Manifold Clustering of Shapes

1
Manifold Clustering of Shapes

• Dragomir Yankov, Eamonn Keogh
• Dept. of Computer Science Eng.
• University of California Riverside

2
Outline

• Problem formulation
• Shape space representation. Similarity metric.
• Manifold clustering of shapes
• Handling noisy and bridged clusters
• Experimental evaluation

3
Problem formulation

• Object recognition systems dependent heavily on
  the accurate identification of shapes
• Learning the shapes without supervision is
  essential when large image collections are
  available

• In this work we propose a robust approach for
  clustering of 2D shapes

The malaria images are part of the Hoslink
medical databank, and the diatoms images are part
of the collection used in the ADIAC project.
4
Data representation

• Requirements
• invariant to basic geometric transformations
• handle limited rotations
• low dimensionality for meaningful clustering

• Centroid-based time series representation
• All extracted time series are further
  standardised and resampled to the same length

5
Measuring shape similarity

• The Euclidean distance does not capture the real
  similarities
• Rotationally invariant distance rd
• approximate rotations as
• and define
• Metric properties of rd

6
Manifold clustering of shapes

• Vision data often reside on a nonlinear embedding
  that linear projections fail to reconstruct
• We apply Isomap to detect the intrinsic
  dimensionality of the shapes data.

• Isomap moves further apart different clusters,
  preserving their convexity

7
Handling noisy and bridged clusters

• Instability of the Isomap projection
• The degree-k-bounded minimum spanning tree
  (k-MST) problem
• The b-Isomap algorithm

8
Experimental evaluation

• Diatom dataset
• 4classes
• 2 classes (Stauroneis
• and Flagilaria)

Dataset Method Dim k Acc() Std()
4-class diatoms MDS 3D N/A 62.3 5.2
4-class diatoms Isomap 3D 16 86.2 3.0
4-class diatoms b-Isomap 3D 4 83.0 3.6
2-class diatoms MDS 3D N/A 90.2 1.3
2-class diatoms Isomap 3D 5 92.7 1.3
2-class diatoms b-Isomap 3D 3 98.3 0.9
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Experimental evaluation

• Marine creatures

Data Method Dim k Acc
Marine creatures MDS 2D N/A 61.0
Marine creatures Isomap 3D 4 77.6
Marine creatures b-Isomap 3D 4 80.0

• Arrowheads

Data Method Dim k Acc
Arrow heads MDS 3D N/A 75.6
Arrow heads Isomap 3D 14 85.2
Arrow heads b-Isomap 2D 6 85.1
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Conclusions and future work

• We presented a method for clustering of shapes
  data invariantly to basic geometric
  transformations
• We demonstrated that the Isomap projection built
  on top of a rotationally invariant distance
  metric can reconstruct correctly the intrinsic
  nonlinear embedding in which the shape examples
  reside.
• The degree-bounded MST modification of the Isomap
  algorithm can decreases the effect of bridging
  elements and noise in the data.
• Our future efforts are targeted towards an
  automatic adaptive approach for combining the
  features of Isomap and b-Isomap

Thank you!