Cluster Analysis

Cluster analysis is the grouping a set of objects in such a way that objects in the same cluster group are more similar to each other than to those in other clusters.

Types of Cluster Analysis

There are a number of approaches to cluster analysis, including:

Centroid - clusters are represented by a central vector, which may not necessarily be a member of the data set; and example is k-means clustering
Density - clusters are defined as areas of higher density than the remainder of the data set
Distribution - based on probability distributions; clusters are defined as objects belonging most likely to the same distribution
Grid - analysis is performed on grid cells
Hierarchical - based on the core idea of objects being more related to nearby objects than to objects farther away

Cluster Algorithm Analysis

There are a number of methods for evaluating how well a clustering has been performed. One example is the Davies-Bouldin Index:

$\\P = \frac{1}{n} \sum_{i=1}^{n}\max_{j\neq i} \left (\frac{\sigma _{i}+\sigma _{j}}{d\left ( c_{i},c_{j} \right )} \right ) \\\\\mathrm{\textup{where:}} \\\\P\,\,\,\,\,\mathrm{\textup{performance index}} \\c\,\,\,\,\,\,\,\mathrm{\textup{centroid (geometric center)}} \\\sigma \,\,\,\,\,\,\mathrm{\textup{a verage distance of cluster elements to the centroid}} \\n\,\,\,\,\,\,\mathrm{\textup{number of clusters}} \\i\,\,\,\,\,\,\,\,\mathrm{\textup{index over elements}} \\j\,\,\,\,\,\,\,\mathrm{\textup{index over elements}}$

Cluster Analysis

Types of Cluster Analysis

Cluster Algorithm Analysis

References