14.7AIAug 21, 2024
Advances in Preference-based Reinforcement Learning: A ReviewYoussef Abdelkareem, Shady Shehata, Fakhri Karray
Reinforcement Learning (RL) algorithms suffer from the dependency on accurately engineered reward functions to properly guide the learning agents to do the required tasks. Preference-based reinforcement learning (PbRL) addresses that by utilizing human preferences as feedback from the experts instead of numeric rewards. Due to its promising advantage over traditional RL, PbRL has gained more focus in recent years with many significant advances. In this survey, we present a unified PbRL framework to include the newly emerging approaches that improve the scalability and efficiency of PbRL. In addition, we give a detailed overview of the theoretical guarantees and benchmarking work done in the field, while presenting its recent applications in complex real-world tasks. Lastly, we go over the limitations of the current approaches and the proposed future research directions.
3.7CVJul 9, 2024
AstroSpy: On detecting Fake Images in Astronomy via Joint Image-Spectral RepresentationsMohammed Talha Alam, Raza Imam, Mohsen Guizani et al.
The prevalence of AI-generated imagery has raised concerns about the authenticity of astronomical images, especially with advanced text-to-image models like Stable Diffusion producing highly realistic synthetic samples. Existing detection methods, primarily based on convolutional neural networks (CNNs) or spectral analysis, have limitations when used independently. We present AstroSpy, a hybrid model that integrates both spectral and image features to distinguish real from synthetic astronomical images. Trained on a unique dataset of real NASA images and AI-generated fakes (approximately 18k samples), AstroSpy utilizes a dual-pathway architecture to fuse spatial and spectral information. This approach enables AstroSpy to achieve superior performance in identifying authentic astronomical images. Extensive evaluations demonstrate AstroSpy's effectiveness and robustness, significantly outperforming baseline models in both in-domain and cross-domain tasks, highlighting its potential to combat misinformation in astronomy.
FLARE up your data: Diffusion-based Augmentation Method in Astronomical ImagingMohammed Talha Alam, Raza Imam, Mohsen Guizani et al.
The intersection of Astronomy and AI encounters significant challenges related to issues such as noisy backgrounds, lower resolution (LR), and the intricate process of filtering and archiving images from advanced telescopes like the James Webb. Given the dispersion of raw images in feature space, we have proposed a \textit{two-stage augmentation framework} entitled as \textbf{FLARE} based on \underline{f}eature \underline{l}earning and \underline{a}ugmented \underline{r}esolution \underline{e}nhancement. We first apply lower (LR) to higher resolution (HR) conversion followed by standard augmentations. Secondly, we integrate a diffusion approach to synthetically generate samples using class-concatenated prompts. By merging these two stages using weighted percentiles, we realign the feature space distribution, enabling a classification model to establish a distinct decision boundary and achieve superior generalization on various in-domain and out-of-domain tasks. We conducted experiments on several downstream cosmos datasets and on our optimally distributed \textbf{SpaceNet} dataset across 8-class fine-grained and 4-class macro classification tasks. FLARE attains the highest performance gain of 20.78\% for fine-grained tasks compared to similar baselines, while across different classification models, FLARE shows a consistent increment of an average of +15\%. This outcome underscores the effectiveness of the FLARE method in enhancing the precision of image classification, ultimately bolstering the reliability of astronomical research outcomes. % Our code and SpaceNet dataset will be released to the public soon. Our code and SpaceNet dataset is available at \href{https://github.com/Razaimam45/PlanetX_Dxb}{\textit{https://github.com/Razaimam45/PlanetX\_Dxb}}.
FusionEnsemble-Net: An Attention-Based Ensemble of Spatiotemporal Networks for Multimodal Sign Language RecognitionMd. Milon Islam, Md Rezwanul Haque, S M Taslim Uddin Raju et al.
Accurate recognition of sign language in healthcare communication poses a significant challenge, requiring frameworks that can accurately interpret complex multimodal gestures. To deal with this, we propose FusionEnsemble-Net, a novel attention-based ensemble of spatiotemporal networks that dynamically fuses visual and motion data to enhance recognition accuracy. The proposed approach processes RGB video and range Doppler map radar modalities synchronously through four different spatiotemporal networks. For each network, features from both modalities are continuously fused using an attention-based fusion module before being fed into an ensemble of classifiers. Finally, the outputs of these four different fused channels are combined in an ensemble classification head, thereby enhancing the model's robustness. Experiments demonstrate that FusionEnsemble-Net outperforms state-of-the-art approaches with a test accuracy of 99.44% on the large-scale MultiMeDaLIS dataset for Italian Sign Language. Our findings indicate that an ensemble of diverse spatiotemporal networks, unified by attention-based fusion, yields a robust and accurate framework for complex, multimodal isolated gesture recognition tasks. The source code is available at: https://github.com/rezwanh001/Multimodal-Isolated-Italian-Sign-Language-Recognition.
MDD-Net: Multimodal Depression Detection through Mutual TransformerMd Rezwanul Haque, Md. Milon Islam, S M Taslim Uddin Raju et al.
Depression is a major mental health condition that severely impacts the emotional and physical well-being of individuals. The simple nature of data collection from social media platforms has attracted significant interest in properly utilizing this information for mental health research. A Multimodal Depression Detection Network (MDD-Net), utilizing acoustic and visual data obtained from social media networks, is proposed in this work where mutual transformers are exploited to efficiently extract and fuse multimodal features for efficient depression detection. The MDD-Net consists of four core modules: an acoustic feature extraction module for retrieving relevant acoustic attributes, a visual feature extraction module for extracting significant high-level patterns, a mutual transformer for computing the correlations among the generated features and fusing these features from multiple modalities, and a detection layer for detecting depression using the fused feature representations. The extensive experiments are performed using the multimodal D-Vlog dataset, and the findings reveal that the developed multimodal depression detection network surpasses the state-of-the-art by up to 17.37% for F1-Score, demonstrating the greater performance of the proposed system. The source code is accessible at https://github.com/rezwanh001/Multimodal-Depression-Detection.
MMFformer: Multimodal Fusion Transformer Network for Depression DetectionMd Rezwanul Haque, Md. Milon Islam, S M Taslim Uddin Raju et al.
Depression is a serious mental health illness that significantly affects an individual's well-being and quality of life, making early detection crucial for adequate care and treatment. Detecting depression is often difficult, as it is based primarily on subjective evaluations during clinical interviews. Hence, the early diagnosis of depression, thanks to the content of social networks, has become a prominent research area. The extensive and diverse nature of user-generated information poses a significant challenge, limiting the accurate extraction of relevant temporal information and the effective fusion of data across multiple modalities. This paper introduces MMFformer, a multimodal depression detection network designed to retrieve depressive spatio-temporal high-level patterns from multimodal social media information. The transformer network with residual connections captures spatial features from videos, and a transformer encoder is exploited to design important temporal dynamics in audio. Moreover, the fusion architecture fused the extracted features through late and intermediate fusion strategies to find out the most relevant intermodal correlations among them. Finally, the proposed network is assessed on two large-scale depression detection datasets, and the results clearly reveal that it surpasses existing state-of-the-art approaches, improving the F1-Score by 13.92% for D-Vlog dataset and 7.74% for LMVD dataset. The code is made available publicly at https://github.com/rezwanh001/Large-Scale-Multimodal-Depression-Detection.
9.6CVDec 4, 2024
UrbanGS: Semantic-Guided Gaussian Splatting for Urban Scene ReconstructionZiwen Li, Jiaxin Huang, Runnan Chen et al.
Reconstructing urban scenes is challenging due to their complex geometries and the presence of potentially dynamic objects. 3D Gaussian Splatting (3DGS)-based methods have shown strong performance, but existing approaches often incorporate manual 3D annotations to improve dynamic object modeling, which is impractical due to high labeling costs. Some methods leverage 4D Gaussian Splatting (4DGS) to represent the entire scene, but they treat static and dynamic objects uniformly, leading to unnecessary updates for static elements and ultimately degrading reconstruction quality. To address these issues, we propose UrbanGS, which leverages 2D semantic maps and an existing dynamic Gaussian approach to distinguish static objects from the scene, enabling separate processing of definite static and potentially dynamic elements. Specifically, for definite static regions, we enforce global consistency to prevent unintended changes in dynamic Gaussian and introduce a K-nearest neighbor (KNN)-based regularization to improve local coherence on low-textured ground surfaces. Notably, for potentially dynamic objects, we aggregate temporal information using learnable time embeddings, allowing each Gaussian to model deformations over time. Extensive experiments on real-world datasets demonstrate that our approach outperforms state-of-the-art methods in reconstruction quality and efficiency, accurately preserving static content while capturing dynamic elements.
6.7CLOct 24, 2025
Vision Language Models for Dynamic Human Activity Recognition in Healthcare SettingsAbderrazek Abid, Thanh-Cong Ho, Fakhri Karray
As generative AI continues to evolve, Vision Language Models (VLMs) have emerged as promising tools in various healthcare applications. One area that remains relatively underexplored is their use in human activity recognition (HAR) for remote health monitoring. VLMs offer notable strengths, including greater flexibility and the ability to overcome some of the constraints of traditional deep learning models. However, a key challenge in applying VLMs to HAR lies in the difficulty of evaluating their dynamic and often non-deterministic outputs. To address this gap, we introduce a descriptive caption data set and propose comprehensive evaluation methods to evaluate VLMs in HAR. Through comparative experiments with state-of-the-art deep learning models, our findings demonstrate that VLMs achieve comparable performance and, in some cases, even surpass conventional approaches in terms of accuracy. This work contributes a strong benchmark and opens new possibilities for the integration of VLMs into intelligent healthcare systems.
13.0LGMay 30, 2023
Clip21: Error Feedback for Gradient ClippingSarit Khirirat, Eduard Gorbunov, Samuel Horváth et al.
Motivated by the increasing popularity and importance of large-scale training under differential privacy (DP) constraints, we study distributed gradient methods with gradient clipping, i.e., clipping applied to the gradients computed from local information at the nodes. While gradient clipping is an essential tool for injecting formal DP guarantees into gradient-based methods [1], it also induces bias which causes serious convergence issues specific to the distributed setting. Inspired by recent progress in the error-feedback literature which is focused on taming the bias/error introduced by communication compression operators such as Top-$k$ [2], and mathematical similarities between the clipping operator and contractive compression operators, we design Clip21 -- the first provably effective and practically useful error feedback mechanism for distributed methods with gradient clipping. We prove that our method converges at the same $\mathcal{O}\left(\frac{1}{K}\right)$ rate as distributed gradient descent in the smooth nonconvex regime, which improves the previous best $\mathcal{O}\left(\frac{1}{\sqrt{K}}\right)$ rate which was obtained under significantly stronger assumptions. Our method converges significantly faster in practice than competing methods.
3.3MEOct 18, 2021
Sufficient Dimension Reduction for High-Dimensional Regression and Low-Dimensional Embedding: Tutorial and SurveyBenyamin Ghojogh, Ali Ghodsi, Fakhri Karray et al.
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.
17.7OCOct 5, 2021
KKT Conditions, First-Order and Second-Order Optimization, and Distributed Optimization: Tutorial and SurveyBenyamin Ghojogh, Ali Ghodsi, Fakhri Karray et al.
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....
Vector Transport Free Riemannian LBFGS for Optimization on Symmetric Positive Definite Matrix ManifoldsReza Godaz, Benyamin Ghojogh, Reshad Hosseini et al.
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.
21.4HCAug 25, 2021
Uniform Manifold Approximation and Projection (UMAP) and its Variants: Tutorial and SurveyBenyamin Ghojogh, Ali Ghodsi, Fakhri Karray et al.
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.
5.1CYJun 24, 2021
Smart Healthcare in the Age of AI: Recent Advances, Challenges, and Future ProspectsMahmoud Nasr, MD. Milon Islam, Shady Shehata et al.
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.
9.7MENov 2, 2020
Sampling Algorithms, from Survey Sampling to Monte Carlo Methods: Tutorial and Literature ReviewBenyamin Ghojogh, Hadi Nekoei, Aydin Ghojogh et al.
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.
17.4IVAug 9, 2020
A Review on Deep Learning Techniques for the Diagnosis of Novel Coronavirus (COVID-19)Md. Milon Islam, Fakhri Karray, Reda Alhajj et al.
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.
Batch-Incremental Triplet Sampling for Training Triplet Networks Using Bayesian Updating TheoremMilad Sikaroudi, Benyamin Ghojogh, Fakhri Karray et al.
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.
Roweisposes, Including Eigenposes, Supervised Eigenposes, and Fisherposes, for 3D Action RecognitionBenyamin Ghojogh, Fakhri Karray, Mark Crowley
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.
Quantized Fisher Discriminant AnalysisBenyamin Ghojogh, Ali Saheb Pasand, Fakhri Karray et al.
This paper proposes a new subspace learning method, named Quantized Fisher Discriminant Analysis (QFDA), which makes use of both machine learning and information theory. There is a lack of literature for combination of machine learning and information theory and this paper tries to tackle this gap. QFDA finds a subspace which discriminates the uniformly quantized images in the Discrete Cosine Transform (DCT) domain at least as well as discrimination of non-quantized images by Fisher Discriminant Analysis (FDA) while the images have been compressed. This helps the user to throw away the original images and keep the compressed images instead without noticeable loss of classification accuracy. We propose a cost function whose minimization can be interpreted as rate-distortion optimization in information theory. We also propose quantized Fisherfaces for facial analysis in QFDA. Our experiments on AT&T face dataset and Fashion MNIST dataset show the effectiveness of this subspace learning method.
Fisher and Kernel Fisher Discriminant Analysis: TutorialBenyamin Ghojogh, Fakhri Karray, Mark Crowley
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.
Eigenvalue and Generalized Eigenvalue Problems: TutorialBenyamin Ghojogh, Fakhri Karray, Mark Crowley
This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also provide examples from machine learning, including principal component analysis, kernel supervised principal component analysis, and Fisher discriminant analysis, which result in eigenvalue and generalized eigenvalue problems. Finally, we introduce the solutions to both eigenvalue and generalized eigenvalue problems.
Fitting A Mixture Distribution to Data: TutorialBenyamin Ghojogh, Aydin Ghojogh, Mark Crowley et al.
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.