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... Quantum computer vision is an emerging field. Recently, several classical problems were reformulated to enable quantum optimization, including recognition [47,15] and matching tasks [55,10]. Promising results were shown so far, thus encouraging further research. ...

... Also the second term is constant, since m i is known for each image i by assumption. Thus, the objective function (6) is equivalent to (15). Observe that we should add extra constraints to take into account our additional assumptions, which force the amount of points per motion to be equal to some predefined values in every image, namely 1 T p i X i = m T i (see also Remark 1). ...

... Quantum Computer Vision. Several quantum techniques are available for computer vision tasks, such as recognition and classification [47,15], object tracking [35], transformation estimation [25], point set and shape alignment [44,56], graph matching [55] and permutation synchronization [10]. Most of these methods are designed for an AQC. ...

Motion segmentation is a challenging problem that seeks to identify independent motions in two or several input images. This paper introduces the first algorithm for motion segmentation that relies on adiabatic quantum optimization of the objective function. The proposed method achieves on-par performance with the state of the art on problem instances which can be mapped to modern quantum annealers.

... Also, inherent in many ML and DL approaches are optimization techniques while many of them are fast solvable by QCs [9] that represent the most disruptive type of computing today. Despite being in its infancy, Quantum Annealer (QA)s are specific forms of QC used by remote sensing and health researchers to search for solutions to optimization problems already [10], [11]. This paper reveals practice and experience using the heterogenous MSA that has been co-designed by 15 applications during the course of the DEEP 7 series of projects. ...

... QA represents an innovative computing approach used for simple RS data analysis problems to solve certain ML algorithms' optimisation problems [9]. We used a quantum SVM that reveals that on QA modules of MSA-based HPC systems such as a D-Wave system 43 with 2000 qubits enables new approaches for RS research, but are still limited by having only binary classification or the requirement to sub-sample from large quantities of data and using ensemble methods [11]. More recent lessons learned from us revealed that QA evolution bears a lot of potentials since we are already using D-Wave Leap 44 with the QQ Advantage system using 5000 qubits and 35000 couplers. ...

... Inherent in many ML and DL approaches are optimization techniques while many of them are incredibly fast solvable by QCs [9] that represent the most innovative type of computing today. Despite being in its infancy, QAs are specific forms of QC used by RS researchers [10], [11] to search for solutions to optimization problems already today. Using GPUs in the context of Unmanned Aerial Vehicle (UAV)s is shown in [34]. ...

We observe a continuously increased use of Deep
Learning (DL) as a specific type of Machine Learning (ML)
for data-intensive problems (i.e., ’big data’) that requires powerful
computing resources with equally increasing performance.
Consequently, innovative heterogeneous High-Performance Computing
(HPC) systems based on multi-core CPUs and many-core
GPUs require an architectural design that addresses end user
communities’ requirements that take advantage of ML and DL.
Still the workloads of end user communities of the simulation
sciences (e.g., using numerical methods based on known physical
laws) needs to be equally supported in those architectures.
This paper offers insights into the Modular Supercomputer
Architecture (MSA) developed in the Dynamic Exascale Entry
Platform (DEEP) series of projects to address the requirements
of both simulation sciences and data-intensive sciences such as
High Performance Data Analytics (HPDA). It shares insights into
implementing the MSA in the Jülich Supercomputing Centre
(JSC) hosting Europe No. 1 Supercomputer Jülich Wizard
for European Leadership Science (JUWELS). We augment the
technical findings with experience and lessons learned from
two application communities case studies (i.e., remote sensing
and health sciences) using the MSA with JUWELS and the
DEEP systems in practice. Thus, the paper provides details into
specific MSA design elements that enable significant performance
improvements of ML and DL algorithms. While this paper
focuses on MSA-based HPC systems and application experience, we are not losing sight of advances in Cloud Computing (CC)
and Quantum Computing (QC) relevant for ML and DL.

... Hybrid computer vision methods that can be executed partially on a quantum computer (QC) are an emerging research area [4,7,10,60]. Compared to classical methods, such approaches promise to solve computationally demanding (e.g., combinatorial) sub-problems faster, with improved scaling, and without relaxations that often lead to approximate solutions. ...

... In contrast to circuit-based machines, quantum annealers can already solve various real-world problems formulated as QUBOs [42,46,52,[63][64][65]. Hence, the last few years in quantum computer vision (QCV) are characterised by a rapid transition from theoretical considerations [11,47,48,69] to practical algorithms leveraging quantum-mechanical effects of quantum computers, ranging from image retrieval and processing [69,74], classification [7,10,20,49,72] and object tracking [37,75], to problems on graphs [41,59,76], consensus maximisation [22], shape alignment [50,60] and ensuring cycle-consistency [4]. ...

Modern quantum annealers can find high-quality solutions to combinatorial optimisation objectives given as quadratic unconstrained binary optimisation (QUBO) problems. Unfortunately, obtaining suitable QUBO forms in computer vision remains challenging and currently requires problem-specific analytical derivations. Moreover, such explicit formulations impose tangible constraints on solution encodings. In stark contrast to prior work, this paper proposes to learn QUBO forms from data through gradient backpropagation instead of deriving them. As a result, the solution encodings can be chosen flexibly and compactly. Furthermore, our methodology is general and virtually independent of the specifics of the target problem type. We demonstrate the advantages of learnt QUBOs on the diverse problem types of graph matching, 2D point cloud alignment and 3D rotation estimation. Our results are competitive with the previous quantum state of the art while requiring much fewer logical and physical qubits, enabling our method to scale to larger problems. The code and the new dataset will be open-sourced.

... Binary classification on remote sensing (RS) of multispectral images can be achieved on D_WAVE 2000Q Quantum Annealer machine using Quantum SVM [17]. This method formulates the classification as a Quadratic Unconstrained Binary Optimization (QUBO) and implements the RBF kernel method on two ID datasets: Im16, and Im40. ...

... The method achieved AUROC score of 0.886 and AUPRC score of 0.930 for Im16 dataset, respectively. AURCOC of 0.882 and AURPC of 0.870 were achieved for the other dataset Im40, respectively [17]. Similar RS testing for image classification on 50 samples from SemCity Toulouse dataset on an upgraded quantum machine-D-WAVE Advantageproduced an overall accuracy of 0.874 with 0.734 F1 score which were comparable to classical SVM models and outshone the IBM quantum machines that lagged with 0.609 and 0.569 scores respectively [21]. ...

Quantum Computing (QC) has gained immense popularity as a potential solution to deal with the ever-increasing size of data and associated challenges leveraging the concept of quantum random access memory (QRAM). QC promises-quadratic or exponential increases in computational time with quantum parallelism and thus offer a huge leap forward in the computation of Machine Learning algorithms. This paper analyzes speed up performance of QC when applied to machine learning algorithms, known as Quantum Machine Learning (QML). We applied QML methods such as Quantum Support Vector Machine (QSVM), and Quantum Neural Network (QNN) to detect Software Supply Chain (SSC) attacks. Due to the access limitations of real quantum computers, the QML methods were implemented on open-source quantum simulators such as IBM Qiskit and TensorFlow Quantum. We evaluated the performance of QML in terms of processing speed and accuracy and finally, compared with its classical counterparts. Interestingly, the experimental results differ to the speed up promises of QC by demonstrating higher computational time and lower accuracy in comparison to the classical approaches for SSC attacks.

... Binary classification on remote sensing (RS) of multispectral images can be achieved on D_WAVE 2000Q Quantum Annealer machine using Quantum SVM [17]. This method formulates the classification as a Quadratic Unconstrained Binary Optimization (QUBO) and implements the RBF kernel method on two ID datasets: Im16, and Im40. ...

... The method achieved AUROC score of 0.886 and AUPRC score of 0.930 for Im16 dataset, respectively. AURCOC of 0.882 and AURPC of 0.870 were achieved for the other dataset Im40, respectively [17]. Similar RS testing for image classification on 50 samples from SemCity Toulouse dataset on an upgraded quantum machine-D-WAVE Advantage-produced an overall accuracy of 0.874 with 0.734 F1 score which were comparable to classical SVM models and outshone the IBM quantum machines that lagged with 0.609 and 0.569 scores respectively [21]. ...

Quantum Computing (QC) has gained immense popularity as a potential solution to deal with the ever-increasing size of data and associated challenges leveraging the concept of quantum random access memory (QRAM). QC promises quadratic or exponential increases in computational time with quantum parallelism and thus offer a huge leap forward in the computation of Machine Learning algorithms. This paper analyzes speed up performance of QC when applied to machine learning algorithms, known as Quantum Machine Learning (QML). We applied QML methods such as Quantum Support Vector Machine (QSVM), and Quantum Neural Network (QNN) to detect Software Supply Chain (SSC) attacks. Due to the access limitations of real quantum computers, the QML methods were implemented on open-source quantum simulators such as IBM Qiskit and TensorFlow Quantum. We evaluated the performance of QML in terms of processing speed and accuracy and finally, compared with its classical counterparts. Interestingly, the experimental results differ to the speed up promises of QC by demonstrating higher computational time and lower accuracy in comparison to the classical approaches for SSC attacks.

... These layers contain several quanvolutional filters that transform the input data into different output feature maps by using a number of random quantum circuits, in an analogous way to standard convolutional networks. Quantum circuitbased neural network classifiers for multi-spectral land cover classification have been introduced in preliminary proof-ofconcept applications as presented in [24], and an ensemble of support vector machines running on the D-Wave quantum annealer has been proposed for remote sensing image classification in [25]. In our preliminary work [26] hybrid quantumclassical neural networks for remote sensing applications are discussed, and a proof-of-concept for binary classification, using multispectral optical data, is reported. ...

... • QC is applied to land-cover classification on the reference benchmark EuroSAT dataset [28] for optical multispectral images, thus by going further than initial proofs-ofconcept on a few images [24], [25]. • QCNN multiclass classification is tackled, with respect to the simple binary classification already discussed in [26], and better results are obtained through the quantum-based networks with respect to their fully-classical counterpart. ...

This article aims to investigate how circuit-based hybrid Quantum Convolutional Neural Networks (QCNNs) can be successfully employed as image classifiers in the context of remote sensing. The hybrid QCNNs enrich the classical architecture of CNNs by introducing a quantum layer within a standard neural network. The novel QCNN proposed in this work is applied to the Land Use and Land Cover (LULC) classification, chosen as an Earth Observation (EO) use case, and tested on the EuroSAT dataset used as reference benchmark. The results of the multiclass classification prove the effectiveness of the presented approach, by demonstrating that the QCNN performances are higher than the classical counterparts. Moreover, investigation of various quantum circuits shows that the ones exploiting quantum entanglement achieve the best classification scores. This study underlines the potentialities of applying quantum computing to an EO case study and provides the theoretical and experimental background for futures investigations.

... The D-Wave QA has a very small number of input qubits and a specific Pegasus topology for the connectivity of its qubits [19], and it is solely designed for solving a Quadratic Unconstrained Binary Optimization (QUBO) problem [14], [20]. For practical EO data, there is a benchmark and a demonstration example for training an SVM with binary quantum classifiers when using a D-Wave QA [21], [22]. Here, the SVM is a quadratic programming problem considered as a QUBO problem. ...

... Here, the SVM is a quadratic programming problem considered as a QUBO problem. Furthermore, there is a challenge to embed the variables of a given SVM problem into the Pegasus topology (i.e., the connectivity constraint of qubits), and to overcome this constraint of a D-Wave QA, the authors of [21] employed a k-fold approach to their EO data such that the size of variables in the SVM satisfies the connectivity constraint of qubits of a D-Wave QA. ...

Satellite instruments monitor the Earth’s surface day and night, and, as a result, the size of Earth observation (EO) data is dramatically increasing. Machine Learning (ML) techniques are employed routinely to analyze and process these big EO data, and one well-known ML technique is a Support Vector Machine (SVM). An SVM poses a quadratic programming problem, and quantum computers including quantum annealers (QA) as well as gate-based quantum computers promise to solve an SVM more efficiently than a conventional computer; training the SVM by employing a quantum computer/conventional computer represents a quantum SVM (qSVM)/classical SVM (cSVM) application. However, quantum computers cannot tackle many practical EO problems by using a qSVM due to their very low number of input qubits. Hence, we assembled a coreset (“core of a dataset") of given EO data for training a weighted SVM on a small quantum computer, a D-Wave quantum annealer with around 5000 input quantum bits. The coreset is a small, representative weighted subset of an original dataset, and its performance can be analyzed by using the proposed weighted SVM on a small quantum computer in contrast to the original dataset. As practical data, we use synthetic data, Iris data, a Hyperspectral Image (HSI) of Indian Pine, and a Polarimetric Synthetic Aperture Radar (PolSAR) image of San Francisco. We measured the closeness between an original dataset and its coreset by employing a Kullback–Leibler (KL) divergence test, and, in addition, we trained a weighted SVM on our coreset data by using both a D-Wave quantum annealer (D-Wave QA) and a conventional computer. Our findings show that the coreset approximates the original dataset with very small KL divergence (smaller is better), and the weighted qSVM even outperforms the weighted cSVM on the coresets for a few instances of our experiments. As a side result (or a by-product result), we also present our KL divergence findings for demonstrating the closeness between our original data (i.e., our synthetic data, Iris data, hyperspectral image, and PolSAR image) and the assembled coreset.

... These layers contain several quanvolutional filters that transform the input data into different output feature maps by using a number of random quantum circuits, in an analogous way to standard convolutional networks. Quantum-circuit-based neural network classifiers for multispectral land-cover classification have been introduced in preliminary proof-of-concept applications, as presented in [24], and an ensemble of support vector machines running on the D-Wave quantum annealer has been proposed for remote sensing image classification in [25]. In our preliminary work [26], hybrid quantum-classical neural networks for remote sensing applications are discussed, and a proof of concept for binary classification, using multispectral optical data, is reported. ...

... The main contributions of this work are as follows. 1) QC is applied to land-cover classification on the reference benchmark EuroSAT dataset [28] for optical multispectral images, thus by going further than initial proofs of concept on a few images [24], [25]. 2) QCNN multiclass classification is tackled with respect to the simple binary classification already discussed in [26], and better results are obtained through the quantum-based networks with respect to their fully classical counterpart. ...

This article aims to investigate how circuit-based hybrid Quantum Convolutional Neural Networks (QCNNs) can be successfully employed as image classifiers in the context of remote sensing. The hybrid QCNNs enrich the classical architecture of CNNs by introducing a quantum layer within a standard neural network. The novel QCNN proposed in this work is applied to the Land Use and Land Cover (LULC) classification, chosen as an Earth Observation (EO) use case, and tested on the EuroSAT dataset used as reference benchmark. The results of the multiclass classification prove the effectiveness of the presented approach, by demonstrating that the QCNN performances are higher than the classical counterparts. Moreover, investigation of various quantum circuits shows that the ones exploiting quantum entanglement achieve the best classification scores. This study underlines the potentialities of applying quantum computing to an EO case study and provides the theoretical and experimental background for futures investigations.

... Inherent in many ML and DL approaches are optimization techniques while many of them are incredibly fast solvable by QCs [5] that represent the most innovative type of computing today. Despite being in its infancy, Quantum Annealer (QA)s are specific forms of QC used by RS researchers [6,7] to search for solutions to optimization problems already today. ...

... QA emerged as a promising and highly innovative computing approach used for simple RS data analysis problems to solve ML algorithms' optimisation problems [5]. Our experience with using quantum SVMs reveals that on QA architectures such as a D-Wave system 17 with 2000 qubits, RS researchers' possibilities are still limited by having only binary classification techniques or the requirement to subsample from large datasets and using ensemble methods [7]. Recent experience revealed that QA evolutions bears a lot of potentials since we are already using D-Wave Leap 18 with the QQ Advantage system that offers more than 5000 qubits and 35000 couplers enabling powerful RS data analysis. ...

Using computationally efficient techniques for transforming the massive amount of Remote Sensing (RS) data into scientific understanding is critical for Earth science. The utilization of efficient techniques through innovative computing systems in RS applications has become more widespread in recent years. The continuously increased use of Deep Learning (DL) as a specific type of Machine Learning (ML) for data-intensive problems (i.e., 'big data') requires powerful computing resources with equally increasing performance. This paper reviews recent advances in High-Performance Computing (HPC), Cloud Computing (CC), and Quantum Computing (QC) applied to RS problems. It thus represents a snapshot of the state-of-the-art in ML in the context of the most recent developments in those computing areas, including our lessons learned over the last years. Our paper also includes some recent challenges and good experiences by using Europeans fastest supercomputer for hyper-spectral and multi-spectral image analysis with state-of-the-art data analysis tools. It offers a thoughtful perspective of the potential and emerging challenges of applying innovative computing paradigms to RS problems.

... Ways for representing, retrieving and processing images on a quantum computer have been extensively investigated in the theory literature [68,15,64,71]. Methods for image recognition and classification are among the first low-level techniques evaluated on a real AQCer [47,10,49,16,40]. O'Malley et al. [54] learn facial features and reproduce image collections of human faces with the help of AQCing. ...

... O'Malley et al. [54] learn facial features and reproduce image collections of human faces with the help of AQCing. Cavallaro et al. [16] classify multi-spectral images with an ensemble of quantum support vector machines [70]. To account for the limited connectivity of the physical qubit graph of D-Wave 2000Q, they split the training set into multiple disjoint subsets and train the classifier on each of them independently. ...

Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) that becomes infeasible for shapes with high sampling density. A promising research direction is to tackle such quadratic optimization problems over binary variables with quantum annealing, which, in theory, allows to find globally optimal solutions relying on a new computational paradigm. Unfortunately, enforcing the linear equality constraints in QAPs via a penalty significantly limits the success probability of such methods on currently available quantum hardware. To address this limitation, this paper proposes Q-Match, i.e., a new iterative quantum method for QAPs inspired by the alpha-expansion algorithm, which allows solving problems of an order of magnitude larger than current quantum methods. It works by implicitly enforcing the QAP constraints by updating the current estimates in a cyclic fashion. Further, Q-Match can be applied for shape matching problems iteratively, on a subset of well-chosen correspondences, allowing us to scale to real-world problems. Using the latest quantum annealer, the D-Wave Advantage, we evaluate the proposed method on a subset of QAPLIB as well as on isometric shape matching problems from the FAUST dataset.

... As for applying QML/QNNs to classify remote sensing images, some researchers focused on using quantum annealers for classification [50], [51], [52]. Besides that, studies based on quantum circuits also have been conducted to analyze remote sensing data. ...

Image classification plays an important role in remote sensing. Earth observation (EO) has inevitably arrived in the big data era, but the high requirement on computation power has already become a bottleneck for analyzing large amounts of remote sensing data with sophisticated machine learning models. Exploiting quantum computing might contribute to a solution to tackle this challenge by leveraging quantum properties. This article introduces a hybrid quantum-classical convolutional neural network (QC-CNN) that applies quantum computing to effectively extract high-level critical features from EO data for classification purposes. Besides that, the adoption of the amplitude encoding technique reduces the required quantum bit resources. The complexity analysis indicates that the proposed model can accelerate the convolutional operation in comparison with its classical counterpart. The model’s performance is evaluated with different EO benchmarks, including Overhead-MNIST, So2Sat LCZ42, PatternNet, RSI-CB256, and NaSC-TG2, through the TensorFlow Quantum platform, and it can achieve better performance than its classical counterpart and have higher generalizability, which verifies the validity of the QC-CNN model on EO data classification tasks.

... One significant challenge in the medical application of QC is the limited number of available qubits. Adiabatic QC produced by D-Wave has increased the number of qubits to be utilized, which has enhanced the field of QC [29][30][31][32][33][34]. Binary-or integer-based reconstruction has been proposed in recent years, but integer-based reconstruction still has difficulty reproducing quantitative images due to the shortage of qubits to represent pixel values [8]. ...

Objective: Despite recent advancements in quantum computing, the limited number of available qubits has hindered progress in CT reconstruction. This study investigates the feasibility of utilizing quantum annealing-based computed tomography (QACT) with current quantum bit levels. Approach: The QACT algorithm aims to precisely solve quadratic unconstrained binary optimization (QUBO) problems. Furthermore, a novel approach is proposed to reconstruct images by approximating real numbers using the variational method. This approach allows for accurate CT image reconstruction using a small number of qubits. The study examines the impact of projection data quantity and noise on various image sizes ranging from 4x4 to 24x24 pixels. The reconstructed results are compared against conventional reconstruction algorithms, namely maximum likelihood expectation maximization (MLEM) and filtered back projection (FBP). Main result: By employing the variational approach and utilizing two qubits for each pixel of the image, accurate reconstruction was achieved with an adequate number of projections. Under conditions of abundant projections and lower noise levels, the image quality in QACT outperformed that of MLEM and FBP. However, in situations with limited projection data and in the presence of noise, the image quality in QACT was inferior to that in MLEM. Significance: This study developed the QACT reconstruction algorithm using the variational approach for real-number reconstruction. Remarkably, only 2 qubits were required for each pixel representation, demonstrating their sufficiency for accurate reconstruction.

... In Synthetic Aperture Radar (SAR) imaging, problems related to system design [22] and phase ambiguity [23] have been addressed. In the context of QML, a feature selection method for hyperspectral images has been proposed [24], and a QAbased Quantum SVM (QSVM) method has been successfully used for binary classification of multispectral images [25] [26]. ...

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.

... The performance of QML implemented for big data applications is compared with the performance of classical computation [6][7][8]. Two major providers of cloud QC environments are IBM (gate-based systems) [5,9] and D-Wave (based on quantum annealing) [10,11]. The main goal of many researchers in this field is to search for potential applications that demonstrate quantum speed-ups [6]. ...

A quantum machine is a human-made device whose collective motion follows the laws of quantum mechanics. Quantum machine learning (QML) is machine learning for quantum computers. The availability of quantum processors has led to practical applications of QML algorithms in the remote sensing field. Quantum machines can learn from fewer data than non-quantum machines, but because of their low processing speed, quantum machines cannot be applied to an image that has hundreds of thousands of pixels. Researchers around the world are exploring applications for QML and in this work, it is applied for pseudo-labelling of samples. Here, a PRISMA (PRecursore IperSpettrale della Missione Applicativa) hyperspectral dataset is prepared by quantum-based pseudo-labelling and 11 different machine learning algorithms viz., support vector machine (SVM), K-nearest neighbour (KNN), random forest (RF), light gradient boosting machine (LGBM), XGBoost, support vector classifier (SVC) + decision tree (DT), RF + SVC, RF + DT, XGBoost + SVC, XGBoost + DT, and XGBoost + RF with this dataset are evaluated. An accuracy of 86% was obtained for the classification of pine trees using the hybrid XGBoost + decision tree technique.

... More precisely, it is responsible for training the model parameters from a set of labeled training data to make correct guesses on the test data. These SVMs are known to have higher stability than decision trees or deep neural networks that perform the same role [64], [65]. Therefore, there is an advantage that small fluctuations made by some data in the training data do not have a large effect on the classification result. ...

A combinatorial optimization problem (COP) is the problem of finding the optimal solution in a finite set. When the size of the feasible solution set is large, the complexity of the problem increases, and it is not easy to solve in a reasonable time with the current classical computer technology. Quantum annealing (QA) is a method that replaces classical simulated annealing (SA) methods that do not solve these cases. Therefore, several attempts have been made to solve this problem using a special-purpose quantum annealer to which the QA method is applied. In this survey, we analyze recent studies that solve real-scale COPs using quantum annealers. Through this, we discuss how to reduce the size of the COP to be input to overcome the hardware limitations of the existing quantum annealer. Additionally, we demonstrated the applicability of quantum annealer to COP on a practical scale by comparing and analyzing the results of the classical simulated annealing (SA) and QA method from each study.

... Building a support vector ML model requires the use to specify the kernel type [38] . Some popular kernels in remote sensing are polynomial kernels and the radial basis function (RBF) kernel [39] . Classification of satellite based imagery, detection of features like roads, wetlands, grasslands, can be solved using SVM models. ...

Machine learning (ML) is a subdivision of artificial intelligence in which the machine learns from machine-readable data and information. It uses data, learns the pattern and predicts the new outcomes. Its popularity is growing because it helps to understand the trend and provides a solution that can be either a model or a product. Applications of ML algorithms have increased drastically in G.I.S. and remote sensing in recent years. It has a broad range of applications, from developing energy-based models to assessing soil liquefaction to creating a relation between air quality and mortality. Here, in this paper, we discuss the most popular supervised ML models (classification and regression) in G.I.S. and remote sensing. The motivation for writing this paper is that ML models produce higher accuracy than traditional parametric classifiers, especially for complex data with many predictor variables. This paper provides a general overview of some popular supervised non-parametric ML models that can be used in most of the G.I.S. and remote sensing based projects. We discuss classification (Naïve Bayes (NB), Support Vector Machine (SVM), Random Forest (RF), Decision Trees (DT)) and regression models (Random Forest (RF), Support Vector Machine (SVM), Linear and Non-Linear) here. Therefore, the article can be a guide to those interested in using ML models in their G.I.S. and remote sensing based projects.

... It's an ML model that can be applied to classification and regression problems(Mountrakis, Im, Ogole, & Sensing, 2011).It fits the data based on a distinct line known as a hyperplane (Sheykhmousa et al., 2020). As the model is easy to build and robust to outliers, it is widely used in the G.I.S. and remote sensing domains (Cavallaro, Willsch, Willsch, Michielsen, & Riedel, 2020). Building a support vector ML model requires the use to specify the kernel type (Waske, Benediktsson, & Sveinsson, 2009). ...

Machine learning (ML) is a subdivision of artificial intelligence in which the machine learns from machine-readable data and information. It uses data, learns the pattern and predicts the new outcomes. Its popularity is growing because it helps to understand the trend and provides a solution that can be either a model or a product. Applications of ML algorithms have increased drastically in G.I.S. and remote sensing in recent years. It has a broad range of applications, from developing energy-based models to assessing soil liquefaction to creating a relation between air quality and mortality. Here, in this paper, we discuss the most popular supervised ML models (clas-sification and regression) in G.I.S. and remote sensing. The motivation for writing this paper is that ML models produce higher accuracy than traditional parametric classifiers, especially for complex data with many predictor variables. This paper provides a general overview of some popular supervised non-parametric ML models that can be used in most of the G.I.S. and remote sensing-based projects. We discuss classification (Naïve Bayes (NB), Support Vector Machine (SVM), Random Forest (RF), Decision Trees (DT)) and regression models (Random Forest (RF), Support Vector Machine (SVM), Linear and Non-Linear) here. Therefore, the article can be a guide to those interested in using ML models in their G.I.S. and remote sensing-based projects.

... It's an ML model that can be applied to classification and regression problems (Mountrakis, Im, Ogole, & Sensing, 2011).It fits the data based on a distinct line known as a hyperplane (Sheykhmousa et al., 2020). As the model is easy to build and robust to outliers, it is widely used in the G.I.S. and remote sensing domains (Cavallaro, Willsch, Willsch, Michielsen, & Riedel, 2020). Building a support vector ML model requires the use to specify the kernel type (Waske, Benediktsson, & Sveinsson, 2009). ...

Machine learning (ML) is a subdivision of artificial intelligence in which the machine learns from machine-readable data and information. It uses data, learns the pattern and predicts the new outcomes. Its popularity is growing because it helps to understand the trend and provides a solution that can be either a model or a product. Applications of ML algorithms have increased drastically in G.I.S. and remote sensing in recent years. It has a broad range of applications, from developing energy-based models to assessing soil liquefaction to creating a relation between air quality and mortality. Here, in this paper, we discuss the most popular supervised ML models (classification and regression) in G.I.S. and remote sensing. The motivation for writing this paper is that ML models produce higher accuracy than traditional parametric classifiers, especially for complex data with many predictor variables. This paper provides a general overview of some popular supervised non-parametric ML models that can be used in most of the G.I.S. and remote sensing-based projects. We discuss classification (Naïve Bayes (NB), Support Vector Machine (SVM), Random Forest (RF), Decision Trees (DT)) and regression models (Random Forest (RF), Support Vector Machine (SVM), Linear and Non-Linear) here. Therefore, the article can be a guide to those interested in using ML models in their G.I.S. and remote sensing-based projects.

... Regarding using QML for EO data classification, several studies have used quantum annealers [1,2]. Additionally, applying quantum circuits to analyze EO images also attracts great attention. ...

Due to the rapid growth of earth observation (EO) data and the complexity of machine learning models, the high requirement on the computation power for EO data analysis becomes a bottleneck. Exploiting quantum computing might tackle this challenge in the future. In this paper, we present a hybrid quantum-classical convolutional neural network (QC-CNN) to classify EO data which can accelerate feature extraction compared with its classical counterpart and handle multi-category classification tasks with reduced quantum resources. The model’s validity is verified with the Overhead-MNIST dataset through the TensorFlow Quantum platform.

... Despite the fact that quantum machine learning is a recently surging field, it already encompasses a rich set of quantum techniques and approaches, for example linear regression [19], [20], [21], clustering analysis [22], dimensionality reduction [23], [24], data classification [25], [26], [27], [28], and neural networks [29], [30], [31]. Besides, quantum machine learning algorithms have been applied to channel discrimination [7], vehicle classification [32], and image classification [33]. Support vector machine (SVM) is a supervised machine learning technique for solving classification. ...

Quantum algorithms can enhance machine learning in different aspects. In 2014, Rebentrost $et~al.$ constructed a least squares quantum support vector machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the classification. However, as the output states of a previous test cannot be reused for a new test in the Swap Test, the quantum algorithm LS-QSVM has to be repeated in preparing qubits, manipulating operations, and carrying out the measurement. This paper proposes a QSVM based on the generalized quantum amplitude estimation (AE-QSVM) which gets rid of the constraint of repetitive processes and saves the quantum resources. At first, AE-QSVM is trained by using the quantum singular value decomposition. Then, a query sample is classified by using the generalized quantum amplitude estimation in which high accuracy can be achieved by adding auxiliary qubits instead of repeating the algorithm. The complexity of AE-QSVM is reduced to $O(\kappa^{3}\varepsilon^{-3}(log(mn)+1))$ with an accuracy $\varepsilon$, where $m$ is the number of training vectors, $n$ is the dimension of the feature space, and $\kappa$ is the condition number. Experiments demonstrate that AE-QSVM is advantageous in terms of training matrix, the number of iterations, space complexity, and time complexity.

... For analysing practical RS datasets, there are several approaches of training ML models and solving RS optimization problems on a D-Wave QA [11], [12], [13], and even on a gate-based quantum computer [14], [15]. The D-Wave QA has around 5, 000 input qubits and a specific Pegasus topology for the connectivity of its qubits [16], and it is designed for solving a Quadratic Unconstrained Binary Optimization (QUBO) problem [9]. ...

Machine Learning (ML) techniques are employed to analyze and process big Remote Sensing (RS) data, and one well-known ML technique is a Support Vector Machine (SVM). An SVM is a quadratic programming (QP) problem, and a D-Wave quantum annealer (D-Wave QA) promises to solve this QP problem more efficiently than a conventional computer. However, the D-Wave QA cannot solve directly the SVM due to its very few input qubits. Hence, we use a coreset ("core of a dataset") of given EO data for training an SVM on this small D-Wave QA. The coreset is a small, representative weighted subset of an original dataset, and any training models generate competitive classes by using the coreset in contrast to by using its original dataset. We measured the closeness between an original dataset and its coreset by employing a Kullback-Leibler (KL) divergence measure. Moreover, we trained the SVM on the coreset data by using both a D-Wave QA and a conventional method. We conclude that the coreset characterizes the original dataset with very small KL divergence measure. In addition, we present our KL divergence results for demonstrating the closeness between our original data and its coreset. As practical RS data, we use Hyperspectral Image (HSI) of Indian Pine, USA.

... (1) Comparison with detailed real-time simulations of quantum annealing systems based on solving the time-dependent Schrödinger equation [24,25] or the timedependent master equation [5,6,[26][27][28][29][30]. (2) Direct QPU benchmarks (including comparison with other quantum annealing systems and optimization problem solvers) for problems of intermediate size that may or may not need embeddings and solve either real-world or artificial problems [11,[31][32][33][34][35][36][37][38][39][40][41]. (3) Benchmarks of hybrid solvers that use a combination of QPUs and CPUs or GPUs to solve large-scale application problems [12,18,42,43]. ...

We benchmark the quantum processing units of the largest quantum annealers to date, the $$5000+$$ 5000 + qubit quantum annealer Advantage and its 2000+ qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios. The benchmark set contains small, intermediate, and large problems with both sparsely connected and almost fully connected instances. We find that Advantage outperforms D-Wave 2000Q for almost all problems, with a notable increase in success rate and problem size. In particular, Advantage is also able to solve the largest problems with 120 logical qubits that D-Wave 2000Q cannot solve anymore. Furthermore, problems that can still be solved by D-Wave 2000Q are solved faster by Advantage. We find, however, that D-Wave 2000Q can achieve better success rates for sparsely connected problems that do not require the many new couplers present on Advantage, so improving the connectivity of a quantum annealer does not per se improve its performance.

... This young field seeks to identify how challenging problems can be formulated for and benefit from quantum hardware. While it remained predominantly theoretical at early stages [63,21], QCV methods from various domains were evaluated on real quantum hardware during the recent few years, including image classification [62,64,19], object detection [55], graph matching [72], mesh alignment [6], robust fitting [29] and permutation synchronisation [9]. ...

We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linearly-constrained, binary optimization problems on quantum annealers (QA). The computational premise of quantum computers has cultivated the re-design of various existing vision problems into quantum-friendly forms. Experimental QA realizations can solve a particular non-convex problem known as the quadratic unconstrained binary optimization (QUBO). Yet a naive-QUBO cannot take into account the restrictions on the parameters. To introduce additional structure in the parameter space, researchers have crafted ad-hoc solutions incorporating (linear) constraints in the form of regularizers. However, this comes at the expense of a hyper-parameter, balancing the impact of regularization. To date, a true constrained solver of quadratic binary optimization (QBO) problems has lacked. Q-FW first reformulates constrained-QBO as a copositive program (CP), then employs Frank-Wolfe iterations to solve CP while satisfying linear (in)equality constraints. This procedure unrolls the original constrained-QBO into a set of unconstrained QUBOs all of which are solved, in a sequel, on a QA. We use D-Wave Advantage QA to conduct synthetic and real experiments on two important computer vision problems, graph matching and permutation synchronization, which demonstrate that our approach is effective in alleviating the need for an explicit regularization coefficient.

... In particular, various attempts to tackle land-use / land-cover classification recently emerged. Gwaron and Levinsky proposed Quantum Neural Networks (QNN) for multiclass classification of multispectral (Sentinel-2) images [5], while Cavallaro et al. used quantum versions of an ensemble of Support-Vector Machines (SVMs) to perform land-cover binary classification of Landsat images [6]. ...

... The Quantum Support Vector Machine (QSVM) is the class of algorithms that is considered in this work. In [9], we have already trained a QA-based QSVM algorithm on the D-Wave 2000Q quantum annealer and tested it on RS multispectral images classification problems. In this paper, we run the experiments on the D-Wave's next-generation quantum processor Advantage. ...

Recent developments in Quantum Computing (QC) have paved the way for an enhancement of computing capabilities. Quantum Machine Learning (QML) aims at developing Machine Learning (ML) models specifically designed for quantum computers. The availability of the first quantum processors enabled further research, in particular the exploration of possible practical applications of QML algorithms. In this work, quantum formulations of the Support Vector Machine (SVM) are presented. Then, their implementation using existing quantum technologies is discussed and Remote Sensing (RS) image classification is considered for evaluation.

... (2) Direct QPU benchmarks (including comparison with other quantum annealing systems and optimization problem solvers) for problems of intermediate size that may or may not need embeddings and solve either real-world or artificial problems [10,[29][30][31][32][33][34][35][36][37][38]. * Corresponding author: Dennis Willsch; d.willsch@fz-juelich.de ...

We benchmark the quantum processing units of the largest quantum annealers to date, the 5000+ qubit quantum annealer Advantage and its 2000+ qubit predecessor D-Wave 2000Q, using tail assignment and exact cover problems from aircraft scheduling scenarios. The benchmark set contains small, intermediate, and large problems with both sparsely connected and almost fully connected instances. We find that Advantage outperforms D-Wave 2000Q for almost all problems, with a notable increase in success rate and problem size. In particular, Advantage is also able to solve the largest problems with 120 logical qubits that D-Wave 2000Q cannot solve anymore. Furthermore, problems that can still be solved by D-Wave 2000Q are solved faster by Advantage. We find that D-Wave 2000Q can only achieve better success rates for a few very sparsely connected problems.

... In particular, various attempts to tackle land-use / land-cover classification recently emerged. Gwaron and Levinsky proposed quantum neural networks for multiclass classification of multispectral (Sentinel-2) images [6], while Cavallaro et al. used quantum versions of an ensemble of SVMs to perform land-cover binary classification of Landsat images [7]. ...

This concept paper aims to provide a brief outline of quantum computers, explore existing methods of quantum image classification techniques, so focusing on remote sensing applications, and discuss the bottlenecks of performing these algorithms on currently available open source platforms. Initial results demonstrate feasibility. Next steps include expanding the size of the quantum hidden layer and increasing the variety of output image options.

... The modularity will be key for Cyberinfrastructures to support, not only to support traditional simulation sciences and more emerging AI workloads but also to integrate innovative computing aspects (e.g., quantum computing, neuromorphic computing, etc.). We have already started to use an SVM based on the quantum annealing approach [19] to solve an inherent optimization problem in remote sensing applications [18]. Hence, Quantum computing is in reach and need to be part of future 'modular' concepts of Cyberinfrastructures. Another example of the need for modularity are MSA-enabled reinforcement learning environments that, for example, may help to deal with the large complexity of finding the right hyper-parameters in deep learning networks. ...

There is a wide variety of activities of developing ‘Cyberinfrastructures in Europe‘ (i.e., rather known as Research infrastructures) in several application domains such as those driven forward by the European Strategy Forum for Research Infrastructures (ESFRI) that are primarily based on domain-specific use of data, computing, and tools. A key European Artificial Intelligence (AI) – driven effort that can not directly be considered as a ‘Cyberinfrastructure‘, but is rather a ‘AI on-demand platform‘ (AI4EU) shares several ambitious goals with Cyberinfrastructures. This ‘top-down‘ initiated platform is
currently in a very early stage of development but aims to inform the AI community about AI news, new AI tools, emerging AI services, and enable the sharing of AI techniques and algorithms between users of the platform and AI-related EU projects. In addition to European activities also national AI activities emerge like the Helmholtz AI initiative funded by the Helmholtz Association in Germany. At the same time, we observe that ‘European Cyberinfrastructures‘ primarily focussed on computing and storage like the Partnership for Advanced Computing in Europe (PRACE) or the European Grid
Initiative (EGI) work on satisfying an increasing number of requests related to AI applications. For example, this includes annual PRACE training courses such as ‘Parallel and Scalable Machine Learning‘ or ‘Introduction to Deep Learning Model‘. The feedback of users in these training courses and the below outlined research activities contributed to lessons learned summarized as top five recommendations below for NSF w.r.t. development of smart cyberinfrastructures for AI in the future.

Quantum Machine Learning (QML) is an emerging technology that only recently has begun to take root in the research fields of Earth Observation (EO) and Remote Sensing (RS), and whose state of the art is roughly divided into one group oriented to fully quantum solutions, and in another oriented to hybrid solutions. Very few works applied QML to EO tasks, and none of them explored a methodology able to give guidelines on the hyperparameter tuning of the quantum part for Land Cover Classification (LCC). As a first step in the direction of quantum advantage for RS data classification, this letter opens new research lines, allowing us to demonstrate that there are more convenient solutions to simply increasing the number of qubits in the quantum part. To pave the first steps for researchers interested in the above, the structure of a new hybrid quantum neural network for EO data and LCC is proposed with a strategy to choose the number of qubits to find the most efficient combination in terms of both system complexity and results accuracy. We sampled and tried a number of configurations, and using the suggested method we came up with the most efficient solution (in terms of the selected metrics). Better performance is achieved with less model complexity when tested and compared with state-of-the-art (SOTA) and standard techniques for identifying volcanic eruptions chosen as a case study. Additionally, the method makes the model more resilient to dataset imbalance, a significant problem when training classical models. Lastly, the code is freely available so that interested researchers can reproduce and extend the results.

We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linearly-constrained, binary optimization problems on quantum annealers (QA). The computational premise of quantum computers has cultivated the re-design of various existing vision problems into quantum-friendly forms. Experimental QA realisations can solve a particular non-convex problem known as the quadratic unconstrained binary optimization (QUBO). Yet a naive-QUBO cannot take into account the restrictions on the parameters. To introduce additional structure in the parameter space, researchers have crafted ad-hoc solutions incorporating (linear) constraints in the form of regularizers. However, this comes at the expense of a hyper-parameter, balancing the impact of regularization. To date, a true constrained solver of quadratic binary optimization (QBO) problems has lacked. Q-FW first reformulates constrained-QBO as a copositive program (CP), then employs Frank-Wolfe iterations to solve CP while satisfying linear (in)equality constraints. This procedure unrolls the original constrained-QBO into a set of unconstrained QUBOs all of which are solved, in a sequel, on a QA. We use D-Wave Advantage QA to conduct synthetic and real experiments on two important computer vision problems, graph matching and permutation synchronization, which demonstrate that our approach is effective in alleviating the need for an explicit regularization coefficient.

Motion segmentation is a challenging problem that seeks to identify independent motions in two or several input images. This paper introduces the first algorithm for motion segmentation that relies on adiabatic quantum optimization of the objective function. The proposed method achieves on-par performance with the state of the art on problem instances which can be mapped to modern quantum annealers.KeywordsMotion segmentationQuantum approachSynchronization

Quantum machine learning (QML) focuses on machine learning models developed explicitly for quantum computers. Availability of the first quantum processor led to further research, particularly exploring possible practical applications of QML algorithms in the remote sensing field. The demand for extensive field data for remote sensing applications has started creating bottlenecks for classical machine learning algorithms. QML is becoming a potential solution to tackle big data problems as it can learn from fewer data. This paper presents a QML model based on a quantum support vector machine (QSVM) to classify Holm Oak trees using PRISMA hyperspectral Imagery. Implementation of quantum models was carried on a quantum simulator and a real-time superconducting quantum processor of IBM. The performance of the QML model is validated in terms of dataset size, overall accuracy, number of qubits, training and predicting speed. Results were indicative that (i) QSVM offered 5% higher accuracy than classical SVM (CSVM) with 50 samples and ≥12 qubits/feature dimensions whereas with 20 samples at 16 Qubits/feature dimension, (ii) training time for QSVM at maximum accuracy was 284 s with 50 samples and with 20 samples was 53.68 s and (iii) predicting time for 400 pixels using the QSVM model trained with 50 samples dataset was 5243 s whereas with 20 samples dataset was 2845 s. Results were indicative that QML offers better accuracy but lack training and predicting speed for hyperspectral data. Another observation is that predicting speed of QSVM depends on the number of samples used to train the model.

The classification of land-cover classes in remote sensing images can suit a variety of interdisciplinary applications such as the interpretation of natural and man-made processes on the Earth surface. The Convolutional Support Vector Machine (CSVM) network was recently proposed as binary classifier for the detection of objects in Unmanned Aerial Vehicle (UAV) images. The training phase of the CSVM is based on convolutional layers that learn the kernel weights via a set of linear Support Vector Machines (SVMs). This paper proposes the Multi-scale Convolutional Support Vector Machine (MCSVM) network, that is an ensemble of CSVM classifiers which process patches of different spatial sizes and can deal with multi-class classification problems. The experiments are carried out on the EuroSAT Sentinel-2 dataset and the results are compared to the one obtained with recent transfer learning approaches based on pre-trained Convolutional Neural Networks (CNNs).

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor¹. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits2,3,4,5,6,7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2⁵³ (about 10¹⁶). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy8,9,10,11,12,13,14 for this specific computational task, heralding a much-anticipated computing paradigm.

Deep learning (DL) algorithms have seen a massive rise in popularity for remote-sensing image analysis over the past few years. In this study, the major DL concepts pertinent to remote-sensing are introduced, and more than 200 publications in this field, most of which were published during the last two years, are reviewed and analyzed. Initially, a meta-analysis was conducted to analyze the status of remote sensing DL studies in terms of the study targets, DL model(s) used, image spatial resolution(s), type of study area, and level of classification accuracy achieved. Subsequently, a detailed review is conducted to describe/discuss how DL has been applied for remote sensing image analysis tasks including image fusion, image registration, scene classification, object detection , land use and land cover (LULC) classification, segmentation, and object-based image analysis (OBIA). This review covers nearly every application and technology in the field of remote sensing, ranging from pre-processing to mapping. Finally, a conclusion regarding the current state-of-the art methods, a critical conclusion on open challenges, and directions for future research are presented.

Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking and control of experimental quantum computing systems, including adaptive quantum phase estimation and designing quantum computing gates. On the other hand, quantum mechanics offers tantalizing prospects to enhance machine learning, ranging from reduced computational complexity to improved generalization performance. The most notable examples include quantum enhanced algorithms for principal component analysis, quantum support vector machines, and quantum Boltzmann machines. Progress has been rapid, fostered by demonstrations of midsized quantum optimizers which are predicted to soon outperform their classical counterparts. Further, we are witnessing the emergence of a physical theory pinpointing the fundamental and natural limitations of learning. Here we survey the cutting edge of this merger and list several open problems.

Evidence is mounting that Convolutional Networks (ConvNets) are the most effective representation learning method for visual recognition tasks. In the common scenario, a ConvNet is trained on a large labeled dataset (source) and the feed-forward units activation of the trained network, at a certain layer of the network, is used as a generic representation of an input image for a task with relatively smaller training set (target). Recent studies have shown this form of representation transfer to be suitable for a wide range of target visual recognition tasks. This paper introduces and investigates several factors affecting the transferability of such representations. It includes parameters for training of the source ConvNet such as its architecture, distribution of the training data, etc. and also the parameters of feature extraction such as layer of the trained ConvNet, dimensionality reduction, etc. Then, by optimizing these factors, we show that significant improvements can be achieved on various (17) visual recognition tasks. We further show that these visual recognition tasks can be categorically ordered based on their distance from the source task such that a correlation between the performance of tasks and their distance from the source task w.r.t. the proposed factors is observed.

We present a heuristic algorithm for finding a graph $H$ as a minor of a
graph $G$ that is practical for sparse $G$ and $H$ with hundreds of vertices.
We also explain the practical importance of finding graph minors in mapping
quadratic pseudo-boolean optimization problems onto an adiabatic quantum
annealer.

HyperLabelMe is a web platform that allows the automatic benchmarking of remote-sensing image classifiers. To demonstrate this platform's attributes, we collected and harmonized a large data set of labeled multispectral and hyperspectral images with different numbers of classes, dimensionality, noise sources, and levels. The registered user can download training data pairs (spectra and land cover/use labels) and submit the predictions for unseen testing spectra. The system then evaluates the accuracy and robustness of the classifier, and it reports different scores as well as a ranked list of the best methods and users. The system is modular, scalable, and ever-growing in data sets and classifier results.

Land-cover mapping in remote sensing (RS) applications renders rich information for decision support and environmental monitoring systems. The derivation of such information increasingly relies on robust classification methods for identifying the complex land-cover area of different categories. Numerous classification techniques have been designed for the analysis of RS imagery. In this context, support vector machines (SVMs) have recently received increasing interest. However, the need for a small-size training set remains a bottleneck to design efficient supervised classifiers, while an adequate number of unlabeled data is readily available in RS images and can be exploited as a supplementary source of information. To fully leverage these precious unlabeled data, a number of promising advanced SVM-based methods, such as active SVMs, semisupervised SVMs (S3VMs), and SVMs combined with other algorithms, have been developed to analyze satellite imagery. In this literature review, we have surveyed these learning techniques to explore RS images. Moreover, we have provided the empirical evidences of SVMs and three representative techniques. It is our hope that this review will provide guidelines to future researchers to enhance further algorithmic developments in RS applications.

A wide range of methods for analysis of airborne- and satellite-derived imagery continues to be proposed and assessed. In this paper, we review remote sensing implementations of support vector machines (SVMs), a promising machine learning methodology. This review is timely due to the exponentially increasing number of works published in recent years. SVMs are particularly appealing in the remote sensing field due to their ability to generalize well even with limited training samples, a common limitation for remote sensing applications. However, they also suffer from parameter assignment issues that can significantly affect obtained results. A summary of empirical results is provided for various applications of over one hundred published works (as of April, 2010). It is our hope that this survey will provide guidelines for future applications of SVMs and possible areas of algorithm enhancement.