Multi-level quantum inspired metaheuristics for automatic clustering of hyperspectral images

Hyperspectral images contain large spectral information with an abundance of redundancy and a curse of dimensionality. Due to the absence of prior knowledge or availability of ground-truth data, clustering of these images becomes a herculean task. Hence, unsupervised cluster detection methods are more beneficial for utilising hyperspectral images in real-life scenarios. In this paper, six multilevel quantum inspired metaheuristics are proposed viz., Qubit Genetic Algorithm, Qutrit Genetic Algorithm, Qubit Multi-exemplar Particle Swarm Optimization Algorithm, Qutrit Multi-exemplar Particle Swarm Optimization Algorithm, Qubit Artificial Humming Bird Algorithm, and Qutrit Artificial Humming Bird Algorithm, for determining the optimal number of clusters in hyperspectral images automatically. Binary and ternary quantum versions of the algorithms are developed to enhance their exploration and exploitation capabilities. Simple algorithms for implementing quantum rotation gates are developed to bring diversity in the population without resorting to look-up tables. One of the main features of quantum gates is that they are reversible in nature. This property has been utilized for implementing quantum disaster operations. The application of a dynamic number of exemplars also enhances the performance of the Multi-exemplar Particle Swarm Optimization Algorithm. The six proposed algorithms are compared to the classical Genetic Algorithm, Multi-exemplar Particle Swarm Optimization Algorithm, and Artificial Humming Bird Algorithm. All the nine algorithms are applied on three hyperspectral image datasets viz., Pavia University, Indian Pines, and Xuzhou HYSPEX datasets. Statistical tests like mean, standard deviation, Kruskal Wallis test, and Tukey’s Post Hoc test are performed on all the nine algorithms to establish their efficiencies. Three cluster validity indices viz., Xie-Beni Index, Object-based Validation with densities, and Correlation Based Cluster Validity Index are used as the fitness function. The F, F’, and Q scores are used to compare the clustered images. The proposed algorithms are found to perform better in most of the cases when compared to their classical counterparts. It is also observed that the qutrit versions of the algorithms are found to converge faster. They also provide the optimal number of clusters almost equivalent to the number of classes identified in the ground-truth image.