Paul Honeine

Ahmed Rida Sekkat, Yohan Dupuis, Varun Ravi Kumar et al.

Surround-view cameras are a primary sensor for automated driving, used for near-field perception. It is one of the most commonly used sensors in commercial vehicles primarily used for parking visualization and automated parking. Four fisheye cameras with a 190° field of view cover the 360° around the vehicle. Due to its high radial distortion, the standard algorithms do not extend easily. Previously, we released the first public fisheye surround-view dataset named WoodScape. In this work, we release a synthetic version of the surround-view dataset, covering many of its weaknesses and extending it. Firstly, it is not possible to obtain ground truth for pixel-wise optical flow and depth. Secondly, WoodScape did not have all four cameras annotated simultaneously in order to sample diverse frames. However, this means that multi-camera algorithms cannot be designed to obtain a unified output in birds-eye space, which is enabled in the new dataset. We implemented surround-view fisheye geometric projections in CARLA Simulator matching WoodScape's configuration and created SynWoodScape. We release 80k images from the synthetic dataset with annotations for 10+ tasks. We also release the baseline code and supporting scripts.

Muhammet Balcilar, Guillaume Renton, Pierre Heroux et al.

This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is designed in the spatial or the spectral domain. The obtained general framework allows to lead a spectral analysis of the most popular ConvGNNs, explaining their performance and showing their limits. Moreover, the proposed framework is used to design new convolutions in spectral domain with a custom frequency profile while applying them in the spatial domain. We also propose a generalization of the depthwise separable convolution framework for graph convolutional networks, what allows to decrease the total number of trainable parameters by keeping the capacity of the model. To the best of our knowledge, such a framework has never been used in the GNNs literature. Our proposals are evaluated on both transductive and inductive graph learning problems. Obtained results show the relevance of the proposed method and provide one of the first experimental evidence of transferability of spectral filter coefficients from one graph to another. Our source codes are publicly available at: https://github.com/balcilar/Spectral-Designed-Graph-Convolutions

Mohamad Dhaini, Paul Honeine, Maxime Berar et al.

Contrastive learning has demonstrated great success in representation learning, especially for image classification tasks. However, there is still a shortage in studies targeting regression tasks, and more specifically applications on hyperspectral data. In this paper, we propose a spectral-spatial contrastive learning framework for regression tasks for hyperspectral data, in a model-agnostic design allowing to enhance backbones such as 3D convolutional and transformer-based networks. Moreover, we provide a collection of transformations relevant for augmenting hyperspectral data. Experiments on synthetic and real datasets show that the proposed framework and transformations significantly improve the performance of all studied backbone models.

Mohamad Dhaini, Maxime Berar, Paul Honeine et al.

Contrastive learning has demonstrated great effectiveness in representation learning especially for image classification tasks. However, there is still a shortage in the studies targeting regression tasks, and more specifically applications on hyperspectral data. In this paper, we propose a contrastive learning framework for the regression tasks for hyperspectral data. To this end, we provide a collection of transformations relevant for augmenting hyperspectral data, and investigate contrastive learning for regression. Experiments on synthetic and real hyperspectral datasets show that the proposed framework and transformations significantly improve the performance of regression models, achieving better scores than other state-of-the-art transformations.

Romain Mussard, Fannia Pacheco, Maxime Berar et al.

Universal Domain Adaptation (UniDA) aims to transfer knowledge from a labeled source domain to an unlabeled target domain, even when their classes are not fully shared. Few dedicated UniDA methods exist for Time Series (TS), which remains a challenging case. In general, UniDA approaches align common class samples and detect unknown target samples from emerging classes. Such detection often results from thresholding a discriminability metric. The threshold value is typically either a fine-tuned hyperparameter or a fixed value, which limits the ability of the model to adapt to new data. Furthermore, discriminability metrics exhibit overconfidence for unknown samples, leading to misclassifications. This paper introduces UniJDOT, an optimal-transport-based method that accounts for the unknown target samples in the transport cost. Our method also proposes a joint decision space to improve the discriminability of the detection module. In addition, we use an auto-thresholding algorithm to reduce the dependence on fixed or fine-tuned thresholds. Finally, we rely on a Fourier transform-based layer inspired by the Fourier Neural Operator for better TS representation. Experiments on TS benchmarks demonstrate the discriminability, robustness, and state-of-the-art performance of UniJDOT.

Romain Mussard, Fannia Pacheco, Maxime Berar et al.

Deep learning models have significantly improved the ability to detect novelties in time series (TS) data. This success is attributed to their strong representation capabilities. However, due to the inherent variability in TS data, these models often struggle with generalization and robustness. To address this, a common approach is to perform Unsupervised Domain Adaptation, particularly Universal Domain Adaptation (UniDA), to handle domain shifts and emerging novel classes. While extensively studied in computer vision, UniDA remains underexplored for TS data. This work provides a comprehensive implementation and comparison of state-of-the-art TS backbones in a UniDA framework. We propose a reliable protocol to evaluate their robustness and generalization across different domains. The goal is to provide practitioners with a framework that can be easily extended to incorporate future advancements in UniDA and TS architectures. Our results highlight the critical influence of backbone selection in UniDA performance and enable a robustness analysis across various datasets and architectures.

José Medina, Amnir Hadachi, Paul Honeine et al.

Deep neural networks (DNNs) have remarkably succeeded in various image processing tasks. However, their large size and computational complexity present significant challenges for deploying them in resource-constrained environments. This paper presents an innovative approach for integrating Mamba Architecture within a Progressive Knowledge Distillation (PKD) process to address the challenge of reducing model complexity while maintaining accuracy in image classification tasks. The proposed framework distills a large teacher model into progressively smaller student models, designed using Mamba blocks. Each student model is trained using Selective-State-Space Models (S-SSM) within the Mamba blocks, focusing on important input aspects while reducing computational complexity. The work's preliminary experiments use MNIST and CIFAR-10 as datasets to demonstrate the effectiveness of this approach. For MNIST, the teacher model achieves 98% accuracy. A set of seven student models as a group retained 63% of the teacher's FLOPs, approximating the teacher's performance with 98% accuracy. The weak student used only 1% of the teacher's FLOPs and maintained 72% accuracy. Similarly, for CIFAR-10, the students achieved 1% less accuracy compared to the teacher, with the small student retaining 5% of the teacher's FLOPs to achieve 50% accuracy. These results confirm the flexibility and scalability of Mamba Architecture, which can be integrated into PKD, succeeding in the process of finding students as weak learners. The framework provides a solution for deploying complex neural networks in real-time applications with a reduction in computational cost.

Rosana El Jurdi, Caroline Petitjean, Veronika Cheplygina et al.

Today, deep convolutional neural networks (CNNs) have demonstrated state-of-the-art performance for medical image segmentation, on various imaging modalities and tasks. Despite early success, segmentation networks may still generate anatomically aberrant segmentations, with holes or inaccuracies near the object boundaries. To enforce anatomical plausibility, recent research studies have focused on incorporating prior knowledge such as object shape or boundary, as constraints in the loss function. Prior integrated could be low-level referring to reformulated representations extracted from the ground-truth segmentations, or high-level representing external medical information such as the organ's shape or size. Over the past few years, prior-based losses exhibited a rising interest in the research field since they allow integration of expert knowledge while still being architecture-agnostic. However, given the diversity of prior-based losses on different medical imaging challenges and tasks, it has become hard to identify what loss works best for which dataset. In this paper, we establish a benchmark of recent prior-based losses for medical image segmentation. The main objective is to provide intuition onto which losses to choose given a particular task or dataset. To this end, four low-level and high-level prior-based losses are selected. The considered losses are validated on 8 different datasets from a variety of medical image segmentation challenges including the Decathlon, the ISLES and the WMH challenge. Results show that whereas low-level prior-based losses can guarantee an increase in performance over the Dice loss baseline regardless of the dataset characteristics, high-level prior-based losses can increase anatomical plausibility as per data characteristics.

Muhammet Balcilar, Pierre Héroux, Benoit Gaüzère et al.

Since the Message Passing (Graph) Neural Networks (MPNNs) have a linear complexity with respect to the number of nodes when applied to sparse graphs, they have been widely implemented and still raise a lot of interest even though their theoretical expressive power is limited to the first order Weisfeiler-Lehman test (1-WL). In this paper, we show that if the graph convolution supports are designed in spectral-domain by a non-linear custom function of eigenvalues and masked with an arbitrary large receptive field, the MPNN is theoretically more powerful than the 1-WL test and experimentally as powerful as a 3-WL existing models, while remaining spatially localized. Moreover, by designing custom filter functions, outputs can have various frequency components that allow the convolution process to learn different relationships between a given input graph signal and its associated properties. So far, the best 3-WL equivalent graph neural networks have a computational complexity in $\mathcal{O}(n^3)$ with memory usage in $\mathcal{O}(n^2)$, consider non-local update mechanism and do not provide the spectral richness of output profile. The proposed method overcomes all these aforementioned problems and reaches state-of-the-art results in many downstream tasks.

Rosana El Jurdi, Caroline Petitjean, Paul Honeine et al.

Today, deep convolutional neural networks (CNNs) have demonstrated state of the art performance for supervised medical image segmentation, across various imaging modalities and tasks. Despite early success, segmentation networks may still generate anatomically aberrant segmentations, with holes or inaccuracies near the object boundaries. To mitigate this effect, recent research works have focused on incorporating spatial information or prior knowledge to enforce anatomically plausible segmentation. If the integration of prior knowledge in image segmentation is not a new topic in classical optimization approaches, it is today an increasing trend in CNN based image segmentation, as shown by the growing literature on the topic. In this survey, we focus on high level prior, embedded at the loss function level. We categorize the articles according to the nature of the prior: the object shape, size, topology, and the inter-regions constraints. We highlight strengths and limitations of current approaches, discuss the challenge related to the design and the integration of prior-based losses, and the optimization strategies, and draw future research directions.

Daniel Alshamaa, Farah Chehade, Paul Honeine

Indoor localization has become an important issue for wireless sensor networks. This paper presents a zoning-based localization technique that uses WiFi signals and works efficiently in indoor environments. The targeted area is composed of several zones, the objective being to determine the zone of the sensor using an observation model based on statistical learning.

Yuan Liu, Stéphane Canu, Paul Honeine et al.

Sparse representation learning has recently gained a great success in signal and image processing, thanks to recent advances in dictionary learning. To this end, the $\ell_0$-norm is often used to control the sparsity level. Nevertheless, optimization problems based on the $\ell_0$-norm are non-convex and NP-hard. For these reasons, relaxation techniques have been attracting much attention of researchers, by priorly targeting approximation solutions (e.g. $\ell_1$-norm, pursuit strategies). On the contrary, this paper considers the exact $\ell_0$-norm optimization problem and proves that it can be solved effectively, despite of its complexity. The proposed method reformulates the problem as a Mixed-Integer Quadratic Program (MIQP) and gets the global optimal solution by applying existing optimization software. Because the main difficulty of this approach is its computational time, two techniques are introduced that improve the computational speed. Finally, our method is applied to image denoising which shows its feasibility and relevance compared to the state-of-the-art.

Xi Liu, Badong Chen, Bin Xu et al.

The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilizing a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for nonlinear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearization regression based on the maximum correntropy criterion (MCC) is then used to obtain the posterior estimates of the state and covariance. The satisfying performance of the new algorithm is confirmed by two illustrative examples.

Fei Zhu, Abderrahim Halimi, Paul Honeine et al.

In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writing the unmixing problem as the maximization of the correntropy criterion subject to the most commonly used constraints. Two unmixing problems are derived: the first problem considers the fully-constrained unmixing, with both the non-negativity and sum-to-one constraints, while the second one deals with the non-negativity and the sparsity-promoting of the abundances. The corresponding optimization problems are solved efficiently using an alternating direction method of multipliers (ADMM) approach. Experiments on synthetic and real hyperspectral images validate the performance of the proposed algorithms for different scenarios, demonstrating that the correntropy-based unmixing is robust to outlier bands.

Paul Honeine, Fei Zhu

Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. In this paper, we propose to revisit the NMF as a multi-objective problem, in particular a bi-objective one, where the objective functions defined in both input and feature spaces are taken into account. By taking the advantage of the sum-weighted method from the literature of multi-objective optimization, the proposed bi-objective NMF determines a set of nondominated, Pareto optimal, solutions instead of a single optimal decomposition. Moreover, the corresponding Pareto front is studied and approximated. Experimental results on unmixing real hyperspectral images confirm the efficiency of the proposed bi-objective NMF compared with the state-of-the-art methods.

Paul Honeine

In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the orthogonality condition of the atoms, yielding overcomplete dictionaries with an extended number of atoms. More generally than the linear decomposition, overcomplete kernel dictionaries provide an elegant nonlinear extension by defining the atoms through a mapping kernel function (e.g., the gaussian kernel). Models based on such kernel dictionaries are used in neural networks, gaussian processes and online learning with kernels. The quality of an overcomplete dictionary is evaluated with a diversity measure the distance, the approximation, the coherence and the Babel measures. In this paper, we develop a framework to examine overcomplete kernel dictionaries with the entropy from information theory. Indeed, a higher value of the entropy is associated to a further uniform spread of the atoms over the space. For each of the aforementioned diversity measures, we derive lower bounds on the entropy. Several definitions of the entropy are examined, with an extensive analysis in both the input space and the mapped feature space.

Paul Honeine

Many machine learning frameworks, such as resource-allocating networks, kernel-based methods, Gaussian processes, and radial-basis-function networks, require a sparsification scheme in order to address the online learning paradigm. For this purpose, several online sparsification criteria have been proposed to restrict the model definition on a subset of samples. The most known criterion is the (linear) approximation criterion, which discards any sample that can be well represented by the already contributing samples, an operation with excessive computational complexity. Several computationally efficient sparsification criteria have been introduced in the literature, such as the distance, the coherence and the Babel criteria. In this paper, we provide a framework that connects these sparsification criteria to the issue of approximating samples, by deriving theoretical bounds on the approximation errors. Moreover, we investigate the error of approximating any feature, by proposing upper-bounds on the approximation error for each of the aforementioned sparsification criteria. Two classes of features are described in detail, the empirical mean and the principal axes in the kernel principal component analysis.

Paul Honeine

Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines, with new challenges emerging in online learning with kernels. To this end, several sparsity measures have been proposed in the literature to quantify sparse dictionaries and constructing relevant ones, the most prolific ones being the distance, the approximation, the coherence and the Babel measures. In this paper, we analyze sparse dictionaries based on these measures. By conducting an eigenvalue analysis, we show that these sparsity measures share many properties, including the linear independence condition and inducing a well-posed optimization problem. Furthermore, we prove that there exists a quasi-isometry between the parameter (i.e., dual) space and the dictionary's induced feature space.

Fei Zhu, Paul Honeine, Maya Kallas

The nonnegative matrix factorization (NMF) is widely used in signal and image processing, including bio-informatics, blind source separation and hyperspectral image analysis in remote sensing. A great challenge arises when dealing with a nonlinear formulation of the NMF. Within the framework of kernel machines, the models suggested in the literature do not allow the representation of the factorization matrices, which is a fallout of the curse of the pre-image. In this paper, we propose a novel kernel-based model for the NMF that does not suffer from the pre-image problem, by investigating the estimation of the factorization matrices directly in the input space. For different kernel functions, we describe two schemes for iterative algorithms: an additive update rule based on a gradient descent scheme and a multiplicative update rule in the same spirit as in the Lee and Seung algorithm. Within the proposed framework, we develop several extensions to incorporate constraints, including sparseness, smoothness, and spatial regularization with a total-variation-like penalty. The effectiveness of the proposed method is demonstrated with the problem of unmixing hyperspectral images, using well-known real images and results with state-of-the-art techniques.

Paul Honeine

Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least squares regression, canonical-correlation analysis and Fisher discriminant analysis. Recently, many researchers advocate working on non-centered data. This is the case for instance with the singular value decomposition approach, with the (kernel) entropy component analysis, with the information-theoretic learning framework, and even with nonnegative matrix factorization. Moreover, one can also consider a non-centered PCA by using the second-order non-central moment. The main purpose of this paper is to bridge the gap between these two viewpoints in designing machine learning methods. To provide a study at the cornerstone of kernel-based machines, we conduct an eigenanalysis of the inner product matrices from centered and non-centered data. We derive several results connecting their eigenvalues and their eigenvectors. Furthermore, we explore the outer product matrices, by providing several results connecting the largest eigenvectors of the covariance matrix and its non-centered counterpart. These results lay the groundwork to several extensions beyond conventional centering, with the weighted mean shift, the rank-one update, and the multidimensional scaling. Experiments conducted on simulated and real data illustrate the relevance of this work.