Exploring Algorithms and Mechanics of Fuzzy and Hard Clustering in Universal Cluster Analysis

Abstract

A cluster is a collection of data objects which  can  be  based  on similarity to one another within the same cluster or dissimilar to the objects in other clusters. Therefore, cluster analysis refers to the grouping a set o f data objects into clusters. It involves organizing data into classes such that there is both high intra class similarity as well as low inter- class similarity. Cluster analysis is a group of multivariate  techniques  whose  purpose is to group objects (for example, test items, respondents, products, or other entities) based on the characteristics they possess. It is a means of grouping such objects based upon attributes that make them similar. If plotted  geometrically,  the  objects  within the clusters will be close together, while the distance between clusters will be farther apart. Statisticians  conceptualize  clustering as unsupervised classification where there are no predefined classes; psychologists conceptualize it as sorting by psychologists while marketing experts consider it as segmentation. It is the algorithmic process of finding natural groupings among objects. Cluster variate represents a mathematical representation of the selected set of variables which compares the  object’s similarities. Clustering     may  specify  the  relationship of the clusters to each other, for example, a hierarchy of clusters embedded in each other. There are two types of clustering thus: (1) Soft clustering (which is also known as fuzzy clustering) in which each object belongs to each cluster to a certain degree (for instance, a likelihood of belonging to the cluster) and, (2) Hard clustering in which each object belongs to a cluster or not. The paper explores the algorithms  and  mechanics  of  carrying  out clustering in both hard and soft clustering.