This paper mainly deals with the analysis of IPP in clustering. Clustering is exemplified by the unsupervised learning of patterns and clusters that may exist in a given database and is a useful tool for Knowledge Discovery in Database (KDD). A mathematical programming formulation of this problem is proposed that is theoretically justifiable and computationally implementable in a finite number of steps. The clustering algorithm applies the hierarchical clustering methodology [1] where points or clusters with the shortest distance are merged into a cluster until the desired number of clusters is achieved. Numerical examples are given for the above algorithmic approach.