Cluster Analysis

As in the previous chapter this chapter mainly deals with multivariate data. A multivariate data set can conveniently be expressed in the form of a matrix as follows: $$X = \left[ {\begin{array}{*{20}{c}} {{X_{11}}} \\ {{X_{21}}} \\ \vdots \\ {{X_{n1}}} \end{array}\,\,\,\,\begin{array}{*{20}{c}} {{X_{12}}} \\ {{X_{22}}} \\ \vdots \\ {{X_{n2}}} \end{array}\,\,\,\begin{array}{*{20}{c}} \ldots \\ \ldots \\ \, \\ \ldots \end{array}\,\,\,\begin{array}{*{20}{c}} {{X_{1p}}} \\ {{X_{2p}}} \\ \vdots \\ {{X_{np}}} \end{array}} \right]\, = \,\left[ {\begin{array}{*{20}{c}} {{{X'}_1}} \\ {{{X'}_2}} \\ \vdots \\ {{{X'}_n}} \end{array}} \right]\,.$$ The rows of X therefore, represent the n different cases while the columns represent the p variables.