Quantum annealing is an experimental and potentially breakthrough computational technology for handling hard optimization problems, including problems of computer vision. We present a case study in training a production-scale classifier of tree cover in remote sensing imagery, using early-generation quantum annealing hardware built by D-wave Systems, Inc. Beginning within a known boosting framework, we train decision stumps on texture features and vegetation indices extracted from four-band, one-meter-resolution aerial imagery from the state of California. We then impose a regulated quadratic training objective to select an optimal voting subset from among these stumps. The votes of the subset define the classifier. For optimization, the logical variables in the objective function map to quantum bits in the hardware device, while quadratic couplings encode as the strength of physical interactions between the quantum bits. Hardware design limits the number of couplings between these basic physical entities to five or six. To account for this limitation in mapping large problems to the hardware architecture, we propose a truncation and rescaling of the training objective through a trainable metaparameter. The boosting process on our basic 108- and 508-variable problems, thus constituted, returns classifiers that incorporate a diverse range of color- and texture-based metrics and discriminate tree cover with accuracies as high as 92% in validation and 90% on a test scene encompassing the open space preserves and dense suburban build of Mill Valley, CA.
Quantum annealing is an experimental and potentially breakthrough computational technology for handling hard optimization problems, including problems of computer vision. We present a case study in training a production-scale classifier of tree cover in remote sensing imagery, using early-generation quantum annealing hardware built by D-wave Systems, Inc. Beginning within a known boosting framework, we train decision stumps on texture features and vegetation indices extracted from four-band, one-meter-resolution aerial imagery from the state of California. We then impose a regulated quadratic training objective to select an optimal voting subset from among these stumps. The votes of the subset define the classifier. For optimization, the logical variables in the objective function map to quantum bits in the hardware device, while quadratic couplings encode as the strength of physical interactions between the quantum bits. Hardware design limits the number of couplings between these basic physical entities to five or six. To account for this limitation in mapping large problems to the hardware architecture, we propose a truncation and rescaling of the training objective through a trainable metaparameter. The boosting process on our basic 108- and 508-variable problems, thus constituted, returns classifiers that incorporate a diverse range of color- and texture-based metrics and discriminate tree cover with accuracies as high as 92% in validation and 90% on a test scene encompassing the open space preserves and dense suburban build of Mill Valley, CA.
Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or quadratic unconstrained binary optimization (QUBO) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the maximum clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters, such as the D-Wave’s chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem will be solvable to optimality with the D-Wave 2000Q. We extend these results by training a machine learning regression model that predicts the clique size found by D-Wave.
The increasing complexity and volume of remote sensing data necessitate advanced computational techniques for efficient and accurate image classification. This study explores the efficacy of Quantum Annealing based Support Vector Machines (QASVM) in comparison to classical Support Vector Machines (SVM) for classifying cloud features in remote sensing images. Quantum annealing, leveraging principles of quantum mechanics, promises to solve optimization problems more efficiently and accurately than classical methods, particularly in high-dimensional data spaces typical of remote sensing applications. Our experimental framework involved the classification of cloud features using a comprehensive dataset of Indian Nano Satellite (INS-2B) Nano-MX satellite imagery. The QA-SVM is implemented on a D-Wave quantum annealer based on the Adiabatic Quantum Computation (AQC) model, while the classical SVM utilizes a traditional computing setup. Performance metrics, including overall accuracy and F1 score, are evaluated. The results demonstrated that QA-SVM achieved higher overall accuracy and F1 score compared to its classical counterpart on the Nano-MX test image. It is found that the overall accuracy of QA-SVM is increased by 6.7% while the F1 score is increased by 4.5% with respect to classical SVM. This performance gain is attributed to the quantum annealer’s ability to explore a vast solution space more effectively, avoiding local minima that often hinder classical SVMs.
In recent years, the development of quantum annealers has enabled experimental demonstrations and has increased research interest in applications of quantum annealing, such as in quantum machine learning and in particular for the popular quantum SVM. Several versions of the quantum SVM have been proposed, and quantum annealing has been shown to be effective in them. Extensions to multiclass problems have also been made, which consist of an ensemble of multiple binary classifiers. This work proposes a novel quantum SVM formulation for direct multiclass classification based on quantum annealing, called Quantum Multiclass SVM (QMSVM). The multiclass classification problem is formulated as a single Quadratic Unconstrained Binary Optimization (QUBO) problem solved with quantum annealing. The main objective of this work is to evaluate the feasibility, accuracy, and time performance of this approach. Experiments have been performed on the D-Wave Advantage quantum annealer for a classification problem on remote sensing data. The results indicate that, despite the memory demands of the quantum annealer, QMSVM can achieve accuracy that is comparable to standard SVM methods and, more importantly, it scales much more efficiently with the number of training examples, resulting in nearly constant time. This work shows an approach for bringing together classical and quantum computation, solving practical problems in remote sensing with current hardware.
In recent years, the development of quantum annealers has enabled experimental demonstrations and has increased research interest in applications of quantum annealing, such as in quantum machine learning and in particular for the popular quantum Support Vector Machine (SVM). Several versions of the quantum SVM have been proposed, and quantum annealing has been shown to be effective in them. Extensions to multiclass problems have also been made, which consist of an ensemble of multiple binary classifiers. This work proposes a novel quantum SVM formulation for direct multiclass classification based on quantum annealing, called Quantum Multiclass SVM (QMSVM). The multiclass classification problem is formulated as a single quadratic unconstrained binary optimization problem solved with quantum annealing. The main objective of this work is to evaluate the feasibility, accuracy, and time performance of this approach. Experiments have been performed on the D-Wave Advantage quantum annealer for a classification problem on remote sensing data. Results indicate that, despite the memory demands of the quantum annealer, QMSVM can achieve an accuracy that is comparable to standard SVM methods, such as the one-versus-one (OVO), depending on the dataset (compared to OVO: 0.8663 vs 0.8598 on Toulouse, 0.8123 vs 0.8521 on Potsdam). More importantly, it scales much more efficiently with the number of training examples, resulting in nearly constant time (compared to OVO: 85.72s vs 248.02s on Toulouse, 58.89s vs 580.17s on Potsdam). This work shows an approach for bringing together classical and quantum computation, solving practical problems in remote sensing with current hardware.
We present a novel methodology for automated feature subset selection from a pool of physiological signals using Quantum Annealing (QA). As a case study, we will investigate the effectiveness of QA-based feature selection techniques in selecting the optimal feature subset for stress detection. Features are extracted from four signal sources: foot EDA, hand EDA, ECG, and respiration. The proposed method embeds the feature variables extracted from the physiological signals in a binary quadratic model. The bias of the feature variable is calculated using the Pearson correlation coefficient between the feature variable and the target variable. The weight of the edge connecting the two feature variables is calculated using the Pearson correlation coefficient between two feature variables in the binary quadratic model. Subsequently, D-Wave’s clique sampler is used to sample cliques from the binary quadratic model. The underlying solution is then re-sampled to obtain multiple good solutions and the clique with the lowest energy is returned as the optimal solution. The proposed method is compared with commonly used feature selection techniques for stress detection. Results indicate that QA-based feature subset selection performed equally as that of classical techniques. However, under data uncertainty conditions such as limited training data, the performance of quantum annealing for selecting optimum features remained unaffected, whereas a significant decrease in performance is observed with classical feature selection techniques. Preliminary results show the promise of quantum annealing in optimizing the training phase of a machine learning classifier, especially under data uncertainty conditions.
Support Vector Machine (SVM) is a popular supervised Machine Learning (ML) method that is widely used for classification and regression problems. Recently, a method to train SVMs on a D-Wave 2000Q Quantum Annealer (QA) was proposed for binary classification of some biological data. First, ensembles of weak quantum SVMs are generated by training each classifier on a disjoint training subset that can be fit into the QA. Then, the computed weak solutions are fused for making predictions on unseen data. In this work, the classification of Remote Sensing (RS) multispectral images with SVMs trained on a QA is discussed. Furthermore, an open code repository is released to facilitate an early entry into the practical application of QA, a new disruptive compute technology.