arXiv subjects

Fakhri Karray

Publications and source records attributed to Fakhri Karray.

At least 91 records · Page 5Linked to original sources

arXiv2021

Uniform Manifold Approximation and Projection (UMAP) and its Variants: Tutorial and Survey

Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm where we explain probabilities of neighborhood in the input and embedding spaces, optimization of cost function, training algorithm, derivation of gradients, and supervised and semi-supervised embedding by UMAP. Then, we introduce the theory behind UMAP by algebraic topology and category theory. Then, we introduce UMAP as a neighbor embedding method and compare it with t-SNE and LargeVis algorithms. We discuss negative sampling and repulsive forces in UMAP's cost function. DensMAP is then explained for density-preserving embedding. We then introduce parametric UMAP for embedding by deep learning and progressive UMAP for streaming and out-of-sample data embedding.

cs.HC↗

arXiv2021

Johnson-Lindenstrauss Lemma, Linear and Nonlinear Random Projections, Random Fourier Features, and Random Kitchen Sinks: Tutorial and Survey

This is a tutorial and survey paper on the Johnson-Lindenstrauss (JL) lemma and linear and nonlinear random projections. We start with linear random projection and then justify its correctness by JL lemma and its proof. Then, sparse random projections with $\ell_1$ norm and interpolation norm are introduced. Two main applications of random projection, which are low-rank matrix approximation and approximate nearest neighbor search by random projection onto hypercube, are explained. Random Fourier Features (RFF) and Random Kitchen Sinks (RKS) are explained as methods for nonlinear random projection. Some other methods for nonlinear random projection, including extreme learning machine, randomly weighted neural networks, and ensemble of random projections, are also introduced.

stat.ML↗

arXiv2021

Quantile-Quantile Embedding for Distribution Transformation and Manifold Embedding with Ability to Choose the Embedding Distribution

We propose a new embedding method, named Quantile-Quantile Embedding (QQE), for distribution transformation and manifold embedding with the ability to choose the embedding distribution. QQE, which uses the concept of quantile-quantile plot from visual statistical tests, can transform the distribution of data to any theoretical desired distribution or empirical reference sample. Moreover, QQE gives the user a choice of embedding distribution in embedding the manifold of data into the low dimensional embedding space. It can also be used for modifying the embedding distribution of other dimensionality reduction methods, such as PCA, t-SNE, and deep metric learning, for better representation or visualization of data. We propose QQE in both unsupervised and supervised forms. QQE can also transform a distribution to either an exact reference distribution or its shape. We show that QQE allows for better discrimination of classes in some cases. Our experiments on different synthetic and image datasets show the effectiveness of the proposed embedding method.

stat.ML↗

arXiv2021

Smart Healthcare in the Age of AI: Recent Advances, Challenges, and Future Prospects

The significant increase in the number of individuals with chronic ailments (including the elderly and disabled) has dictated an urgent need for an innovative model for healthcare systems. The evolved model will be more personalized and less reliant on traditional brick-and-mortar healthcare institutions such as hospitals, nursing homes, and long-term healthcare centers. The smart healthcare system is a topic of recently growing interest and has become increasingly required due to major developments in modern technologies, especially in artificial intelligence (AI) and machine learning (ML). This paper is aimed to discuss the current state-of-the-art smart healthcare systems highlighting major areas like wearable and smartphone devices for health monitoring, machine learning for disease diagnosis, and the assistive frameworks, including social robots developed for the ambient assisted living environment. Additionally, the paper demonstrates software integration architectures that are very significant to create smart healthcare systems, integrating seamlessly the benefit of data analytics and other tools of AI. The explained developed systems focus on several facets: the contribution of each developed framework, the detailed working procedure, the performance as outcomes, and the comparative merits and limitations. The current research challenges with potential future directions are addressed to highlight the drawbacks of existing systems and the possible methods to introduce novel frameworks, respectively. This review aims at providing comprehensive insights into the recent developments of smart healthcare systems to equip experts to contribute to the field.

cs.CY↗

arXiv2021

Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nyström Method, and Use of Kernels in Machine Learning: Tutorial and Survey

This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start with reviewing the history of kernels in functional analysis and machine learning. Then, Mercer kernel, Hilbert and Banach spaces, Reproducing Kernel Hilbert Space (RKHS), Mercer's theorem and its proof, frequently used kernels, kernel construction from distance metric, important classes of kernels (including bounded, integrally positive definite, universal, stationary, and characteristic kernels), kernel centering and normalization, and eigenfunctions are explained in detail. Then, we introduce types of use of kernels in machine learning including kernel methods (such as kernel support vector machines), kernel learning by semi-definite programming, Hilbert-Schmidt independence criterion, maximum mean discrepancy, kernel mean embedding, and kernel dimensionality reduction. We also cover rank and factorization of kernel matrix as well as the approximation of eigenfunctions and kernels using the Nystr{ö}m method. This paper can be useful for various fields of science including machine learning, dimensionality reduction, functional analysis in mathematics, and mathematical physics in quantum mechanics.

stat.ML↗

arXiv2021

Generative Locally Linear Embedding

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 propose two novel generative versions of LLE, named Generative LLE (GLLE), whose linear reconstruction steps are stochastic rather than deterministic. GLLE assumes that every data point is caused by its linear reconstruction weights as latent factors. The proposed GLLE algorithms can generate various LLE embeddings stochastically while all the generated embeddings relate to the original LLE embedding. We propose two versions for stochastic linear reconstruction, one using expectation maximization and another with direct sampling from a derived distribution by optimization. The proposed GLLE methods are closely related to and inspired by variational inference, factor analysis, and probabilistic principal component analysis. Our simulations show that the proposed GLLE methods work effectively in unfolding and generating submanifolds of data.

stat.ML↗

arXiv2021

Deep Learning Approaches for Forecasting Strawberry Yields and Prices Using Satellite Images and Station-Based Soil Parameters

Computational tools for forecasting yields and prices for fresh produce have been based on traditional machine learning approaches or time series modelling. We propose here an alternate approach based on deep learning algorithms for forecasting strawberry yields and prices in Santa Barbara county, California. Building the proposed forecasting model comprises three stages: first, the station-based ensemble model (ATT-CNN-LSTM-SeriesNet_Ens) with its compound deep learning components, SeriesNet with Gated Recurrent Unit (GRU) and Convolutional Neural Network LSTM with Attention layer (Att-CNN-LSTM), are trained and tested using the station-based soil temperature and moisture data of SantaBarbara as input and the corresponding strawberry yields or prices as output. Secondly, the remote sensing ensemble model (SIM_CNN-LSTM_Ens), which is an ensemble model of Convolutional NeuralNetwork LSTM (CNN-LSTM) models, is trained and tested using satellite images of the same county as input mapped to the same yields and prices as output. These two ensembles forecast strawberry yields and prices with minimal forecasting errors and highest model correlation for five weeks ahead forecasts.Finally, the forecasts of these two models are ensembled to have a final forecasted value for yields and prices by introducing a voting ensemble. Based on an aggregated performance measure (AGM), it is found that this voting ensemble not only enhances the forecasting performance by 5% compared to its best performing component model but also outperforms the Deep Learning (DL) ensemble model found in literature by 33% for forecasting yields and 21% for forecasting prices

cs.LG↗

arXiv2021

On the Philosophical, Cognitive and Mathematical Foundations of Symbiotic Autonomous Systems (SAS)

Symbiotic Autonomous Systems (SAS) are advanced intelligent and cognitive systems exhibiting autonomous collective intelligence enabled by coherent symbiosis of human-machine interactions in hybrid societies. Basic research in the emerging field of SAS has triggered advanced general AI technologies functioning without human intervention or hybrid symbiotic systems synergizing humans and intelligent machines into coherent cognitive systems. This work presents a theoretical framework of SAS underpinned by the latest advances in intelligence, cognition, computer, and system sciences. SAS are characterized by the composition of autonomous and symbiotic systems that adopt bio-brain-social-inspired and heterogeneously synergized structures and autonomous behaviors. This paper explores their cognitive and mathematical foundations. The challenge to seamless human-machine interactions in a hybrid environment is addressed. SAS-based collective intelligence is explored in order to augment human capability by autonomous machine intelligence towards the next generation of general AI, autonomous computers, and trustworthy mission-critical intelligent systems. Emerging paradigms and engineering applications of SAS are elaborated via an autonomous knowledge learning system that symbiotically works between humans and cognitive robots.

cs.AI↗

arXiv2021

Magnification Generalization for Histopathology Image Embedding

Histopathology image embedding is an active research area in computer vision. Most of the embedding models exclusively concentrate on a specific magnification level. However, a useful task in histopathology embedding is to train an embedding space regardless of the magnification level. Two main approaches for tackling this goal are domain adaptation and domain generalization, where the target magnification levels may or may not be introduced to the model in training, respectively. Although magnification adaptation is a well-studied topic in the literature, this paper, to the best of our knowledge, is the first work on magnification generalization for histopathology image embedding. We use an episodic trainable domain generalization technique for magnification generalization, namely Model Agnostic Learning of Semantic Features (MASF), which works based on the Model Agnostic Meta-Learning (MAML) concept. Our experimental results on a breast cancer histopathology dataset with four different magnification levels show the proposed method's effectiveness for magnification generalization.

eess.IV↗

arXiv2020

Locally Linear Embedding and its Variants: Tutorial and Survey

This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and feature fusion with LLE. Then, we cover out-of-sample embedding using linear reconstruction, eigenfunctions, and kernel mapping. Incremental LLE is explained for embedding streaming data. Landmark LLE methods using the Nystrom approximation and locally linear landmarks are explained for big data embedding. We introduce the methods for parameter selection of number of neighbors using residual variance, Procrustes statistics, preservation neighborhood error, and local neighborhood selection. Afterwards, Supervised LLE (SLLE), enhanced SLLE, SLLE projection, probabilistic SLLE, supervised guided LLE (using Hilbert-Schmidt independence criterion), and semi-supervised LLE are explained for supervised and semi-supervised embedding. Robust LLE methods using least squares problem and penalty functions are also introduced for embedding in the presence of outliers and noise. Then, we introduce fusion of LLE with other manifold learning methods including Isomap (i.e., ISOLLE), principal component analysis, Fisher discriminant analysis, discriminant LLE, and Isotop. Finally, we explain weighted LLE in which the distances, reconstruction weights, or the embeddings are adjusted for better embedding; we cover weighted LLE for deformed distributed data, weighted LLE using probability of occurrence, SLLE by adjusting weights, modified LLE, and iterative LLE.

stat.ML↗

arXiv2020

Sampling Algorithms, from Survey Sampling to Monte Carlo Methods: Tutorial and Literature Review

This paper is a tutorial and literature review on sampling algorithms. We have two main types of sampling in statistics. The first type is survey sampling which draws samples from a set or population. The second type is sampling from probability distribution where we have a probability density or mass function. In this paper, we cover both types of sampling. First, we review some required background on mean squared error, variance, bias, maximum likelihood estimation, Bernoulli, Binomial, and Hypergeometric distributions, the Horvitz-Thompson estimator, and the Markov property. Then, we explain the theory of simple random sampling, bootstrapping, stratified sampling, and cluster sampling. We also briefly introduce multistage sampling, network sampling, and snowball sampling. Afterwards, we switch to sampling from distribution. We explain sampling from cumulative distribution function, Monte Carlo approximation, simple Monte Carlo methods, and Markov Chain Monte Carlo (MCMC) methods. For simple Monte Carlo methods, whose iterations are independent, we cover importance sampling and rejection sampling. For MCMC methods, we cover Metropolis algorithm, Metropolis-Hastings algorithm, Gibbs sampling, and slice sampling. Then, we explain the random walk behaviour of Monte Carlo methods and more efficient Monte Carlo methods, including Hamiltonian (or hybrid) Monte Carlo, Adler's overrelaxation, and ordered overrelaxation. Finally, we summarize the characteristics, pros, and cons of sampling methods compared to each other. This paper can be useful for different fields of statistics, machine learning, reinforcement learning, and computational physics.

stat.ME↗

arXiv2020

Batch-Incremental Triplet Sampling for Training Triplet Networks Using Bayesian Updating Theorem

Variants of Triplet networks are robust entities for learning a discriminative embedding subspace. There exist different triplet mining approaches for selecting the most suitable training triplets. Some of these mining methods rely on the extreme distances between instances, and some others make use of sampling. However, sampling from stochastic distributions of data rather than sampling merely from the existing embedding instances can provide more discriminative information. In this work, we sample triplets from distributions of data rather than from existing instances. We consider a multivariate normal distribution for the embedding of each class. Using Bayesian updating and conjugate priors, we update the distributions of classes dynamically by receiving the new mini-batches of training data. The proposed triplet mining with Bayesian updating can be used with any triplet-based loss function, e.g., triplet-loss or Neighborhood Component Analysis (NCA) loss. Accordingly, Our triplet mining approaches are called Bayesian Updating Triplet (BUT) and Bayesian Updating NCA (BUNCA), depending on which loss function is being used. Experimental results on two public datasets, namely MNIST and histopathology colorectal cancer (CRC), substantiate the effectiveness of the proposed triplet mining method.

stat.ML↗

arXiv2020

Fitting A Mixture Distribution to Data: Tutorial

This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main algorithm. In explaining the main algorithm, first, fitting a mixture of two distributions is detailed and examples of fitting two Gaussians and Poissons, respectively for continuous and discrete cases, are introduced. Thereafter, fitting several distributions in general case is explained and examples of several Gaussians (Gaussian Mixture Model) and Poissons are again provided. Model-based clustering, as one of the applications of mixture distributions, is also introduced. Numerical simulations are also provided for both Gaussian and Poisson examples for the sake of better clarification.

stat.OT↗

arXiv2020

Acceleration of Large Margin Metric Learning for Nearest Neighbor Classification Using Triplet Mining and Stratified Sampling

Metric learning is one of the techniques in manifold learning with the goal of finding a projection subspace for increasing and decreasing the inter- and intra-class variances, respectively. Some of the metric learning methods are based on triplet learning with anchor-positive-negative triplets. Large margin metric learning for nearest neighbor classification is one of the fundamental methods to do this. Recently, Siamese networks have been introduced with the triplet loss. Many triplet mining methods have been developed for Siamese networks; however, these techniques have not been applied on the triplets of large margin metric learning for nearest neighbor classification. In this work, inspired by the mining methods for Siamese networks, we propose several triplet mining techniques for large margin metric learning. Moreover, a hierarchical approach is proposed, for acceleration and scalability of optimization, where triplets are selected by stratified sampling in hierarchical hyper-spheres. We analyze the proposed methods on three publicly available datasets, i.e., Fisher Iris, ORL faces, and MNIST datasets.

cs.LG↗

arXiv2020

Multidimensional Scaling, Sammon Mapping, and Isomap: Tutorial and Survey

Multidimensional Scaling (MDS) is one of the first fundamental manifold learning methods. It can be categorized into several methods, i.e., classical MDS, kernel classical MDS, metric MDS, and non-metric MDS. Sammon mapping and Isomap can be considered as special cases of metric MDS and kernel classical MDS, respectively. In this tutorial and survey paper, we review the theory of MDS, Sammon mapping, and Isomap in detail. We explain all the mentioned categories of MDS. Then, Sammon mapping, Isomap, and kernel Isomap are explained. Out-of-sample embedding for MDS and Isomap using eigenfunctions and kernel mapping are introduced. Then, Nystrom approximation and its use in landmark MDS and landmark Isomap are introduced for big data embedding. We also provide some simulations for illustrating the embedding by these methods.

stat.ML↗

arXiv2020

A Review on Deep Learning Techniques for the Diagnosis of Novel Coronavirus (COVID-19)

Novel coronavirus (COVID-19) outbreak, has raised a calamitous situation all over the world and has become one of the most acute and severe ailments in the past hundred years. The prevalence rate of COVID-19 is rapidly rising every day throughout the globe. Although no vaccines for this pandemic have been discovered yet, deep learning techniques proved themselves to be a powerful tool in the arsenal used by clinicians for the automatic diagnosis of COVID-19. This paper aims to overview the recently developed systems based on deep learning techniques using different medical imaging modalities like Computer Tomography (CT) and X-ray. This review specifically discusses the systems developed for COVID-19 diagnosis using deep learning techniques and provides insights on well-known data sets used to train these networks. It also highlights the data partitioning techniques and various performance measures developed by researchers in this field. A taxonomy is drawn to categorize the recent works for proper insight. Finally, we conclude by addressing the challenges associated with the use of deep learning methods for COVID-19 detection and probable future trends in this research area. This paper is intended to provide experts (medical or otherwise) and technicians with new insights into the ways deep learning techniques are used in this regard and how they potentially further works in combatting the outbreak of COVID-19.

eess.IV↗

arXiv2020

Distributed Nonlinear Model Predictive Control and Metric Learning for Heterogeneous Vehicle Platooning with Cut-in/Cut-out Maneuvers

Vehicle platooning has been shown to be quite fruitful in the transportation industry to enhance fuel economy, road throughput, and driving comfort. Model Predictive Control (MPC) is widely used in literature for platoon control to achieve certain objectives, such as safely reducing the distance among consecutive vehicles while following the leader vehicle. In this paper, we propose a Distributed Nonlinear MPC (DNMPC), based upon an existing approach, to control a heterogeneous dynamic platoon with unidirectional topologies, handling possible cut-in/cut-out maneuvers. The introduced method addresses a collision-free driving experience while tracking the desired speed profile and maintaining a safe desired gap among the vehicles. The time of convergence in the dynamic platooning is derived based on the time of cut-in and/or cut-out maneuvers. In addition, we analyze the improvement level of driving comfort, fuel economy, and absolute and relative convergence of the method by using distributed metric learning and distributed optimization with Alternating Direction Method of Multipliers (ADMM). Simulation results on a dynamic platoon with cut-in and cut-out maneuvers and with different unidirectional topologies show the effectiveness of the introduced method.

math.OC↗

arXiv2020

Roweisposes, Including Eigenposes, Supervised Eigenposes, and Fisherposes, for 3D Action Recognition

Human action recognition is one of the important fields of computer vision and machine learning. Although various methods have been proposed for 3D action recognition, some of which are basic and some use deep learning, the need of basic methods based on generalized eigenvalue problem is sensed for action recognition. This need is especially sensed because of having similar basic methods in the field of face recognition such as eigenfaces and Fisherfaces. In this paper, we propose Roweisposes which uses Roweis discriminant analysis for generalized subspace learning. This method includes Fisherposes, eigenposes, supervised eigenposes, and double supervised eigenposes as its special cases. Roweisposes is a family of infinite number of action recongition methods which learn a discriminative subspace for embedding the body poses. Experiments on the TST, UTKinect, and UCFKinect datasets verify the effectiveness of the proposed method for action recognition.

cs.CV↗