Abstract
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.
Highlights
A QUANTUM Annealer (QA) is a computing machine configured as a graph network G = (E, V ), at each vertex of which particles are residing, and its edges define the interaction strengths among these particles which are in quantum states ups or downs
In the second part of this study, we use binary quantum classifiers, namely a quantum boost (Qboost) and a quantum boost plus (Qboost-Plus) classifier, in contrast to an adaptive boost (Adaboost) classifier [13], [14]. We first apply these quantum classifiers to a two-label dataset of the Indian Pine hyperspectral image (HSI), and secondly, we provide a novel multi-label classifier via an Encoding Output Code (ECOC) when using our binary quantum classifiers [15], [16]; each resulting class is discriminated by the selected bands in the first part of our study
We are employing a D-Wave quantum annealer for feature selection and classification of the Indian Pine HSI as a machine learning technique; our contribution consists of a three-step approach, 1) Feature selection on a D-Wave quantum annealer: the Mutual Information (MI)-based band subset selection, 2) Binary classification on a D-Wave quantum annealer: the binary quantum classifiers to a two-label dataset characterized by those selected bands
Summary
A hyperspectral imaging sensor mounted on a satellite or aircraft measures the electromagnetic spectrum ranging from the visible to the near infrared wavelengths; for instance, the Imaging Spectroscopy and the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) sensor measures 224 continuous spectral bands ranging 400 nm to 2500 nm at 10 nm intervals [17]. As a real-world dataset of HSIs, we consider an Indian Pine HSI obtained by the AVIRIS sensor (see Fig. 1). This low-noise Indian Pine image having the spectral bands of X = {band1, . Not all of these spectral bands are informative for characterizing a specific class; in other words, some bands of X are redundant or noisy. It is advantageous to select a highly-informative band subset of the given spectral bands for a given class. We employ an MI-based band subset selection problem as a global optimization problem
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