modified global k-means algorithm for minimum sum-of-squares clustering problems

Intelligent Database Systems Lab

N.Y.U.S.T.I. M.

Modified global k-means algorithm for

minimum sum-of-squares clustering problems

Pattern Recognition (PR, 2008)

Presenter : Lin, Shu-Han

Authors : Adil M. Bagirov

Intelligent Database Systems Lab

N.Y.U.S.T.I. M.

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Outline

Motivation Objective Methodology Experiments Conclusion Comments

Intelligent Database Systems Lab

N.Y.U.S.T.I. M.Motivation

k-Means algorithm sensitive to the choice of starting points

inefficient for solving clustering problems in large data sets

Global k-Means (GKM) algorithm incremental algorithm (dynamically adds a cluster center at a time)

uses each data point as a candidate for the k-th cluster center

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Intelligent Database Systems Lab

N.Y.U.S.T.I. M.Objectives

Propose a new version of GKM

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Intelligent Database Systems Lab

N.Y.U.S.T.I. M.Methodology – k-Means

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sensitive to the choice of a starting point

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N.Y.U.S.T.I. M.Methodology – The GKM algorithm

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Objective function

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N.Y.U.S.T.I. M.Methodology – Objective function

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Old version

Reformulated version

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N.Y.U.S.T.I. M.Methodology – fast GKM algorithm

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Old version

Proposed version (auxiliary cluster function)

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N.Y.U.S.T.I. M.Methodology – modified GKM algorithm

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Proposed version

Intelligent Database Systems Lab

N.Y.U.S.T.I. M.Methodology – modified GKM algorithm

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N.Y.U.S.T.I. M.Experiments

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MS k-means: Multi-start k-means GKM: fast Global K-Means MGKM: Modified Global K-Means

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N.Y.U.S.T.I. M.Experiments

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N.Y.U.S.T.I. M.Experiments

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Overall (14 datasets, 140 results) The MS k-means algorithm finds the best known (or near best known)

solutions 42 (33.3%) times

GKM algorithm 76 (60.3%) times

MGKM algorithm 102 (81.0%) times

Large k in large data sets (m) The MS k-means algorithm failed to find the best known (or near best

known) solutions

GKM algorithm finds such solutions 22 (45.8%) times

MGKM algorithm 42 (87.5%) times.

Intelligent Database Systems Lab

N.Y.U.S.T.I. M.

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Conclusions

A new version of the GKM Change the computation of starting points

By minimize the auxiliary cluster function

Given tolerance

Is more effective than GKM large dataset especially

The choice of starting points in k-means is crucial

Intelligent Database Systems Lab

N.Y.U.S.T.I. M.

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Comments

Advantage Theoretically analysis

Drawback Describe why they think to modify anything they tend to modify is

important, or need to.

Application GKM outperforms k-means algorithm