A Quantum Annealer for Subset Feature Selection and the Classification of Hyperspectral Images

Hyperspectral images (HSIs) showing objects belonging to several distinct target classes are characterized by dozens of spectral bands being available. However, some of these spectral bands are redundant and/or noisy, and hence, selecting highly informative and trustworthy bands for each class is a vital step for classification and for saving internal storage space; then the selected bands are termed a highly informative spectral band subset. We use a mutual information (MI)-based method to select the spectral band subset of a given class and two additional binary quantum classifiers, namely a quantum boost (Qboost) and a quantum boost plus (Qboost-Plus) classifier, to classify a two-label dataset characterized by the selected band subset. We pose both our MI-based band subset selection problem and the binary quantum classifiers as a quadratic unconstrained binary optimization (QUBO) problem. Such a quadratic problem is solvable with the help of conventional optimization techniques. However, the QUBO problem is an NP-hard global optimization problem, and hence, it is worthwhile for applying a quantum annealer. Thus, we adapted our MI-based optimization problem for selecting highly informative bands for each class of a given HSI to be run on a D-Wave quantum annealer. After the selection of these highly informative bands for each class, we employ our binary quantum classifiers to a two-label dataset on the D-Wave quantum annealer. In addition, we provide a novel multilabel classifier exploiting an error-encoding output code when using our binary quantum classifiers. As a real-world dataset in Earth observation, we used the well-known AVIRIS HSI of Indian Pine, north-western Indiana, USA. We can demonstrate that the MI-based band subset selection problem can be run on a D-Wave quantum annealer that selects the highly informative spectral band subset for each target class in the Indian Pine HSI. We can also prove that our binary quantum classifiers and our novel multilabel classifier generate a correct two- and multilabel dataset characterized by their selected bands and with high accuracy such as having been produced by conventional classifiers-and even better in some instances.