Agglomerative Hierarchical Clustering: An Introduction to Essentials. (3) Standardization, Normalization and Dimensionality Reduction of a Data Matrix

Abstract

In a previous tutorial article I looked at a proximity coefficient and, in the light of that proximity created a vector-distance matrix and used it to construct a hierarchical tree using different hierarchical clustering methods which will be the basis for exploratory multivariate analysis. The present article deals with three topics: (i) standardization for variable scales variation, (ii) normalization for sample length variation, and (iii) dimensionality reduction or minimization of data space. These techniques reflect the author's academic background and particular area of interest and are, by necessity, not a particular purpose and are straightforwardly applicable to other kinds of data, and thus to a wide range of analysis in Linguistics. My treatment of these techniques is, necessarily, introductory and brief. I hope that this article will provide practitioners with an introductory overview of these techniques used for cluster analysis of electronic corpora of linguistic data.