Niall Fitzgerald In June completed Ph.D. in Applied Statistics from University College Cork

2. Modified k-Medoids Clustering of Neuronal Pathways with High Definition Fiber Tracking Data Using a Novel Dissimilarity Measure. IEEE International Conference on Data Mining Miami, Florida, USA 2009 – December 8th 2009

3. Niall Fitzgerald • In June completed Ph.D. in Applied Statistics from University College Cork • PhD Thesis applied statistical methods such as regularization/SVD and GCV to the inverse problem in bolus tracking CT/MR Main Quadrangle, UCC

4. Challenge 2 : Segment the 250,000 fibres of the brain into ≥8 and ≤50 clusters (tracts) using more than 80% of the fibres for each of the 5 scans with an automatic segmentation algorithm that is reliable both within and between subjects. My goal: Achieve a simple understandable solution in the easiest possible way. From ICDM PBC Competition Rules

5. 1: Read in the data 2: Dissimilarity measure 3: Clustering Method -> k-Medoids algorithm 4: K-Medoids algorithm modification 5: Final Results

6. Similarity Measure Motivation How does the human eye measure the similarity between two fibres?

7. Similarity Measure Motivation Overlap in x-dimension Assuming for example

8. More Formally • Linearly transform 1-Di,j to obtain dissimilarity measure • Symmetric (has minimum dissimilarity of 0) • Quick to calculate (only need max and min in each dimension for each fibre)

9. Downside • There are instances where this measure may not perform well • Using the k-means clustering algorithm is not possible with this measure. How could you compare the summary measures for a given fibre to a hypothetical centroid or x,y,z coordinate? A method which operates only on the dissimilarity matrix is required.

10. K-Medoids Clustering Algorithm • Uses within cluster points as cluster medoids • Robust to outlying fibres as it minimizes the sum of dissimilarities instead of a sum of Euclidean distances. • One only needs access to the lower triangle dissimilarity matrix

11. Brief Outline (Unmodified) Step 1 selection of the k initial medoids, Ckwhere k = 1…50 and CkЄ 1…250,000 and is unique for each cluster. Step 2 evaluation for each fibre which of the medoids (Ck) it is nearest (least dissimilar to) and assigning that fibre to cluster k. Step 3 finding, within each cluster, the fibre that minimizes the sum of dissimilarities between itself and all other fibres within that cluster. This gives an updated Ckfor each cluster.

12. The Modification For Step 2, if the distance between a given fibre i and each of the medoids Ck=1…49 is greater than a pre-specified threshold τ, then that fibre is assigned to cluster 50 (Ck=50) Hypothetical example Step 2 for τ = 0.95 Fibres with minimum dissimilarity < τare assigned to cluster (Tract) 50

13. Conclusion Goal of simple understandable solution achieved • Room for Improvement (Challenges for Data Miners) • Better initial medoid selection • Use of a silhouette plot could be investigated as a possible • method for improved k selection. • The proximity measure described by Zhang et al could also possibly offer better results. Comparison between other measures to produce a gold standard method.

14. Thanks for listening Thanks to the ICDM PBC team for a great challenge Thanks to my girlfriend Áine for her patience with my endeavours