This paper deals with batch normalization for SPDnet, a deep learning architecture specifically designed to handle covariance matrices. Current SPDnet batch normalization relies on geometric means, which require expensive iterative computations and lacks formal backpropagation derivations. These limitations are addressed through two contributions: (i) formal backpropagation derivation for SPDnet batch normalization, and (ii) computationally efficient closed-form alternatives to the geometric mean: log-Euclidean, arithmetic and harmonic means, and the geometric mean of arithmetic and harmonic means. Simulation results on the batch normalization layer with different means demonstrate significant reductions in memory consumption and comparable training time by avoiding automatic differentiation, demonstrating the effectiveness of our approach. Numerical experiments on three real datasets show that simpler means can outperform the geometric mean with up to 5% accuracy improvements while reducing training time by a factor of 5.

We consider the problem of classifying a pair of Synthetic Aperture Radar (SAR) images by proposing an explainable and frugal algorithm that integrates a set of divergences. The approach relies on a statistical framework that takes standard probability distributions into account for modelling SAR data. Then, by learning a combination of parameterized Renyi divergences and their parameters from the data, we are able to classify the pair of images with fewer parameters than regular machine learning approaches while also allowing an interpretation of the results related to the priors used. Experiments on real multi-class data demonstrate the virtues of the suggested method when compared to both Random Forest and Convolutional Neural Networks (CNN) classifiers, showing its resilience to disturbances such as polluted labels and variations in the percentage of training data.

This study explores machine learning for classifying X-band Synthetic Aperture Radar (SAR) monovariate time series from four cryospheric zones in the Mont-Blanc massif. We aim to classify ablation zones, accumulation zones, hanging glaciers, and ice aprons using log-cumulants and Dynamic Time Warping Barycentric Averaging. Our approach evaluates distances between time series and estimated reference centroids, employing HH and HV polarimetric channels. We propose an extension to this method by aggregating class membership probabilities from selected polarimetric combinations. Results are compared across polarimetric channels, revealing insights into classification performance.

We propose a new approach for wet snow extent mapping in Synthetic Aperture Radar (SAR) images by using a convolutional neural network (CNN) designed to learn with respect to snowpack outputs from the state-of-the-art snow model Crocus. The CNN was trained to classify the wet snow conditions based on features extracted from the SAR images, using both the VV,VH channel and the ratio between these channels and those of a reference image in summer. One of the key points of this work is the comprehensive comparison we have made between the performance of the CNN method and other advanced statistical methods. We found that the CNN was able to achieve good accuracy in wet snow classification, and giving a complementary vision of the solutions obtained by other machine learning algorithms such as the Random Forest classifier. The results of this study demonstrate the potential of using CNNs and SAR images for wet snow classification and highlight the importance of using physical information model for training machine learning models in snow state identification, a domain where collecting ground truth is intricate due to the complexity of the snowpack moisture measurement systems.

In this paper, two SAR image time series acquired by PAZ and Sentinel-1 satellites in 2020 (29 and 60 images respectively) are used to investigate surface changes of different ice/snow-covered areas in the Mont-Blanc massif. The evolution of the backscatter coefficient and several statistical parameters in both X and C band SAR images is analyzed on ice aprons, on valley glacier accumulation and ablation areas, and on ice-free areas. Dry and wet snow changes are observed and correlated with meteorological data (temperature at 4 different elevations and snow height) acquired by a weather station.

In this paper, we propose two algorithms to enhance the interpretability of the hyperbola in B-scans obtained with a Ground Penetrating Radar (GPR). These hyperbolas are the responses of buried objects or cavities. To correctly detect and classify them, a denoising is typically necessary for GPR images as the signal-to-noise ratio is low, and the various interfaces naturally present in the earth have a strong response. Both algorithms are based on a sparse convolutional coding model plus a low rank component. It is solved through an Alternating Direction Method of Multipliers (ADMM) framework. In order to take into account the presence of outliers and the artifacts caused by the acquisition, the second algorithm is based on the Huber norm instead of the classicL2-norm. These algorithms are tested on a real dataset labeled by geophysicists. The results show the denoising efficiency of this approach, and in particular the robustness of the second algorithm.

We consider the problem of classifying Ground Penetrating Radar (GPR) signals by using covariance matrices descriptors computed on convolutional features obtained from MobileNetV2 Convolutional Neural Network (CNN) first layers. This approach allows to leverage the rich data representation obtained from CNNs and the low-dimensionality of second-order statistics. Then the Riemannian geometry of covariance matrices is leveraged to improve classification rate. The proposed approach allows then to perform automatic classification of buried objects with few labeled data available. We also consider the scenario of an airbone radar and provide results at different elevations.

In this paper, we investigate how to compute the throughput of probabilistic and replicated streaming applications. We are given (i) a streaming application whose dependence graph is a linear chain; (ii) a one-to-many mapping of the application onto a fully heterogeneous target, where a processor is assigned at most one application stage, but where a stage can be replicated onto a set of processors; and (iii) a set of IID (Independent and Identically-Distributed) variables to model each computation and communication time in the mapping. How can we compute the throughput of the application, i.e., the rate at which data sets can be processed? We consider two execution models, the STRICT model where the actions of each processor are sequentialized, and the OVERLAP model where a processor can compute and communicate in parallel. The problem is easy when application stages are not replicated, i.e., assigned to a single processor: in that case the throughput is dictated by the critical hardware resource. However, when stages are replicated, i.e., assigned to several processors, the problem becomes surprisingly complicated: even in the deterministic case, the optimal throughput may be lower than the smallest internal resource throughput. To the best of our knowledge, the problem has never been considered in the probabilistic case. The first main contribution of the paper is to provide a general method (although of exponential cost) to compute the throughput when mapping parameters follow IID exponential laws. This general method is based upon the analysis of timed Petri nets deduced from the application mapping; it turns out that these Petri nets exhibit a regular structure in the OVERLAP model, thereby enabling to reduce the cost and provide a polynomial algorithm. The second main contribution of the paper is to provide bounds for the throughput when stage parameters are arbitrary IID and NBUE (New Better than Used in Expectation) variables: the throughput is bounded from below by the exponential case and bounded from above by the deterministic case.

In this paper, we focus on computing the throughput of replicated workflows. Given a streaming application whose dependence graph is a linear chain, and a mapping of this application onto a fully heterogeneous platform, how can we compute the optimal throughput, or equivalently the minimal period? The problem is easy when workflow stages are not replicated, i.e., assigned to a single processor: in that case the period is dictated by the critical hardware resource. But when stages are replicated, i.e., assigned to several processors, the problem gets surprisingly complicated, and we provide examples where the optimal period is larger than the largest cycle-time of any resource. We then show how to model the problem as a timed Petri net to compute the optimal period in the general case, and we provide a polynomial algorithm for the one-port communication model with overlap. Finally, we report comprehensive simulation results on the gap between the optimal period and the largest resource cycle-time.

In this paper, we focus on scheduling jobs on computing grids. In our model, a grid job is made of a large collection of input data sets, which must all be processed by the same task graph or workflow, thus resulting in a collection of task graphs problem. We are looking for a competitive scheduling algorithm not requiring complex control. We thus only consider single-allocation strategies. In addition to a mixed linear programming approach to find an optimal allocation, we present different heuristic schemes. Then, using simulations, we compare the performance of our different heuristics to the performance of a classical scheduling policy in Grids, HEFT. The results show that some of our static-scheduling policies take advantage of their platform and application knowledge and outperform HEFT, especially under communication-intensive scenarios. In particular, one of our heuristics, DELEGATE, almost always achieves the best performance while having lower running times than HEFT.

In this paper, we focus on scheduling jobs on computing Grids. In our model, a Grid job is made of a large collection of input data sets, which must all be processed by the same task graph or workflow, thus resulting in a series of workflow problem. We are looking for an efficient solution with regard to throughput and latency, while avoiding solutions requiring complex control. We thus only consider single-allocation strategies. We present an algorithm based on mixed linear programming to find an optimal allocation, and this for different routing policies depending on how much latitude we have on communications. Then, using simulations, we compare our allocations to reference heuristics. The results show that our algorithm almost always finds an allocation with good throughput and low latency, and that it outperforms the reference heuristics, especially under communication-intensive scenarios.

Min, Veeravalli, and Barlas have recently proposed strategies to minimize the overall execution time of one or several divisible loads on a heterogeneous linear network, using one or more installments [18, 19]. We show on a very simple example that their approach does not always produce a solution and that, when it does, the solution is often suboptimal. We also show how to find an optimal scheduling for any instance, once the number of installments per load is given. Then, we formally prove that any optimal schedule has an infinite number of installments under a linear cost model as the one assumed in [18, 19]. Such a cost model cannot be used to design practical multi-installment strategies. Finally, through extensive simulations we confirmed that the best solution is always produced by the linear programming approach.

In this paper, we study the problem of scheduling file transfers through a switch. This problem is at the heart of a model often used for large grid computations, where the switch represents the core of the network interconnecting the various clusters that compose the grid. We establish several complexity results, and we introduce and analyze various algorithms, from both a theoretical and a practical perspective