Inflated power iteration clustering algorithm to optimize convergence using Lagrangian constraint

Abstract

Spectral clustering is one of the machine learning techniques based on graph theory. It requires finding eigen values and eigen vector of large matrices consuming much time and space. Often, finding an optimal eigen value is sufficient to cluster data. Power Iteration Clustering algorithm (PIC) replaces the eigen values with pseudo eigen vector. Though PIC is fast and scalable it causes inter collision problem when dealing with larger datasets. Accuracy is also a concern. To solve the optimal Eigen value problem, in this paper we proposes an Inflated Power Iteration Clustering algorithm. It uses the modified lagrangian constraint which induces an exponential inflationary growth by increasing the rate of convergence of eigen vector to get an ideal optimal solution. This algorithm is validated by experimenting on various real and synthetic dataset of varying size. On validation it has been found that the performance of the algorithm has been improved in terms of speed up and efficiency. The speed up has been improved by 31% when compared to PIC and almost 40−42% with K-means algorithm. The accuracy has been improved by 7% than k means and 4% than PIC. The proposed algorithm is highly scalable and can be used for clustering Big Data.