Emotion Recognition Using Deep Learning via Facial Expression

Santosh B. Dhekale; S. S. Nikam; D. K. Shedge

doi:https://doi.org/10.54216/JISIoT.180226

Prospects for Applied Mathematics and Data Analysis | 2026

Heat-Semigroup Persistence on Data Graphs: A Multiscale Extension of Normalized Cut for Class-Separability Analysis

Let G = (V,W) be a weighted data graph with symmetric normalized Laplacian L = I−D−1/2WD−1/2, and let u denote the degree-balanced signal associated with a binary partition C∪ ¯C =V. Instead of reducing the partition geometry to the single Rayleigh quotient u⊤Lu/∥u∥22 , we study the heat-semigroup persistence Pu(t) = ∥e−tLu∥22 ∥u∥22 , HT (u) = 1 T Z T 0 Pu(t)dt. Writing Lφj = λjφj and ωj = |⟨u,φj⟩|2/∥u∥22 yields Pu(t) = Σj ωje−2tλj , so the complete curve is the Laplace transform of the label spectral measure νu = Σj ωjδλj . We prove four identities that give this construction a cut-theoretic interpretation. First, Pu is completely monotone. Second, −P′u(0)/2 = Ncut(C, ¯C). Third, for the instantaneous leakage rate κu(t) = −12 d logPu(t)/dt, one has κu(0) = Ncut and κ′u (t) = −2Varνu,t (λ) ≤ 0 under the exponentially tilted spectral measure. Fourth, when u ⊥ kerL, R ∞ 0 Pu(t)dt = u⊤L†u/(2∥u∥22). Hence normalized cut is only the zero-time slope of a multiscale diffusion object whose higher derivatives recover all spectral moments. A perturbation bound |HT (L)−HT (eL)| ≤ T∥L−eL∥2 is also established for a fixed partition signal. Numerical evaluation on a 1,797-sample, 64-variable handwritten-digit benchmark uses all 45 class pairs and ten repeated stratified train/test splits. With graphs formed exclusively from training observations, mean H1 has Spearman correlation −0.924 with held-out pairwise error (95% bootstrap interval [−0.957,−0.850]); normalized cut gives 0.927, and the second spectral central moment gives 0.930. The comparable predictive rankings are material: the proposed functional is not presented as a replacement for normalized cut, but as its multiscale completion, retaining spectral information that a first moment necessarily discards.

groups

Nader Taffach mail -

Mohammad Al-Shiekh mail

link https://doi.org/10.54216/PAMDA.060102

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Pure Mathematics for Theoretical Computer Science | 2026

Comparative Study of Two Optimization Algorithms for Solving Nonlinear Differential Equations: A Performance Analysis

The purpose of this work was to benchmark three population-based metaheuristic optimizers—Particle Swarm Optimization, Differential Evolution, and Grey Wolf Optimizer—when used to solve nonlinear ordinary differential equations within the Neural Network Trial Solution methodology. Problems used for testing were the Riccati initial value problem, the nonlinear pendulum IVP, the Bratu boundary value problem, and the Lane-Emden equation with index five. All problems were implemented such that their boundary/initial conditions were satisfied exactly through analytical construction while their residuals at collocation points were minimized through unconstrained optimization. Thirty Monte Carlo runs of each algorithm were performed with same underlying settings to facilitate statistical comparisons between algorithms. Metrics used for comparisons were mean absolute error (MAE), root mean square error (RMSE), maximum error at any point, and rate of convergence. All significant testing was performed with the Wilcoxon signed-rank test. PSO is shown to consistently provide the smallest mean absolute error across three of the four problems, with an MAE as small as 2.78×10−5 on the Bratu BVP, while GWO was shown to stagnate prematurely when solving boundary value problems.

groups

Qasim Tayyeh mail

link https://doi.org/10.54216/PMTCS.060201

Volume & Issue

Vol. Volume 6 / Iss. Issue 2

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Prospects for Applied Mathematics and Data Analysis | 2025

A Mathematical Framework for Adaptive Rolling Conformal Quantile Boosting under Temporal Distribution Shift: Application to Hour-Ahead PM2.5 Forecast Intervals

Prediction intervals for temporally dependent data require both conditional quantile estimation and a calibration mechanism capable of responding to distribution shift. An adaptive rolling conformal quantile boosting (ARCQB) formulation is developed in which boosted quantile functions provide a nonlinear base interval and a sequential state variable controls the empirical conformal quantile. For target miscoverage 𝛼, the calibration state follows a projected stochastic recurrence, 𝛼𝑡+1 = ΠA{𝛼𝑡 + 𝛾(𝛼 − 𝑒𝑡 )}, where 𝑒𝑡 is the realized miss indicator. A telescoping identity links the time-averaged miss frequency to the state displacement and projection residuals; in the unprojected bounded case, the calibration error is 𝑂(𝑇−1). The interval width admits the exact decomposition 𝑤𝑡 = 𝑤(0) 𝑡 + 2𝑞𝑡 , separating predictive sharpness from conformal inflation. Numerical evaluation uses a strictly chronological one-hour-ahead design on hourly Beijing air-quality measurements. For nominal 90% coverage, raw boosted quantiles attain 83.18%, static conformal calibration 87.40%, and rolling conformal calibration 89.87%. ARCQB attains 90.05% with mean width 47.14 𝜇gm−3 and the lowest interval score, 72.86. Its maximum seasonal coverage deviation is 0.38 percentage points, compared with 7.99 points for the uncalibrated interval. The numerical behavior is therefore consistent with the feedback relation predicted by the calibration dynamics, while high-pollution regimes remain the principal source of conditional under-coverage.

groups

Aiyared Iampan mail -

Said Broumi mail

link https://doi.org/10.54216/PAMDA.050203

Volume & Issue

Vol. Volume 5 / Iss. Issue 2

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Prospects for Applied Mathematics and Data Analysis | 2026

Generating Neutrosophic Random Variables Based on Generalized Gamma Distribution

In practice, we encounter many systems that cannot be studied directly, either due to high costs or because some of these systems are not directly detectable. Therefore, we resort to simulation, which involves applying the study to systems similar to real-world systems and then projecting the results if they are suitable for the real system. The simulation process requires a thorough understanding of probability distributions and the methods used to transform random numbers following a regular distribution on [0,1] into random variables that follow it. This allows us to maximize the benefits of the simulation process and obtain more accurate results for all emerging conditions. The generalized gamma distribution is a family of three parameters characterized by high flexibility. It includes several important distributions as special cases, including the gamma, Weibull, exponential, and Rayleigh distributions, making it exceptionally valuable in engineering and reliability analysis. In previous research, we presented a neutrosophic view of the process of generating random numbers and some techniques used to generate random variables. In this research, we present a neutrosophic study for generating neutrosophic random variables following the generalized gamma distribution, a distribution widely used in engineering applications. The neutrosophic approach takes into account the uncertainty and indeterminacy of the parameters, resulting in random intervals for the variables rather than specific values, and thus provides more accurate simulation results that adapt to all the conditions that the system in operation may encounter.

groups

Khalifa AlShaqsi mail

link https://doi.org/10.54216/PAMDA.060104

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

Details open_in_new

Prospects for Applied Mathematics and Data Analysis | 2026

Exact Bias–Variance Decomposition and Degrees of Freedom in Ridge Regression: Theory, Verification, and a Disease-Progression Application

Ridge regression estimates β in the linear model y = Xβ +ε by βˆ (λ) = argminβ ∥y−Xβ∥2+λ∥β∥2, trading bias for variance as λ increases. This paper collects six results about βˆ (λ) into a single self-contained development, each proved and then checked numerically. The estimator is written in closed form through the singular value decomposition of X; its effective degrees of freedom, df(λ)=Σj d2j /(d2j +λ), are shown to be strictly decreasing and convex in λ; its exact bias and variance are derived in closed form; a strictly positive λ is shown always to exist that reduces mean squared estimation error below that of ordinary least squares whenever the noise variance is positive; the estimator is shown to coincide with the posterior mean under a Gaussian prior with precision proportional to λ; and the leave-one-out cross-validation error is shown to admit a closed-form shortcut that generalized cross-validation approximates by averaging its leverage terms. Every derived quantity is verified against data: the leave-one-out shortcut matches brute-force refitting exactly, and a calibrated Monte Carlo simulation confirms the closed-form bias and variance to within simulation error at every tested λ. Applied to a standard diabetes disease-progression dataset (n = 442, ten predictors), the theoretical construction correctly locates a strictly risk-reducing regularization region, and repeated cross-validation shows ridge, lasso, and elastic net all lying within one standard error of ordinary least squares in out-of-sample prediction error—consistent with the closed-form theory, which attributes the available gain to reduced parameter-estimation risk on a well-conditioned design rather than to prediction-error reduction.

groups

Dwi Retnowardani mail

link https://doi.org/10.54216/PAMDA.060105

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Journal of Neutrosophic and Fuzzy Systems | 2026

Neutrosophic–Fuzzy Evidence Fusion for Uncertainty-Aware Cultivar Identification from Viticultural Chemical Profiles

Cultivar identification from viticultural chemical profiles is a multiclass recognition problem in which a hard label alone does not reveal whether global chemometric evidence agrees with the local structure of previously observed samples. This paper proposes Neutrosophic–Fuzzy Viticultural Evidence Fusion (NFVEF), an uncertainty-aware classifier that combines a global discriminant probability vector G(x) ∈ ΔK−1 with a Gaussian fuzzy-neighborhood vector L(x) ∈ ΔK−1. For every cultivar k, the two evidence views are converted into Tk = p GkLk, Fk = p (1−Gk)(1−Lk), Ik = 1−Tk −Fk. where Ik is exactly the squared Hellinger disagreement between the Bernoulli support views Gk and Lk. A logarithmic fuzzy opinion pool Hk ∝ Gηk L1−η k is then attenuated by neutrosophic disagreement, Rk ∝ Hk exp(−κIk), before classification. The winning class is accompanied by an uncertainty score U = 1−Tˆk (1−Iˆk)(1−Fˆk ), enabling uncertain chemical profiles to be flagged rather than reported with unqualified confidence. The method is evaluated on the UCI Wine cultivar dataset using 60 repeated stratified splits at four synthetic analytical-perturbation levels δ ∈ {0,0.1,0.2,0.3} measured relative to training-feature standard deviations. NFVEF obtains mean accuracies of 0.9858, 0.9836, 0.9744, and 0.9728, respectively. At δ = 0.3, its paired accuracy advantage over linear discriminant analysis is 0.00278 with a 95% bootstrap interval [0.00123,0.00463], while RBF-SVM remains slightly better in raw accuracy. The uncertainty score detects NFVEF errors with mean AUC 0.9520 at the strongest perturbation, and retaining the lowest-uncertainty 90% of cases yields 0.9922 accuracy. The contribution is therefore not universal classifier dominance, but a mathematically interpretable fuzzy–neutrosophic evidence layer for cultivar identification from ambiguous chemical measurements.

groups

Amine Saddik mail -

Ika Agustin mail

link https://doi.org/10.54216/JNFS.110101

Volume & Issue

Vol. Volume 11 / Iss. Issue 1

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International Journal of Neutrosophic Science | 2026

On Division of Symbolic n-Plithogenic Numbers

The main goal of this article is to study the division of symbolic n-plithogenic numbers using the identification method and n-plithogenic AH-isometry. In particular, we discuss the division of symbolic 2-plithogenic numbers and 3-plithogenic numbers, and we generalize these divisions. Additionally, we prove the validity of the formulas using AH-isometry and provide four worked examples to enhance understanding.

groups

P. Arulpandy mail -

S. Kalaiselvan mail -

M. Sundar mail -

G. Govindharaj mail -

P. Sugapriya mail

link https://doi.org/10.54216/IJNS.270228

Volume & Issue

Vol. Volume 27 / Iss. Issue 2

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Fusion: Practice and Applications | 2026

Optimizing Navigation: Adaptive Map Reshaping and Shortest Path Analysis for Mobile Robots

To facilitate the practical deployment of robotics, efficient path planning is essential to ensure that robotic movement is accurate, safe, and goal-oriented. This study explores new approaches to map adaptation and path optimization for robot navigation between specified locations. The initial phase of the research involves designing an environment that enables the safe operation of robots. Subsequently, the collected data is processed to construct a graph using Dijkstra’s algorithm, which is employed to determine the shortest path between key points. When multiple paths are available, the algorithm selects the most efficient one, while ensuring safety in point-to-point transitions and when navigating around obstacles. In addition to this, a reinforced method is introduced to enhance the security of path planning. This approach expands the original trajectory to incorporate a safety buffer equal to half of the robot’s safety radius, thus maintaining a safe distance along the traveled route. The key contribution of this work lies in the development of novel maps featuring secure pathways, which can be utilized by optimization algorithms to improve navigation in unfamiliar terrains. Experimental results using PRM* and RRT* validate the accuracy of these maps, especially in complex, maze-like environments.

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Mohammed Rabeea Hashim Al-Dahhan mail -

Mahmood Abdulrazzaq Alsaadi mail -

Ruqayah R. Al-Dahhan mail -

Salah A. Aliesawi mail -

Omar Q. Mohsin mail

link https://doi.org/10.54216/FPA.210213

Volume & Issue

Vol. Volume 21 / Iss. Issue 2

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Journal of Intelligent Systems and Internet of Things | 2026

Deep Neural Network Graph with Reinforcement Learning for Test Case Prioritization

Recently, Deep learning (DL) models are increasingly used in Test Case Prioritization (TCP) tasks combining partial and imperfect test case (TC) information into accurate prediction models. Various DL algorithms have been created to improve TC failure prediction and prioritization in CI settings. Among them, Deep Reinforcement Prioritizer (DeepRP) model is developed using Deep Reinforcement Learning (DRL) and Deep Neural Network (DNN) for efficient TCP on huge test suites. But, the model's labelling task is interrupted early, creating difficulty in learning TC features for unlabeled training TCs due to limited resources. To solve this, Deep Graph Reinforcement Prioritizer (DeepGRP) is proposed in this paper to learn the TC features from unlabeled training data for efficient TCP in Regression Testing (RT). In this method, graph neuron stimulation attributes for TCs are created to retrieve the activation graph across DNN layers of DeepRP. The connectivity neuron link defines the activation graph. The proposed deep graph (DG) recognizes the DNN neurons as nodes and the adjacency matrix as the connectivity link among the nodes. Also, the message passing mechanism is applied to aggregate the structural information from the adjacency matrix with neighbouring node features to enhance TCP. By applying this mechanism, DeepGRP captures the high-order dependencies among neurons for efficient activation features which overcomes the traditional activation models and improves the TCP at large scale RT.  The DG model prioritizes TCs using Learning-to-Rank (L2R) which learns node attributes from TCs. This enables for better DNN testing efficiency by detecting vulnerabilities early and lower development time for efficient TCP and tackling the difficulty of learning TC characteristics for efficient TCP. Finally, the testing findings suggest that the DeepRP can improve the TCP for large TSs when compared to other common algorithms.

groups

Shankar Ramakrishnan mail -

E. K. Girisan mail

link https://doi.org/10.54216/JISIoT.180225

Volume & Issue

Vol. Volume 18 / Iss. Issue 2

Details open_in_new

Journal of Intelligent Systems and Internet of Things | 2026

Emotion Recognition Using Deep Learning via Facial Expression

Human-computer interaction (HCI), artificial intelligence (AI), and HI are in high demand these days. In fields like marketing, client feedback analysis, security, and healthcare, facial expression- grounded emotion recognition becomes a pivotal tool for comprehending mortal feelings. Facial expressions like fear, disgust, surprise, anger, sadness, and happiness are pivotal pointers of emotional countries. Businesses can ameliorate client gests by relating these pointers and measuring client satisfaction with goods or services. The discovery of mortal feelings has been achieved with machine literacy algorithms like support vector machines and arbitrary timbers. The effectiveness of deep literacy models for emotion discovery has been validated by earlier studies that employed Convolutional Neural Networks (CNNs) to reliably classify feelings grounded on facial expressions. Likewise, recent developments in deep literacy, particularly the operation of Convolutional Neural Networks (CNNs), have significantly increased the delicacy of facial emotion recognition and interpretation from images and live camera aqueducts. In order to reuse face images with CNN models for real- time emotion recognition, our exploration attempts to produce an emotion recognition system using Python and OpenCV. The current study describes how to watch live videotape aqueducts for facial expressions to identify which of the seven linked feelings is most likely to do. This system provides emotional behavior in real time when needed.

groups

Santosh B. Dhekale mail -

S. S. Nikam mail -

D. K. Shedge mail

link https://doi.org/10.54216/JISIoT.180226

Volume & Issue

Vol. Volume 18 / Iss. Issue 2

Details open_in_new