Pattern Recognition, 4th Edition

14.5.1. The Isodata or k-Means or c-Means Algorithm

This is one of the most popular and well-known clustering algorithms [Duda 01, Ball 67, Lloy 82]. It can be viewed as a special case of the generalized hard clustering algorithmic scheme when point representatives are used and the squared Euclidean distance is adopted to measure the dissimilarity between vectors xⁱ and cluster representatives θ^j. Before we state the algorithm explicitly, some further comments may be of interest. For this case Eq. (14.81) becomes

(14.85)

This is nothing but the trace of the within scatter matrix S^w, defined in Chapter 5. That is,

(14.86)

For the above choice ...