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Robust Information-theoretic Clustering

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”.

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Robust Information-theoretic Clustering

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

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

  3. 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

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

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

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

  7. 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

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

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

  10. 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

  11. Final Result

  12. Experiment results

  13. Example

  14. Thank You • Questions?

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