Robust Information-theoretic Clustering By C. Bohm, C. Faloutsos, J-Y. Pan, and C. Plant Presenter: Niyati Parikh

Objective Find natural clustering in a dataset Two questions: Goodness of a clustering Efficient algorithm for good clustering

Define “goodness” Ability to describe the clusters succinctly Adopt VAC (Volume after Compression) Record #bytes for number of clusters k Record #bytes to record their type (guassian, uniform,..) Compressed location of each point

VAC Tells which grouping is better Lower VAC => better grouping Formula using decorrelation matrix Decorrelation matrix = matrix with eigenvectors

Computing VAC Steps: Compute covariance matrix of cluster C Compute PCA and obtain eigenvector matrix Compute VAC from the matrix

Efficient algorithm Take initial clustering given by any algorithm Refine that clustering to remove outliers/noise Output a better clustering by doing post processing

Refining Clusters Use VAC to refine existing clusters Removing outliers from the given cluster C Define Core and Out as set of points for core and outliers in C Initially Out contains all points in C Arrange points in ascending order of its distance from center Compute VAC Pick the closest point from Out and move to Core Compute new VAC If new VAC increases then stop, else pick next closest point and repeat

VAC and Robust estimation -Conventional estimation: covariance matrix uses Mean -Robust estimation: covariance matrix uses Median -Median is less affected by outliers than Mean

Sample result -Imperfect clusters formed by K-Means affect purifying process -May result into redundant clusters, that could be merged

Cluster Merging Merge Ci and Cj only if the combined VAC decreases savedCost(Ci, Cj) = VAC(Ci) + VAC(Cj) – VAC(Ci U Cj) If savedCost > 0, then merge Ci and Cj Greedy search to maximize savedCost, hence minimize VAC

Final Result

Experiment results

Example

Thank You Questions?