Editing Cluster analysis (section)

==== Purity ====
Purity is a measure of the extent to which clusters contain a single class.<ref name="Christopher D. Manning, Prabhakar Raghavan & Hinrich Schutze"/> Its calculation can be thought of as follows: For each cluster, count the number of data points from the most common class in said cluster. Now take the sum over all clusters and divide by the total number of data points. Formally, given some set of clusters <math>M</math> and some set of classes <math>D</math>, both partitioning <math>N</math> data points, purity can be defined as:
:<math>
\frac{1}{N}\sum_{m\in M}\max_{d\in D}{|m \cap d|}
</math>
This measure doesn't penalize having many clusters, and more clusters will make it easier to produce a high purity. A purity score of 1 is always possible by putting each data point in its own cluster. Also, purity doesn't work well for imbalanced data, where even poorly performing clustering algorithms will give a high purity value. For example, if a size 1000 dataset consists of two classes, one containing 999 points and the other containing 1 point, then every possible partition will have a purity of at least 99.9%.