arXiv subjects

Aneesh Panchal

Publications and source records attributed to Aneesh Panchal.

4 recordsLinked to original sources

arXiv2026

Empirical Analysis of Nature-Inspired Algorithms for Autism Spectrum Disorder Detection Using 3D Video Dataset

Autism Spectrum Disorder (ASD) is a chronic neurodevelopmental condition characterized by repetitive behaviors and impairments in social and communication skills. Despite the clear manifestation of these symptoms, many individuals with ASD remain undiagnosed. This paper proposes a methodology for ASD detection using a three-dimensional walking video dataset, leveraging supervised machine learning classification algorithms combined with nature-inspired optimization algorithms for feature extraction. The approach employs supervised classifiers to identify ASD cases, while nature-inspired optimization techniques select the most relevant features, enhanced by the use of ranking coefficients to identify initial leading particles. This strategy significantly reduces computational time, thereby improving efficiency and accuracy. Experimental evaluation with various algorithmic combinations demonstrates an exceptional classification accuracy of 100% in the best case when using the Random Forest classifier coupled with the Gravitational Search Algorithm for feature selection. The methodology's application to additional datasets promises improved robustness and generalizability. With its high accuracy and reduced computational requirements, the proposed framework offers significant contributions to both medical and academic fields, providing a foundation for future advances in ASD diagnosis.

cs.LG↗

arXiv2026

Second-Generation Wavelet-inspired Tensor Product with Applications in Hyperspectral Imaging

This paper introduces the $w$-product, a novel wavelet-based tensor multiplication scheme leveraging second-generation wavelet transforms to achieve linear transformation complexity while preserving essential algebraic properties. The $w$-product outperforms existing tensor multiplication approaches by enabling fast and numerically stable tensor decompositions by proposing ``$w$-svd'' and its sparse variant ``sp-$w$-svd'', for efficient low-rank approximations with significantly reduced computational costs. Experiments on low-rank hyperspectral image reconstruction demonstrate up to a $92.21$ times speedup compared to state-of-the-art ``$t$-svd'', with comparable PSNR and SSIM metrics. We discuss the Moore-Penrose inverse of tensors based on the $w$-product and examine its essential properties. Numerical examples are provided to support the theoretical results. Then, hyperspectral image deblurring experiments demonstrate up to $27.88$ times speedup with improved image quality. In particular, the $w$-product and the sp-$w$-product exhibit exponentially increasing acceleration with the decomposition level compared to the traditional approach of the $t$-product. This work provides a scalable framework for multidimensional data analysis, with future research directions including adaptive wavelet designs, higher-order tensor extensions, and real-time implementations.

math.NA↗

arXiv2025

RGDBEK: Randomized Greedy Double Block Extended Kaczmarz Algorithm with Hybrid Parallel Implementation and Applications

Kaczmarz is one of the most prominent iterative solvers for linear systems of equations. Despite substantial research progress in recent years, the state-of-the-art Kaczmarz algorithms have not fully resolved the seesaw effect, a major impediment to convergence stability. Furthermore, while there have been advances in parallelizing the inherently sequential Kaczmarz method, no existing architecture effectively supports initialization-independent parallelism that fully leverages both CPU and GPU resources. This paper proposes the Randomized Greedy Double Block Extended Kaczmarz (RGDBEK) algorithm, a novel Kaczmarz approach designed for efficient large-scale linear system solutions. RGDBEK employs a randomized selection strategy for column and row blocks based on residual-derived probability distributions, thereby mitigating the traditional seesaw effect and enhancing convergence robustness. Theoretical analysis establishes linear convergence of the method under standard assumptions. Extensive numerical experiments on synthetic random matrices and real-world sparse matrices from the SuiteSparse collection demonstrate that RGDBEK outperforms existing Kaczmarz variants, including GRK, FDBK, FGBK, and GDBEK, in both iteration counts and computational time. In addition, a hybrid parallel CPU-GPU implementation utilizing optimized sparse matrix-vector multiplications via the state-of-the-art storage format improves scalability and performance on large sparse problems. Applications in finite element discretizations, image deblurring, and noisy population modeling demonstrate the algorithm's versatility and effectiveness. Future work will explore extending RGDBEK to tensor systems, optimizing parallel parameter selection, and reducing communication overhead to further enhance efficiency and applicability.

math.NA↗

arXiv2024

Predator Prey Scavenger Model using Holling's Functional Response of Type III and Physics-Informed Deep Neural Networks

Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka-Volterra model which defined the interaction between predator and prey species present in nature. However, predators, scavengers, and prey populations coexist in a natural system where scavengers can additionally rely on the dead bodies of predators present in the system. Keeping this in mind, the formulation and simulation of the predator prey scavenger model is introduced in this paper. For the predation response, respective prey species are assumed to have Holling's functional response of type III. The proposed model is tested for various simulations and is found to be showing satisfactory results in different scenarios. After simulations, the American forest dataset is taken for parameter estimation which imitates the real-world case. For parameter estimation, a physics-informed deep neural network is used with the Adam backpropagation method which prevents the avalanche effect in trainable parameters updation. For neural networks, mean square error and physics-informed informed error are considered. After the neural network, the hence-found parameters are fine-tuned using the Broyden-Fletcher-Goldfarb-Shanno algorithm. Finally, the hence-found parameters using a natural dataset are tested for stability using Jacobian stability analysis. Future research work includes minimization of error induced by parameters, bifurcation analysis, and sensitivity analysis of the parameters.

math.DS↗