arXiv subjects

Fakhri Karray

Publications and source records attributed to Fakhri Karray.

At least 73 records · Page 4Linked to original sources

arXiv2022

Integrating Digital Twin and Advanced Intelligent Technologies to Realize the Metaverse

The advances in Artificial Intelligence (AI) have led to technological advancements in a plethora of domains. Healthcare, education, and smart city services are now enriched with AI capabilities. These technological advancements would not have been realized without the assistance of fast, secure, and fault-tolerant communication media. Traditional processing, communication and storage technologies cannot maintain high levels of scalability and user experience for immersive services. The metaverse is an immersive three-dimensional (3D) virtual world that integrates fantasy and reality into a virtual environment using advanced virtual reality (VR) and augmented reality (AR) devices. Such an environment is still being developed and requires extensive research in order for it to be realized to its highest attainable levels. In this article, we discuss some of the key issues required in order to attain realization of metaverse services. We propose a framework that integrates digital twin (DT) with other advanced technologies such as the sixth generation (6G) communication network, blockchain, and AI, to maintain continuous end-to-end metaverse services. This article also outlines requirements for an integrated, DT-enabled metaverse framework and provides a look ahead into the evolving topic.

cs.HC↗

arXiv2022

Offline versus Online Triplet Mining based on Extreme Distances of Histopathology Patches

We analyze the effect of offline and online triplet mining for colorectal cancer (CRC) histopathology dataset containing 100,000 patches. We consider the extreme, i.e., farthest and nearest patches to a given anchor, both in online and offline mining. While many works focus solely on selecting the triplets online (batch-wise), we also study the effect of extreme distances and neighbor patches before training in an offline fashion. We analyze extreme cases' impacts in terms of embedding distance for offline versus online mining, including easy positive, batch semi-hard, batch hard triplet mining, neighborhood component analysis loss, its proxy version, and distance weighted sampling. We also investigate online approaches based on extreme distance and comprehensively compare offline, and online mining performance based on the data patterns and explain offline mining as a tractable generalization of the online mining with large mini-batch size. As well, we discuss the relations of different colorectal tissue types in terms of extreme distances. We found that offline and online mining approaches have comparable performances for a specific architecture, such as ResNet-18 in this study. Moreover, we found the assorted case, including different extreme distances, is promising, especially in the online approach.

cs.CV↗

arXiv2022

Theoretical Connection between Locally Linear Embedding, Factor Analysis, and Probabilistic PCA

Locally Linear Embedding (LLE) is a nonlinear spectral dimensionality reduction and manifold learning method. It has two main steps which are linear reconstruction and linear embedding of points in the input space and embedding space, respectively. In this work, we look at the linear reconstruction step from a stochastic perspective where it is assumed that every data point is conditioned on its linear reconstruction weights as latent factors. The stochastic linear reconstruction of LLE is solved using expectation maximization. We show that there is a theoretical connection between three fundamental dimensionality reduction methods, i.e., LLE, factor analysis, and probabilistic Principal Component Analysis (PCA). The stochastic linear reconstruction of LLE is formulated similar to the factor analysis and probabilistic PCA. It is also explained why factor analysis and probabilistic PCA are linear and LLE is a nonlinear method. This work combines and makes a bridge between two broad approaches of dimensionality reduction, i.e., the spectral and probabilistic algorithms.

stat.ML↗

arXiv2022

Laplacian-Based Dimensionality Reduction Including Spectral Clustering, Laplacian Eigenmap, Locality Preserving Projection, Graph Embedding, and Diffusion Map: Tutorial and Survey

This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation of Laplacian. Then, we cover the cuts of graph and spectral clustering which applies clustering in a subspace of data. Different optimization variants of Laplacian eigenmap and its out-of-sample extension are explained. Thereafter, we introduce the locality preserving projection and its kernel variant as linear special cases of Laplacian eigenmap. Versions of graph embedding are then explained which are generalized versions of Laplacian eigenmap and locality preserving projection. Finally, diffusion map is introduced which is a method based on Laplacian of data and random walks on the data graph.

stat.ML↗

arXiv2022

Restricted Boltzmann Machine and Deep Belief Network: Tutorial and Survey

This is a tutorial and survey paper on Boltzmann Machine (BM), Restricted Boltzmann Machine (RBM), and Deep Belief Network (DBN). We start with the required background on probabilistic graphical models, Markov random field, Gibbs sampling, statistical physics, Ising model, and the Hopfield network. Then, we introduce the structures of BM and RBM. The conditional distributions of visible and hidden variables, Gibbs sampling in RBM for generating variables, training BM and RBM by maximum likelihood estimation, and contrastive divergence are explained. Then, we discuss different possible discrete and continuous distributions for the variables. We introduce conditional RBM and how it is trained. Finally, we explain deep belief network as a stack of RBM models. This paper on Boltzmann machines can be useful in various fields including data science, statistics, neural computation, and statistical physics.

cs.LG↗

arXiv2022

Stochastic Neighbor Embedding with Gaussian and Student-t Distributions: Tutorial and Survey

Stochastic Neighbor Embedding (SNE) is a manifold learning and dimensionality reduction method with a probabilistic approach. In SNE, every point is consider to be the neighbor of all other points with some probability and this probability is tried to be preserved in the embedding space. SNE considers Gaussian distribution for the probability in both the input and embedding spaces. However, t-SNE uses the Student-t and Gaussian distributions in these spaces, respectively. In this tutorial and survey paper, we explain SNE, symmetric SNE, t-SNE (or Cauchy-SNE), and t-SNE with general degrees of freedom. We also cover the out-of-sample extension and acceleration for these methods.

stat.ML↗

arXiv2022

Unified Framework for Spectral Dimensionality Reduction, Maximum Variance Unfolding, and Kernel Learning By Semidefinite Programming: Tutorial and Survey

This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first explain how the spectral dimensionality reduction methods can be unified as kernel Principal Component Analysis (PCA) with different kernels. This unification can be interpreted as eigenfunction learning or representation of kernel in terms of distance matrix. Then, since the spectral methods are unified as kernel PCA, we say let us learn the best kernel for unfolding the manifold of data to its maximum variance. We first briefly introduce kernel learning by SDP for the transduction task. Then, we explain MVU in detail. Various versions of supervised MVU using nearest neighbors graph, by class-wise unfolding, by Fisher criterion, and by colored MVU are explained. We also explain out-of-sample extension of MVU using eigenfunctions and kernel mapping. Finally, we introduce other variants of MVU including action respecting embedding, relaxed MVU, and landmark MVU for big data.

stat.ML↗

arXiv2022

Fisher and Kernel Fisher Discriminant Analysis: Tutorial

This is a detailed tutorial paper which explains the Fisher discriminant Analysis (FDA) and kernel FDA. We start with projection and reconstruction. Then, one- and multi-dimensional FDA subspaces are covered. Scatters in two- and then multi-classes are explained in FDA. Then, we discuss on the rank of the scatters and the dimensionality of the subspace. A real-life example is also provided for interpreting FDA. Then, possible singularity of the scatter is discussed to introduce robust FDA. PCA and FDA directions are also compared. We also prove that FDA and linear discriminant analysis are equivalent. Fisher forest is also introduced as an ensemble of fisher subspaces useful for handling data with different features and dimensionality. Afterwards, kernel FDA is explained for both one- and multi-dimensional subspaces with both two- and multi-classes. Finally, some simulations are performed on AT&T face dataset to illustrate FDA and compare it with PCA.

stat.ML↗

arXiv2022

Factor Analysis, Probabilistic Principal Component Analysis, Variational Inference, and Variational Autoencoder: Tutorial and Survey

This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and generative models. They assume that every data point is generated from or caused by a low-dimensional latent factor. By learning the parameters of distribution of latent space, the corresponding low-dimensional factors are found for the sake of dimensionality reduction. For their stochastic and generative behaviour, these models can also be used for generation of new data points in the data space. In this paper, we first start with variational inference where we derive the Evidence Lower Bound (ELBO) and Expectation Maximization (EM) for learning the parameters. Then, we introduce factor analysis, derive its joint and marginal distributions, and work out its EM steps. Probabilistic PCA is then explained, as a special case of factor analysis, and its closed-form solutions are derived. Finally, VAE is explained where the encoder, decoder and sampling from the latent space are introduced. Training VAE using both EM and backpropagation are explained.

stat.ML↗

arXiv2022

Internet of Behavior (IoB) and Explainable AI Systems for Influencing IoT Behavior

Pandemics and natural disasters over the years have changed the behavior of people, which has had a tremendous impact on all life aspects. With the technologies available in each era, governments, organizations, and companies have used these technologies to track, control, and influence the behavior of individuals for a benefit. Nowadays, the use of the Internet of Things (IoT), cloud computing, and artificial intelligence (AI) have made it easier to track and change the behavior of users through changing IoT behavior. This article introduces and discusses the concept of the Internet of Behavior (IoB) and its integration with Explainable AI (XAI) techniques to provide trusted and evident experience in the process of changing IoT behavior to ultimately improving users' behavior. Therefore, a system based on IoB and XAI has been proposed in a use case scenario of electrical power consumption that aims to influence user consuming behavior to reduce power consumption and cost. The scenario results showed a decrease of 522.2 kW of active power when compared to original consumption over a 200-hours period. It also showed a total power cost saving of 95.04 Euro for the same period. Moreover, decreasing the global active power will reduce the power intensity through the positive correlation.

cs.DC↗

arXiv2022

On Manifold Hypothesis: Hypersurface Submanifold Embedding Using Osculating Hyperspheres

Consider a set of $n$ data points in the Euclidean space $\mathbb{R}^d$. This set is called dataset in machine learning and data science. Manifold hypothesis states that the dataset lies on a low-dimensional submanifold with high probability. All dimensionality reduction and manifold learning methods have the assumption of manifold hypothesis. In this paper, we show that the dataset lies on an embedded hypersurface submanifold which is locally $(d-1)$-dimensional. Hence, we show that the manifold hypothesis holds at least for the embedding dimensionality $d-1$. Using an induction in a pyramid structure, we also extend the embedding dimensionality to lower embedding dimensionalities to show the validity of manifold hypothesis for embedding dimensionalities $\{1, 2, \dots, d-1\}$. For embedding the hypersurface, we first construct the $d$ nearest neighbors graph for data. For every point, we fit an osculating hypersphere $S^{d-1}$ using its neighbors where this hypersphere is osculating to a hypothetical hypersurface. Then, using surgery theory, we apply surgery on the osculating hyperspheres to obtain $n$ hyper-caps. We connect the hyper-caps to one another using partial hyper-cylinders. By connecting all parts, the embedded hypersurface is obtained as the disjoint union of these elements. We discuss the geometrical characteristics of the embedded hypersurface, such as having boundary, its topology, smoothness, boundedness, orientability, compactness, and injectivity. Some discussion are also provided for the linearity and structure of data. This paper is the intersection of several fields of science including machine learning, differential geometry, and algebraic topology.

cs.LG↗

arXiv2022

Human Activity Recognition Using Tools of Convolutional Neural Networks: A State of the Art Review, Data Sets, Challenges and Future Prospects

Human Activity Recognition (HAR) plays a significant role in the everyday life of people because of its ability to learn extensive high-level information about human activity from wearable or stationary devices. A substantial amount of research has been conducted on HAR and numerous approaches based on deep learning and machine learning have been exploited by the research community to classify human activities. The main goal of this review is to summarize recent works based on a wide range of deep neural networks architecture, namely convolutional neural networks (CNNs) for human activity recognition. The reviewed systems are clustered into four categories depending on the use of input devices like multimodal sensing devices, smartphones, radar, and vision devices. This review describes the performances, strengths, weaknesses, and the used hyperparameters of CNN architectures for each reviewed system with an overview of available public data sources. In addition, a discussion with the current challenges to CNN-based HAR systems is presented. Finally, this review is concluded with some potential future directions that would be of great assistance for the researchers who would like to contribute to this field.

eess.SP↗

arXiv2022

UncertaintyFuseNet: Robust Uncertainty-aware Hierarchical Feature Fusion Model with Ensemble Monte Carlo Dropout for COVID-19 Detection

The COVID-19 (Coronavirus disease 2019) pandemic has become a major global threat to human health and well-being. Thus, the development of computer-aided detection (CAD) systems that are capable to accurately distinguish COVID-19 from other diseases using chest computed tomography (CT) and X-ray data is of immediate priority. Such automatic systems are usually based on traditional machine learning or deep learning methods. Differently from most of existing studies, which used either CT scan or X-ray images in COVID-19-case classification, we present a simple but efficient deep learning feature fusion model, called UncertaintyFuseNet, which is able to classify accurately large datasets of both of these types of images. We argue that the uncertainty of the model's predictions should be taken into account in the learning process, even though most of existing studies have overlooked it. We quantify the prediction uncertainty in our feature fusion model using effective Ensemble MC Dropout (EMCD) technique. A comprehensive simulation study has been conducted to compare the results of our new model to the existing approaches, evaluating the performance of competing models in terms of Precision, Recall, F-Measure, Accuracy and ROC curves. The obtained results prove the efficiency of our model which provided the prediction accuracy of 99.08\% and 96.35\% for the considered CT scan and X-ray datasets, respectively. Moreover, our UncertaintyFuseNet model was generally robust to noise and performed well with previously unseen data. The source code of our implementation is freely available at: https://github.com/moloud1987/UncertaintyFuseNet-for-COVID-19-Classification.

eess.IV↗

arXiv2022

Spectral, Probabilistic, and Deep Metric Learning: Tutorial and Survey

This is a tutorial and survey paper on metric learning. Algorithms are divided into spectral, probabilistic, and deep metric learning. We first start with the definition of distance metric, Mahalanobis distance, and generalized Mahalanobis distance. In spectral methods, we start with methods using scatters of data, including the first spectral metric learning, relevant methods to Fisher discriminant analysis, Relevant Component Analysis (RCA), Discriminant Component Analysis (DCA), and the Fisher-HSIC method. Then, large-margin metric learning, imbalanced metric learning, locally linear metric adaptation, and adversarial metric learning are covered. We also explain several kernel spectral methods for metric learning in the feature space. We also introduce geometric metric learning methods on the Riemannian manifolds. In probabilistic methods, we start with collapsing classes in both input and feature spaces and then explain the neighborhood component analysis methods, Bayesian metric learning, information theoretic methods, and empirical risk minimization in metric learning. In deep learning methods, we first introduce reconstruction autoencoders and supervised loss functions for metric learning. Then, Siamese networks and its various loss functions, triplet mining, and triplet sampling are explained. Deep discriminant analysis methods, based on Fisher discriminant analysis, are also reviewed. Finally, we introduce multi-modal deep metric learning, geometric metric learning by neural networks, and few-shot metric learning.

stat.ML↗

arXiv2021

Generative Adversarial Networks and Adversarial Autoencoders: Tutorial and Survey

This is a tutorial and survey paper on Generative Adversarial Network (GAN), adversarial autoencoders, and their variants. We start with explaining adversarial learning and the vanilla GAN. Then, we explain the conditional GAN and DCGAN. The mode collapse problem is introduced and various methods, including minibatch GAN, unrolled GAN, BourGAN, mixture GAN, D2GAN, and Wasserstein GAN, are introduced for resolving this problem. Then, maximum likelihood estimation in GAN are explained along with f-GAN, adversarial variational Bayes, and Bayesian GAN. Then, we cover feature matching in GAN, InfoGAN, GRAN, LSGAN, energy-based GAN, CatGAN, MMD GAN, LapGAN, progressive GAN, triple GAN, LAG, GMAN, AdaGAN, CoGAN, inverse GAN, BiGAN, ALI, SAGAN, Few-shot GAN, SinGAN, and interpolation and evaluation of GAN. Then, we introduce some applications of GAN such as image-to-image translation (including PatchGAN, CycleGAN, DeepFaceDrawing, simulated GAN, interactive GAN), text-to-image translation (including StackGAN), and mixing image characteristics (including FineGAN and MixNMatch). Finally, we explain the autoencoders based on adversarial learning including adversarial autoencoder, PixelGAN, and implicit autoencoder.

cs.LG↗

arXiv2021

Sufficient Dimension Reduction for High-Dimensional Regression and Low-Dimensional Embedding: Tutorial and Survey

This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality reduction. We start with introducing inverse regression methods including Sliced Inverse Regression (SIR), Sliced Average Variance Estimation (SAVE), contour regression, directional regression, Principal Fitted Components (PFC), Likelihood Acquired Direction (LAD), and graphical regression. Then, we introduce forward regression methods including Principal Hessian Directions (pHd), Minimum Average Variance Estimation (MAVE), Conditional Variance Estimation (CVE), and deep SDR methods. Finally, we explain Kernel Dimension Reduction (KDR) both for supervised and unsupervised learning. We also show that supervised KDR and supervised PCA are equivalent.

stat.ME↗

arXiv2021

KKT Conditions, First-Order and Second-Order Optimization, and Distributed Optimization: Tutorial and Survey

This is a tutorial and survey paper on Karush-Kuhn-Tucker (KKT) conditions, first-order and second-order numerical optimization, and distributed optimization. After a brief review of history of optimization, we start with some preliminaries on properties of sets, norms, functions, and concepts of optimization. Then, we introduce the optimization problem, standard optimization problems (including linear programming, quadratic programming, and semidefinite programming), and convex problems. We also introduce some techniques such as eliminating inequality, equality, and set constraints, adding slack variables, and epigraph form. We introduce Lagrangian function, dual variables, KKT conditions (including primal feasibility, dual feasibility, weak and strong duality, complementary slackness, and stationarity condition), and solving optimization by method of Lagrange multipliers. Then, we cover first-order optimization including gradient descent, line-search, convergence of gradient methods, momentum, steepest descent, and backpropagation. Other first-order methods are explained, such as accelerated gradient method, stochastic gradient descent, mini-batch gradient descent, stochastic average gradient, stochastic variance reduced gradient, AdaGrad, RMSProp, and Adam optimizer, proximal methods (including proximal mapping, proximal point algorithm, and proximal gradient method), and constrained gradient methods (including projected gradient method, projection onto convex sets, and Frank-Wolfe method). We also cover non-smooth and $\ell_1$ optimization methods including lasso regularization, convex conjugate, Huber function, soft-thresholding, coordinate descent, and subgradient methods. Then, we explain second-order methods including Newton's method for unconstrained, equality constrained, and inequality constrained problems....

math.OC↗

arXiv2021

Vector Transport Free Riemannian LBFGS for Optimization on Symmetric Positive Definite Matrix Manifolds

This work concentrates on optimization on Riemannian manifolds. The Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm is a commonly used quasi-Newton method for numerical optimization in Euclidean spaces. Riemannian LBFGS (RLBFGS) is an extension of this method to Riemannian manifolds. RLBFGS involves computationally expensive vector transports as well as unfolding recursions using adjoint vector transports. In this article, we propose two mappings in the tangent space using the inverse second root and Cholesky decomposition. These mappings make both vector transport and adjoint vector transport identity and therefore isometric. Identity vector transport makes RLBFGS less computationally expensive and its isometry is also very useful in convergence analysis of RLBFGS. Moreover, under the proposed mappings, the Riemannian metric reduces to Euclidean inner product, which is much less computationally expensive. We focus on the Symmetric Positive Definite (SPD) manifolds which are beneficial in various fields such as data science and statistics. This work opens a research opportunity for extension of the proposed mappings to other well-known manifolds.

math.OC↗