮ knee in error curve ◮ categorizable by people ◮ example ◮ red, green, blue, specular, diffuse, glossy, ◮ which distance metric: Euclidean or other? ◮ measured materials from graphics metallic, plastic-y, roughness, rubbery, ◮ linear PCA: 25 ◮ computation ◮ get physically impossible intermediate points greasiness, dustiness... ◮ naive: O ( n 3 ) ◮ better: O ( n 2 ) Chalmers 96 ◮ themescapes: terrain/landscapes ◮ hybrid: O ( n √ n ) [A Data-Driven Reflectance Model, SIGGRAPH 2003, W Matusik, H. Pfister M. Brand [A Data-Driven Reflectance Model, SIGGRAPH 2003, W Matusik, H. Pfister M. Brand and L. McMillan, graphics.lcs.mit.edu/ ∼ wojciech/pubs/sig2003.pdf] and L. McMillan, graphics.lcs.mit.edu/ ∼ wojciech/pubs/sig2003.pdf] [www.pnl.gov/infoviz/graphics.html] Cluster Stability Approach Graph Layout Barrier Jumping ◮ same idea as simulated annealing ◮ criteria ◮ but compute directly ◮ display ◮ geometric distance matching graph-theoretic ◮ just ignore repulsion for fraction of vertices ◮ also terrain metaphor distance ◮ solves start position sensitivity problem ◮ underlying computation ◮ vertices one hop away close ◮ vertices many hops away far ◮ energy minimization (springs) vs. MDS ◮ insensitive to random starting positions ◮ weighted edges ◮ major problem with previous work! ◮ normalize within each column ◮ do same clusters form with different random ◮ tractable computation ◮ similarity metric start points? ◮ force-directed placement ◮ ”ordination” ◮ discussion: Pearson’s correllation coefficient ◮ discussion: energy minimization ◮ threshold value for marking as similar ◮ spatial layout of graph nodes ◮ others: gradient descent, etc ◮ discussion: finding critical value ◮ discussion: termination criteria