We use the maximum a posteriori estimation principle for learning representations distributed on the unit sphere. We propose to use the angular Gaussian distribution, which corresponds to a Gaussian projected on the unit-sphere and derive the associated loss function. We also consider the von Mises-Fisher distribution, which is the conditional of a Gaussian in the unit-sphere. The learned representations are pushed toward fixed directions, which are the prior means of the Gaussians; allowing for a learning strategy that is resilient to data drift. This makes it suitable for online continual learning, which is the problem of training neural networks on a continuous data stream, where multiple classification tasks are presented sequentially so that data from past tasks are no longer accessible, and data from the current task can be seen only once. To address this challenging scenario, we propose a memory-based representation learning technique equipped with our new loss functions. Our approach does not require negative data or knowledge of task boundaries and performs well with smaller batch sizes while being computationally efficient. We demonstrate with extensive experiments that the proposed method outperforms the current state-of-the-art methods on both standard evaluation scenarios and realistic scenarios with blurry task boundaries. For reproducibility, we use the same training pipeline for every compared method and share the code at https://github.com/Nicolas1203/ocl-fd.

Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the filter graph distance. It is an optimal transport based distance which drives graph comparison through the probability distribution of filtered graph signals. This creates a highly flexible distance, capable of prioritising different spectral information in observed graphs, offering a wide range of choices for a comparison metric. We tackle the problem of graph alignment by computing graph permutations that minimise our new filter distances, which implicitly solves the graph comparison problem. We then propose a new approximate cost function that circumvents many computational difficulties inherent to graph comparison and permits the exploitation of fast algorithms such as mirror gradient descent, without grossly sacrificing the performance. We finally propose a novel algorithm derived from a stochastic version of mirror gradient descent, which accommodates the non-convexity of the alignment problem, offering a good trade-off between performance accuracy and speed. The experiments on graph alignment and classification show that the flexibility gained through filter graph distances can have a significant impact on performance, while the difference in speed offered by the approximation cost makes the framework applicable in practical settings.

This work addresses the problem of hyperspectral image classification when the number of labeled samples is very small (few shot learning). Our work is based on the recently proposed framework of convolutional transform learning. In this work, we propose a semi-supervised version of deep convolutional transform learning. We compare with four recent studies which are tailored for solving the few-shot learning problem in hyperspectral classification. Results show that our method can improve over the state-of-the-art.

Conventional Convolutional Neural Network (CNN) based clustering formulations are based on the encoder-decoder based framework, where the clustering loss is incorporated after the encoder network. The problem with this approach is that it requires training an additional decoder network; this, in turn, means learning additional weights which can lead to over-fitting in data constrained scenarios. This work introduces a Deep Convolutional Transform Learning (DCTL) based clustering framework. The advantage of our proposed formulation is that we do not require learning the additional decoder network. Therefore our formulation is less prone to over-fitting. Comparison with state-of-the-art deep learning based clustering solutions on benchmark image datasets shows that our proposed method improves over the rest in challenging scenarios where there are many clusters with limited samples.

We study Online Continual Learning with missing labels and propose SemiCon, a new contrastive loss designed for partly labeled data. We demonstrate its efficiency by devising a memory-based method trained on an unlabeled data stream, where every data added to memory is labeled using an oracle. Our approach outperforms existing semi-supervised methods when few labels are available, and obtain similar results to state-of-the-art supervised methods while using only 2.6% of labels on Split-CIFAR10 and 10% of labels on Split-CIFAR100.

The objective of this letter is to propose a novel computational method to learn the state of an appliance (ON / OFF) given the aggregate power consumption recorded by the smart-meter. We formulate a multi-label classification problem where the classes correspond to the appliances. The proposed approach is based on our recently introduced framework of convolutional transform learning. We propose a deep supervised version of it relying on an original multi-label cost. Comparisons with state-of-the-art techniques show that our proposed method improves over the benchmarks on popular non-intrusive load monitoring datasets.

Proximal splitting methods are standard tools for nonsmooth optimization. While primal-dual methods have become very popular in the last decade for their flexibility, primal methods may still be preferred for two reasons: acceleration schemes are more effective, and only a single stepsize is required. In this paper, we propose a primal proximal method derived from a three-operator splitting in a product space and accelerated with Anderson extrapolation. The proposed algorithm can activate smooth functions via their gradients, and allows for linear operators in nonsmooth functions. Numerical results show the good performance of our algorithm with respect to well-established modern optimization methods.

Convolutional transform learning is an unsupervised framework we introduced recently, for feature generation based on learnt convolutions. In this work, we propose a supervised formulation for convolutional transform so as to address the multi-label classification problem. Unlike the simple multiclass classification, in multi-label problems, each sample can correspond to multiple classes simultaneously, making the problem quite challenging. We propose to make use of a label consistency penalty and develop a suitable minimization algorithm for the training step. We illustrate the performance of the developed formulation on the practical problem of nonintrusive load monitoring. Comparisons with popular techniques show that our proposed approach yields better results on benchmark datasets.

Component-graphs provide powerful and complex structures for multi-band image processing. We propose a multiband astronomical source detection framework with the component-graphs relying on a new set of component attributes. We propose two modules to differentiate nodes belong to distinct objects and to detect partial object nodes. Experiments demonstrate an improved capacity at detecting faint objects on a multi-band astronomical dataset.

In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to large-scale graphs. Our contribution consists of reformulating spectral embedding so that it can be solved via stochastic optimization. The idea is to replace the orthogonality constraint with an orthogonalization matrix injected directly into the criterion. As the gradient can be computed through a Cholesky factorization, our reformulation allows us to develop an efficient algorithm based on mini-batch gradient descent. Experimental results, both on synthetic and real data, confirm the efficiency of the proposed method in term of execution speed with respect to similar existing techniques.

We study the problem of fitting an ultrametric distance to a dissimilarity graph in the context of hierarchical cluster analysis. Standard hierarchical clustering methods are specified procedurally, rather than in terms of the cost function to be optimized. We aim to overcome this limitation by presenting a general optimization framework for ultrametric fitting. Our approach consists of modeling the latter as a constrained optimization problem over the continuous space of ultrametrics. So doing, we can leverage the simple, yet effective, idea of replacing the ultrametric constraint with a min-max operation injected directly into the cost function. The proposed reformulation leads to an unconstrained optimization problem that can be efficiently solved by gradient descent methods. The flexibility of our framework allows us to investigate several cost functions, following the classic paradigm of combining a data fidelity term with a regularization. While we provide no theoretical guarantee to find the global optimum, the numerical results obtained over a number of synthetic and real datasets demonstrate the good performance of our approach with respect to state-of-the-art agglomerative algorithms. This makes us believe that the proposed framework sheds new light on the way to design a new generation of hierarchical clustering methods. Our code is made publicly available at https://github.com/PerretB/ultrametric-fitting.

We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows us to derive an explicit expression of the Wasserstein distance between graph signal distributions in terms of the graph Laplacian matrices. This leads to a structurally meaningful measure for comparing graphs, which is able to take into account the global structure of graphs, while most other measures merely observe local changes independently. Our measure is then used for formulating a new graph alignment problem, whose objective is to estimate the permutation that minimizes the distance between two graphs. We further propose an efficient stochastic algorithm based on Bayesian exploration to accommodate for the non-convexity of the graph alignment problem. We finally demonstrate the performance of our novel framework on different tasks like graph alignment, graph classification and graph signal prediction, and we show that our method leads to significant improvement with respect to the-state-of-art algorithms.

While φ-divergences have been extensively studied in convex analysis, their use in optimization problems often remains challenging. In this regard, one of the main shortcomings of existing methods is that the minimization of φ-divergences is usually performed with respect to one of their arguments, possibly within alternating optimization techniques. In this paper, we overcome this limitation by deriving new closed-form expressions for the proximity operator of such two-variable functions. This makes it possible to employ standard proximal methods for efficiently solving a wide range of convex optimization problems involving φ-divergences. In addition, we show that these proximity operators are useful to compute the epigraphical projection of several functions. The proposed proximal tools are numerically validated in the context of optimal query execution within database management systems, where the problem of selectivity estimation plays a central role. Experiments are carried out on small to large scale scenarios.

In this paper we investigate the use of discriminative model learning through Convolutional Neural Networks (CNNs) for SAR image despeckling. The network uses a residual learning strategy, hence it does not recover the filtered image, but the speckle component, which is then subtracted from the noisy one. Training is carried out by considering a large multitemporal SAR image and its multilook version, in order to approximate a clean image. Experimental results, both on synthetic and real SAR data, show the method to achieve better performance with respect to state-of-the-art techniques.

We propose a despeckling algorithm for multitemporal synthetic aperture radar (SAR) images based on the concepts of block-matching and collaborative filtering. It relies on the nonlocal approach, and it is the extension of SAR-BM3D for dealing with multitemporal data. The technique comprises two passes, each one performing grouping, collaborative filtering, and aggregation. In particular, the first pass performs both the spatial and temporal filtering, while the second pass only the spatial one. To avoid increasing the computational cost of the technique, we resort to lookup tables for the distance computation in the block-matching phases. The experiments show that the proposed algorithm compares favorably with respect to state-of-the-art reference techniques, with better results both on simulated speckled images and on real multitemporal SAR images.

Optimal rate allocation is among the most challenging tasks to perform in the context of predictive video coding, because of the dependencies between frames induced by motion compensation. In this paper, using a recursive rate-distortion model that explicitly takes into account these dependencies, we approach the frame-level rate allocation as a convex optimization problem. This technique is integrated into the recent HEVC encoder, and tested on several standard sequences. Experiments indicate that the proposed rate allocation ensures a better performance (in the rate-distortion sense) than the standard HEVC rate control, and with a little loss with respect to an optimal exhaustive research, which is largely compensated by a much shorter execution time.

Optimal rate allocation is among the most challenging tasks to perform in the context of multi-view video coding, because of the dependency between frames induced by motion compensation and depth image-based rendering. In this paper, using a recursive rate-distortion model that explicitly takes into account these dependencies, we approach the frame-level rate allocation as a convex optimization problem. Within this framework, we provide an efficient algorithm for exactly solving the above problem with recent convex optimization tools. Experiments on standard sequences demonstrate the interest of considering the proposed rate allocation method and confirm that our approach ensures a better performance (in ratedistortion sense) than the standard MV-HEVC rate control.

PRNU-based techniques guarantee a good forgery detection performance irrespective of the specific type of forgery. The presence or absence of the camera PRNU pattern is detected by a correlation test. Given the very low power of the PRNU signal, however, the correlation must be averaged over a pretty large window, reducing the algorithm's ability to reveal small forgeries. To improve resolution, we estimate correlation with a spatially adaptive filtering technique, with weights computed over a suitable pilot image. Implementation efficiency is achieved by resorting to the recently proposed guided filters. Experiments prove that the proposed filtering strategy allows for a much better detection performance in the case of small forgeries.

Sparsity inducing penalizations are useful tools in variational methods for machine learning. In this paper, we design a learning algorithm for multiclass support vector machines that allows us to enforce sparsity through various nonsmooth regularizations, such as the mixed ℓ1, p-norm with p ≥ 1. The proposed constrained convex optimization approach involves an epigraphical constraint for which we derive the closed-form expression of the associated projection. This sparse multiclass SVM problem can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments carried out for handwritten digits demonstrate the interest of considering nonsmooth sparsity-inducing regularizations and the efficiency of the proposed epigraphical projection method.

Optimal rate allocation is among the most challenging tasks to perform in the context of predictive video coding, because of the dependencies between frames induced by motion compensation. In this paper, we derive an analytical rate-distortion model that explicitly takes into account the dependencies between frames. The proposed approach allows us to formulate the frame-level optimal rate allocation as a convex optimization problem. Within this framework, we are able to achieve the exact solution in limited time (even for large-size problems), thanks to the flexibility offered by recent convex optimization techniques. Experiments on standard sequences demonstrate the interest of considering the proposed rate-distortion model and confirm that the optimal rate allocation ensures a better distribution of the total bit budget, with superior results (in the rate-distortion sense) with respect to the standard H.264/AVC rate control.

Graphics editing programs of the last generation provide ever more powerful tools, which allow for the retouching of digital images leaving little or no traces of tampering. The reliable detection of image forgeries requires, therefore, a battery of complementary tools that exploit different image properties. Techniques based on the photo-response non-uniformity (PRNU) noise are among the most valuable such tools, since they do not detect the inserted object but rather the absence of the camera PRNU, a sort of camera fingerprint, dealing successfully with forgeries that elude most other detection strategies. In this paper, we propose a new approach to detect image forgeries using sensor pattern noise. Casting the problem in terms of Bayesian estimation, we use a suitable Markov random field prior to model the strong spatial dependences of the source, and take decisions jointly on the whole image rather than individually for each pixel. Modern convex optimization techniques are then adopted to achieve a globally optimal solution and the PRNU estimation is improved by resorting to nonlocal denoising. Large-scale experiments on simulated and real forgeries show that the proposed technique largely improves upon the current state of the art, and that it can be applied with success to a wide range of practical situations.

Nonlocal total variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the structure tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the nonlocal variations, jointly for the different components, through various l(1, p)-matrix-norms with p ≥ 1. To facilitate the choice of the hyperparameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented because of the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for color, multispectral, and hyperspectral images. The results demonstrate the interest of introducing a nonlocal ST regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods, such as the alternating direction method of multipliers.

TV-like constraints/regularizations are useful tools in variational methods for multicomponent image restoration. In this paper, we design more sophisticated non-local TV constraints which are derived from the structure tensor. The proposed approach allows us to measure the non-local variations, jointly for the different components, through various ℓ1,pmatrix norms with p ≥ 1. The related convex constrained optimization problems are solved through a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments carried out for color images demonstrate the interest of considering a Non-Local Structure Tensor TV and show that the proposed epigraphical projection method leads to significant improvements in terms of convergence speed over existing numerical solutions.

Detection of image forgeries is an important topic for forensics applications. One of the most interesting approaches to forgery detection relies on the photo-response non uniformity noise (PRNU), that can be considered as a sort of camera fingerprint and used as such to accomplish forgery detection. In fact, while genuine parts of an image exhibit the camera PRNU, this is not present in tampered areas. In this work, we present a new method to detect forgeries by using PRNU. In particular, we propose a minimum-risk Bayesian classification, aimed at minimizing the probability of error or, more in general, a weighted average of the two types of errors (false alarm, missing detection) according to their importance for the application. Then, we introduce a regularization term in the decision process to take into account prior information on the classification map. This step weights optimally the observed data and the regularity constraints to minimize the Bayesian risk. Since the regularization term is based on spatial properties of the decision map, classification cannot work on each pixel individually but must be carried out jointly on the whole image. The ensuing problem is NP-hard but we use relaxation and convex optimization techniques, based on proximal methods, to obtain a global optimum solution in limited time. Preliminary experiments with digital forgeries of different sizes and shapes prove that the improved technique provides a significant performance gain w.r.t. the original, at the cost of a limited increase in complexity.

The concept of cosparsity has been recently introduced in the arena of compressed sensing. In cosparse modelling, the ℓ0(or ℓ1) cost of an analysis-based representation of the target signal isminimized under a data fidelity constraint. By taking benefit from recent advances in proximal algorithms, we show that it is possible to efficiently address a more general framework where a convex block sparsity measure is minimized under various convex constraints. The main contribution of this work is the introduction of a new epigraphical projection technique, which allows us to consider more flexible data fidelity constraints than the standard linear or quadratic ones. The validity of our approach is illustrated through an application to an image reconstruction problem in the presence of Poisson noise.

The Parallel Proximal Algorithm (PPXA+) has been recently introduced as an efficient tool for solving convex optimization problems. It has proved particularly effective in the context of stereo vision, used as the methodological core of a novel disparity estimation technique. In this work, the main methodological issues limiting the efficient parallelization of this technique are addressed, and further modifications are proposed to enable and optimize the design of parallel implementations. Finally, actual implementations that fit both the multi-core CPU and GPU devices are provided and tested to validate the performance potential of the proposed technique.