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