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WIREs Data Mining Knowl Discov

Objective function‐based clustering

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Clustering is typically applied for data exploration when there are no or very few labeled data available. The goal is to find groups or clusters of like data. The clusters will be of interest to the person applying the algorithm. An objective function‐based clustering algorithm tries to minimize (or maximize) a function such that the clusters that are obtained when the minimum/maximum is reached are homogeneous. One needs to choose a good set of features and the appropriate number of clusters to generate a good partition of the data into maximally homogeneous groups. Objective functions for clustering are introduced. Clustering algorithms generated from the given objective functions are shown, with a number of examples of widely used approaches discussed. © 2012 Wiley Periodicals, Inc.

Figure 1.

k‐Means clustering algorithm.

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Figure 2.

The Iris data (a) with labels (b) clustered by k‐means with a Good initialization and (c) clustered by k‐means with a Bad initialization.

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Figure 3.

FKM algorithm.

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Figure 4.

The EM clustering algorithm.

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Figure 5.

The Iris data clustered by the EM algorithm.

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Figure 6.

Three cluster problem that is difficult.

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Figure 7.

PKM algorithm.

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Figure 8.

Relational k‐means clustering algorithm.

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Figure 9.

Relational fuzzy k‐means clustering algorithm.

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Figure 10.

Kernel‐based k‐means/FKM algorithm.

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Figure 11.

Finding the right number of clusters with a partition validity metric. Any validity metric that applies to a particular objective function‐based clustering algorithm can be applied.

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Figure 12.

An approach to speeding up k‐means (applied in step 2) with one pass through the data.

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Algorithmic Development > Scalable Statistical Methods
Technologies > Machine Learning
Technologies > Structure Discovery and Clustering
Algorithmic Development > Structure Discovery
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