On the performance of bisecting K-means and PDDP

The problem this paper focuses on is the unsupervised clustering of a data-set. The dataset is given by the matrix [ ] N p N x x x M × R ∈ = ,..., , 2 1 , where each column of M, p i x R ∈ , is a single data-point. This is one of the more basic and common problems in fields like pattern analysis, data mining, document retrieval, image segmentation, decision making, etc. ([12, 13]). The specific problem we want to solve herein is the partition of M into two sub-matrices (or sub-clusters) L N p L M × R ∈ and R N p R M × R ∈ , N N N R L = + . This problem is known as bisecting divisive clustering. Note that by recursively using a divisive bisecting clustering procedure, the dataset can be partitioned into any given number of clusters. Interestingly enough, the clusters so-obtained are structured as a hierarchical binary tree (or a binary taxonomy). This is the reason why the bisecting divisive approach is very attractive in many applications (e.g. in document-retrieval/indexing problems – see e.g. [17] and references cited therein). Among the divisive clustering algorithms which have been proposed in the literature in the last two decades ([13]), in this paper we will focus on two techniques: • the bisecting K-means algorithm; • the Principal Direction Divisive Partitioning (PDDP) algorithm.