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Does 3D Really Make Sense for Visual Cluster Analysis? Yes! Bing Wang and Klaus Mueller Visual Analytics and Imaging Lab Computer Science Department Stony.

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Presentation on theme: "Does 3D Really Make Sense for Visual Cluster Analysis? Yes! Bing Wang and Klaus Mueller Visual Analytics and Imaging Lab Computer Science Department Stony."— Presentation transcript:

1 Does 3D Really Make Sense for Visual Cluster Analysis? Yes! Bing Wang and Klaus Mueller Visual Analytics and Imaging Lab Computer Science Department Stony Brook University and SUNY Korea

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5 but they’re just illusions….

6 still just illusions….

7 Why Do These Work So Well? Because they appeal to learned depth cues:  shading  occlusion  shadows  perspective  depth of field And they are also illusions of known 3D objects  learned in childhood  often in conjunction with touching  no need for stereo  motion parallax is just as good

8 Indexing the Brain Next time a similar object is seen the 3D shape is retrieved Already recognized by H. von Helmholtz in the 19 th century  see also G. Hatfield “Perception as Unconscious Inference”

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10 What’s Cluster Analysis Goal  tries to find shapes and trends in ND point clouds  a common tool is the Scatterplot matrix

11 Scatterplot Matrices Don’t Scale Can’t see multivariate relationships  especially not when D is high

12 What Can 3D Do for Cluster Analysis Cluster analysis research and practice is reluctant to use 3D  but why not take advantage of this collection of learnt 3D shapes A common argument is  what will you do when the data is 4D, 5D, …, ND?  so we tested how many datasets are truly way beyond 3D  here we looked at each cluster separately, as a low-D subspace

13 Workflow Unclustered data Clustered data DBSCAN Eigenvalues Principal Components PCA Intrinsic Dimensionality Elbow Subspace Similarity Cosine

14 What’s DBSCAN Can find arbitrary shaped clusters based on density  DBSCAN = Density-Based Spatial Clustering of Applications with Noise  recruits points to a cluster based on reachability  two parameters -neighborhood radius ε -the minimum number of points minPtn a cluster needs to have -difficult to find good settings

15 DBSCAN – Example

16 Visual Interface for DBSCAN Parameters Distance histogram  shows all pairwise distances  helps to choose  Neighborhood heat map  shows for each point the number of points within a certain   helps to choose minPtn number of neighbors   0 20

17 Intrinsic Dimensionality We used the elbow method on the scree plot  but typically there are long tails due to noise  might be better to use the percentage, say 5% (0.05) ordered normalized Eigenvalue % PCA Eigenvalue

18 Cosine Similarity We computed the cosine similarity of the PCA vectors  did this for every ordered pair of PCA vectors and subspace  determines the similarity of the subspaces  helps to plan transitioning in the visualization

19 Results We studied a (so far) small set of public domain datasets  from the UCI machine learning repository  Boston Housing (n=506, d=14)  Image Segmentation (n=1,200, d=18) We also studied datasets from our own collection  atmospheric dataset ISDAC (n=221, d=33)

20 Boston Housing Analysis  there are 3 representative clusters  according to screeplot 3D seems to be OK  subspace 3 quite different from subspace 1 and 2 which are similar

21 Image Segmentation Analysis  elbow at d=3 and 5% mark is at d=4 or 5  for all clusters d=3 has 15% or lower  PCA similarity analysis showed that all but one subspace pair were quite different

22 ISDAC Analysis  3D with perhaps some transitioning seems to be OK  PCA similarity analysis indicated that subspaces are different

23 Visualization System Overview 2D scatterplot shaded 3D display SPLOM

24 Our System 3D exploration interface with subspace hopping capability  trackball interface for continuous rotation in 3D space  interactions to fluidly transition from one 3D subspace to another local subspace explore (LSE) global subspace explorer (GSE)

25 Interactions Mouse buttons control subspace navigation  left mouse press rotates the trackball within the 3D subspace  right mouse press tilts the trackball into a new subspace  middle press changes the z-axis and goes “deeper” into ND space Cluster chasing

26 Subspace Trail Map Gives an overview about subspaces visited  layout with generalized barycentric coordinates  user can click anywhere to visit the corresponding subspace

27 Switch to 3D Views

28 Demo Video play video

29 Future Work Study more datasets Refine 3D shape display  expand current convex hull to concave topologies  use volume rendering and iso-surface visualization techniques  better visualization of appearances (skew, density fields,…)  better way to visualize outliers  capabilities to intersect solids  multi-resolution, hierarchical representations

30 Questions? Funding provided by:  NSF grants , , and  US Department of Energy (DOE) Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences  The IT Consilience Creative Project through the Ministry of Knowledge Economy, Republic of Korea


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