Eigenvector selection in spectral clustering using Tabu Search

Ng. Jordan Weiss (NJW) is one of the most widely used spectral clustering algorithms. For partitioning data into clusters, this method uses the largest eigenvectors of the normalized affinity matrix derived from the data set. However, this set of features is not always the best selection to represent and reveal the structure of the data. In this paper, we aim to propose a quadratic framework to select the most representative eigenvectors. In this way, we define an objective function which includes two factors. In the first part, the interaction of each pair of eigenvectors is considered. In the second part, the ability of each eigenvector to represent the structure of data is considered separately. Then, we use proposed Tabu Search in [1] to solve this mixed-integer quadratic optimization problem. The experimental results show the success of this method to select relevant eigenvectors.