1. Data Clustering (a very short introduction) Intuition: grouping of data into clusters so that elements from the same cluster are more similar to each other than they are to a element from a different cluster. What is the best clustering? I II III

2. Major decision steps: Pattern representation Definition of a pattern proximity measure Method for clustering Data abstraction (cluster representation, e.g. centroids …) Assessment of output (evaluation of the output)

3. Proper pattern representation can simplify clustering Identify circles: Cartesian coordinates? -> use polar coordinates (r,θ)

4. Definition of a pattern proximity measure Similarity between two clusters C1 ={x i } C2 ={y j } Examples: Single Link min ij dist(x i,y j ) < e Complete Link max ij dist(x i,y j ) < e

5. Pose Clustering Aims to solve the LCP problem. 1)Compute a set of transformations that align one structure with the other. 2)Cluster transformations. 3)Check large clusters. Idea: a large common point set will produce a large number of similar transformations.

6. Example: Clustering of 3D transformations Goal: Prevent redundant solutions Representation: 1) 3x3 matrix + 1x3 vector Problem: how to measure distance between two transformations? 2) Image of points, T(S) dist(T 1,T 2 )= dist(T 1 (S),T 2 (S)) (for example RMSD or bottleneck) Problem: time complexity Solution: use less points, 3-4 farthest points are stable enough