arXiv subjects

Mohamed El Amine Seddik

Publications and source records attributed to Mohamed El Amine Seddik.

29 records · Page 2Linked to original sources

arXiv2023

A Nested Matrix-Tensor Model for Noisy Multi-view Clustering

In this paper, we propose a nested matrix-tensor model which extends the spiked rank-one tensor model of order three. This model is particularly motivated by a multi-view clustering problem in which multiple noisy observations of each data point are acquired, with potentially non-uniform variances along the views. In this case, data can be naturally represented by an order-three tensor where the views are stacked. Given such a tensor, we consider the estimation of the hidden clusters via performing a best rank-one tensor approximation. In order to study the theoretical performance of this approach, we characterize the behavior of this best rank-one approximation in terms of the alignments of the obtained component vectors with the hidden model parameter vectors, in the large-dimensional regime. In particular, we show that our theoretical results allow us to anticipate the exact accuracy of the proposed clustering approach. Furthermore, numerical experiments indicate that leveraging our tensor-based approach yields better accuracy compared to a naive unfolding-based algorithm which ignores the underlying low-rank tensor structure. Our analysis unveils unexpected and non-trivial phase transition phenomena depending on the model parameters, ``interpolating'' between the typical behavior observed for the spiked matrix and tensor models.

stat.ML↗

arXiv2023

Hotelling Deflation on Large Symmetric Spiked Tensors

This paper studies the deflation algorithm when applied to estimate a low-rank symmetric spike contained in a large tensor corrupted by additive Gaussian noise. Specifically, we provide a precise characterization of the large-dimensional performance of deflation in terms of the alignments of the vectors obtained by successive rank-1 approximation and of their estimated weights, assuming non-trivial (fixed) correlations among spike components. Our analysis allows an understanding of the deflation mechanism in the presence of noise and can be exploited for designing more efficient signal estimation methods.

stat.ML↗

arXiv2023

Optimizing Orthogonalized Tensor Deflation via Random Tensor Theory

This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered efficiently using tensor deflation which consists of successive rank-one approximations, while non-orthogonal components may alter the tensor deflation mechanism, thereby preventing efficient recovery. Relying on recently developed random tensor tools, this paper deals precisely with the non-orthogonal case by deriving an asymptotic analysis of a parameterized deflation procedure performed on an order-three and rank-two spiked tensor. Based on this analysis, an efficient tensor deflation algorithm is proposed by optimizing the parameter introduced in the deflation mechanism, which in turn is proven to be optimal by construction for the studied tensor model. The same ideas could be extended to more general low-rank tensor models, e.g., higher ranks and orders, leading to more efficient tensor methods with a broader impact on machine learning and beyond.

stat.ML↗

arXiv2022

When Random Tensors meet Random Matrices

Relying on random matrix theory (RMT), this paper studies asymmetric order-$d$ spiked tensor models with Gaussian noise. Using the variational definition of the singular vectors and values of (Lim, 2005), we show that the analysis of the considered model boils down to the analysis of an equivalent spiked symmetric \textit{block-wise} random matrix, that is constructed from \textit{contractions} of the studied tensor with the singular vectors associated to its best rank-1 approximation. Our approach allows the exact characterization of the almost sure asymptotic singular value and alignments of the corresponding singular vectors with the true spike components, when $\frac{n_i}{\sum_{j=1}^d n_j}\to c_i\in (0, 1)$ with $n_i$'s the tensor dimensions. In contrast to other works that rely mostly on tools from statistical physics to study random tensors, our results rely solely on classical RMT tools such as Stein's lemma. Finally, classical RMT results concerning spiked random matrices are recovered as a particular case.

math.PR↗

arXiv2022

On the Accuracy of Hotelling-Type Tensor Deflation: A Random Tensor Analysis

Leveraging on recent advances in random tensor theory, we consider in this paper a rank-$r$ asymmetric spiked tensor model of the form $\sum_{i=1}^r β_i A_i + W$ where $β_i\geq 0$ and the $A_i$'s are rank-one tensors such that $\langle A_i, A_j \rangle\in [0, 1]$ for $i\neq j$, based on which we provide an asymptotic study of Hotelling-type tensor deflation in the large dimensional regime. Specifically, our analysis characterizes the singular values and alignments at each step of the deflation procedure, for asymptotically large tensor dimensions. This can be used to construct consistent estimators of different quantities involved in the underlying problem, such as the signal-to-noise ratios $β_i$ or the alignments between the different signal components $\langle A_i, A_j \rangle$.

math.ST↗

arXiv2022

Node Feature Kernels Increase Graph Convolutional Network Robustness

The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a GCN utilised for node classification on six real datasets further confirms the theoretical findings and demonstrates that perturbations of the graph structure can result in GCNs performing significantly worse than Multi-Layer Perceptrons run on the node features alone. In practice, adding a node feature kernel to the message passing of perturbed graphs results in a significant improvement of the GCN's performance, thereby rendering it more robust to graph perturbations. Our code is publicly available at:https://github.com/ChangminWu/RobustGCN.

cs.LG↗

arXiv2021

Deep Miner: A Deep and Multi-branch Network which Mines Rich and Diverse Features for Person Re-identification

Most recent person re-identification approaches are based on the use of deep convolutional neural networks (CNNs). These networks, although effective in multiple tasks such as classification or object detection, tend to focus on the most discriminative part of an object rather than retrieving all its relevant features. This behavior penalizes the performance of a CNN for the re-identification task, since it should identify diverse and fine grained features. It is then essential to make the network learn a wide variety of finer characteristics in order to make the re-identification process of people effective and robust to finer changes. In this article, we introduce Deep Miner, a method that allows CNNs to "mine" richer and more diverse features about people for their re-identification. Deep Miner is specifically composed of three types of branches: a Global branch (G-branch), a Local branch (L-branch) and an Input-Erased branch (IE-branch). G-branch corresponds to the initial backbone which predicts global characteristics, while L-branch retrieves part level resolution features. The IE-branch for its part, receives partially suppressed feature maps as input thereby allowing the network to "mine" new features (those ignored by G-branch) as output. For this special purpose, a dedicated suppression procedure for identifying and removing features within a given CNN is introduced. This suppression procedure has the major benefit of being simple, while it produces a model that significantly outperforms state-of-the-art (SOTA) re-identification methods. Specifically, we conduct experiments on four standard person re-identification benchmarks and witness an absolute performance gain up to 6.5% mAP compared to SOTA.

cs.CV↗

arXiv2020

Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixtures

This paper shows that deep learning (DL) representations of data produced by generative adversarial nets (GANs) are random vectors which fall within the class of so-called \textit{concentrated} random vectors. Further exploiting the fact that Gram matrices, of the type $G = X^T X$ with $X=[x_1,\ldots,x_n]\in \mathbb{R}^{p\times n}$ and $x_i$ independent concentrated random vectors from a mixture model, behave asymptotically (as $n,p\to \infty$) as if the $x_i$ were drawn from a Gaussian mixture, suggests that DL representations of GAN-data can be fully described by their first two statistical moments for a wide range of standard classifiers. Our theoretical findings are validated by generating images with the BigGAN model and across different popular deep representation networks.

cs.LG↗

arXiv2019

Deep Multi-class Adversarial Specularity Removal

We propose a novel learning approach, in the form of a fully-convolutional neural network (CNN), which automatically and consistently removes specular highlights from a single image by generating its diffuse component. To train the generative network, we define an adversarial loss on a discriminative network as in the GAN framework and combined it with a content loss. In contrast to existing GAN approaches, we implemented the discriminator to be a multi-class classifier instead of a binary one, to find more constraining features. This helps the network pinpoint the diffuse manifold by providing two more gradient terms. We also rendered a synthetic dataset designed to help the network generalize well. We show that our model performs well across various synthetic and real images and outperforms the state-of-the-art in consistency.

cs.CV↗

arXiv2019

Generative Collaborative Networks for Single Image Super-Resolution

A common issue of deep neural networks-based methods for the problem of Single Image Super-Resolution (SISR), is the recovery of finer texture details when super-resolving at large upscaling factors. This issue is particularly related to the choice of the objective loss function. In particular, recent works proposed the use of a VGG loss which consists in minimizing the error between the generated high resolution images and ground-truth in the feature space of a Convolutional Neural Network (VGG19), pre-trained on the very "large" ImageNet dataset. When considering the problem of super-resolving images with a distribution "far" from the ImageNet images distribution (\textit{e.g.,} satellite images), their proposed \textit{fixed} VGG loss is no longer relevant. In this paper, we present a general framework named \textit{Generative Collaborative Networks} (GCN), where the idea consists in optimizing the \textit{generator} (the mapping of interest) in the feature space of a \textit{features extractor} network. The two networks (generator and extractor) are \textit{collaborative} in the sense that the latter "helps" the former, by constructing discriminative and relevant features (not necessarily \textit{fixed} and possibly learned \textit{mutually} with the generator). We evaluate the GCN framework in the context of SISR, and we show that it results in a method that is adapted to super-resolution domains that are "far" from the ImageNet domain.

cs.CV↗

arXiv2018

Learning More Universal Representations for Transfer-Learning

A representation is supposed universal if it encodes any element of the visual world (e.g., objects, scenes) in any configuration (e.g., scale, context). While not expecting pure universal representations, the goal in the literature is to improve the universality level, starting from a representation with a certain level. To do so, the state-of-the-art consists in learning CNN-based representations on a diversified training problem (e.g., ImageNet modified by adding annotated data). While it effectively increases universality, such approach still requires a large amount of efforts to satisfy the needs in annotated data. In this work, we propose two methods to improve universality, but pay special attention to limit the need of annotated data. We also propose a unified framework of the methods based on the diversifying of the training problem. Finally, to better match Atkinson's cognitive study about universal human representations, we proposed to rely on the transfer-learning scheme as well as a new metric to evaluate universality. This latter, aims us to demonstrates the interest of our methods on 10 target-problems, relating to the classification task and a variety of visual domains.

cs.CV↗