Quaternion Domain k-Means Clustering for Improved Real Time Classification of E-Nose Data

This paper proposes a novel clustering technique implemented in the quaternion domain for qualitative classification of E-nose data. The proposed technique is in many ways similar to the popular k-means clustering algorithm. However, computations carried out in the quaternion space have yielded better class separability and higher cluster validity. A pool of possible cluster centers was created by subjecting each initial center to a fixed rotation in the quaternion space. The test samples were then compared with each of the centers in the pool and assigned to an appropriate center using minimum Euclidean distance criterion. The evolving clusters have been evaluated periodically for their compactness and interclass separation using the Davis-Bouldin (DB) index. The set of clusters having minimum DB index was chosen as an optimal one. It was observed that using the proposed technique the inverse DB index remains significantly higher with successive iterations implying a consistent performance on the cluster validity front. Furthermore, clusters formed using quaternion algebra have been observed to have a smaller DB index. Finally, when compared with the traditional k-means algorithm, the proposed technique performed significantly better in terms of percentage classification of unlabeled samples.