Agglomerative Mean Shift Cluster Using Shortest Path and Fuzzification Algorithm

In this research paper, an agglomerative mean shift with fuzzy clustering algorithm for numerical data and image data, an extension to the standard fuzzy C-Means algorithm by introducing a penalty term to the objective function to make the clustering process not sensitive to the initial cluster centers. The new algorithm of Shortest path and Fuzzification algorithm can produce more consistent clustering results from different sets of initial clusters centers. In fuzzy clustering, data elements may belong to more than one cluster, and associated with each element we have a set of membership levels. These indicate a degree of belonging to clusters, or the “strength of connectivity (Fitness Similarity)” of the association between that data element and a particular cluster. Fuzzy clustering is a process of assigning these membership levels, and then using them to assign data elements to one or more clusters. Thus, border nodes of a cluster, may be in the cluster to a lesser degree than inner nodes.The main ideas behind the above concept of the fuzzy membership function μik are that the edges connecting the inner nodes in a cluster may have a larger “degree of belonging” to a cluster than the “peripheral” edges (which, in a sense, reflects a greater “strength of connectivity” between a pair of nodes). For instance, the edges (indexed i) connecting the inner nodes in a cluster (indexed k) are assigned μik = 1 whereas the edges linking the boundary nodes in a cluster have μik < 1.