A new validity index with K-means algorithm and its applications in electrical tomography

Many validity indices have been proposed for quantitatively assessing the performance of any clustering algorithms. But so far these validity indices generally depend on common trail-and-error methods and are inefficient when processing large or real-time needed datasets. In this paper we propose a Gerschgorin disk estimation-based criterion to estimate the optimal number of clusters when applying c-means algorithm. The clustering results first consist of a correlation matrix, then the eigenvalue decomposition is performed to obtain all eigenvalues and eigenvectors of the matrix, and finally in terms of the classical Gerschgorin disk theorem, the optimal number of clusters is estimated. On the other hand, a validity index plays an important role in electrical tomography of multiple-phase flow where the number of clusters has to be determined in advance. Experimental results on electrical tomography situation demonstrate that the new method outperforms the recently published approaches, while the efficiency is significantly improved.