Clustering Algorithm Based on Triple-Stranded and 3-armed DNA Model

Abstract

The quality of traditional grid-clustering and pure hierarchical clustering methods suffers from some limitations, especially the inability of hierarchical clustering to perform adjustment on once merge or split decision. However, DNA computations can be introduced here to do global search and find the best clusters. Since the grid-clustering can be transformed into HPP (Hamilton Path Problem) and the other one equals to MST (Minimal Spanning Tree) algorithm while using the minimum distance measure, this paper proposes to solve grid-clustering using triple-stranded DNA model and nearest neighbor clustering by 3-armed DNA model based on the above thought. Firstly, it is needed to get the initial data pool containing all the possibilities, then screen those owning all data points to be clustered, and finally get the best one(s). Accordingly, under the special designed biological algorithm, both of the DNA algorithms have the time complexity of O(n), which n represents the number of processed data waiting to be clustered. In fact, the way of using triple-stranded structures to select solutions satisfying the paticularly restricted conditions could be further extended to more DNA algorithms using double-helix. Meanwhile, if other applications are on the basis of binary tree constructions, 3-armed DNA molecules designed here can be made more use.