Support Vector Machines

Urban air quality forecasting is challenging because pollutant concentrations are nonlinear, nonstationary, spatiotemporally dependent, and often affected by anomalous observations caused by traffic congestion, industrial emissions, and seasonal meteorological variability. This study proposes a Graph Convolutional Support Vector Regression (GraphSVR) framework for robust spatiotemporal forecasting of urban air pollution. The model combines graph convolutional learning to capture inter-station spatial dependence with support vector regression to model nonlinear temporal dynamics while reducing sensitivity to outlier observations. The proposed framework is evaluated using air quality records from 37 monitoring stations in Delhi and 18 stations in Mumbai, representing inland and coastal metropolitan environments in India. Forecasting performance is assessed across multiple horizons and compared with established temporal and spatiotemporal benchmarks. The results show that GraphSVR consistently improves predictive accuracy and maintains stable performance across seasons and outlier-prone pollution episodes. Statistical test further confirms the reliability of the proposed approach across the datasets. Furthermore, the conformal prediction approach is integrated with GraphSVR to generate calibrated prediction intervals, enhancing its practical value for uncertainty-aware air quality monitoring and public health decision-making.

The rapid growth of electronic communication has necessitated more robust systems for email classification and sentiment detection. This study presents a comparative performance analysis between traditional machine learning algorithms and deep learning architectures, specifically focusing on Support Vector Machines (SVMs), Logistic Regression, Naive Bayes, and Long Short-Term Memory (LSTM). Utilizing Word2Vec embeddings for feature representation, our experimental results indicate that the SVM model with a linear kernel achieves the highest efficiency and accuracy, reaching a peak performance of 98.74%. While the LSTM model demonstrates exceptional recall capabilities in detecting spam-related sentiments, it requires significantly more computational time compared to discriminative statistical models. Detailed evaluations via confusion matrices further reveal that traditional classifiers remain highly robust for dense vector spaces. This research concludes that for email detection tasks, SVM offers the most optimal balance between predictive precision and processing speed. These findings provide critical insights for developing high-performance automated email filtering systems in professional and academic environments.

Support vector machines (SVMs) are a standard tool for binary classification, but their classical formulations are purely data-driven and offer no direct way to encode trusted benchmark models or structured preferences on selected subsets of the data. We propose Elite-Driven Support Vector Machines (EDSVM), a general framework that augments regularized empirical risk minimization by guiding the slack variables for a curated set of elite observations (typically the union of support vectors from one or more reference SVMs). EDSVM combines the usual slack loss with a deviation penalty that shrinks new slacks toward benchmark slack values, defining a localized, margin-aligned notion of proximity to reference models, unlike global function penalties in knowledge distillation or teacher-student methods, and without requiring privileged features as in SVM+/LUPI. Within this framework we develop two concrete models, C-EDSVM and LS-EDSVM, based respectively on hinge-type and squared-slack losses. For both variants we derive dual quadratic programs that can be implemented with modest modifications of standard SVM solvers, and we give simple sufficient conditions under which the induced margin losses are classification calibrated. Simulation studies and experiments on several UCI benchmarks show that EDSVMs closely track the behaviour induced by reference SVMs while achieving predictive performance that is competitive with, and sometimes better than, C-SVM, LINEX-SVM, and LS-SVM.

Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive empirical study of quantum kernel support vector machines (QSVMs) across nine binary classification datasets, four quantum feature maps, three classical kernels, and multiple noise models, totalling 970 experiments with strict nested cross-validation. Our analysis spans four phases: (i) statistical significance testing, revealing that none of 29 pairwise quantum-classical comparisons reach significance at $α= 0.05$; (ii) learning curve analysis over six training fractions, showing steeper quantum slopes on six of eight datasets that nonetheless fail to close the gap to the best classical baseline; (iii) hardware validation on IBM ibm_fez (Heron r2), demonstrating kernel fidelity $r \geq 0.976$ across six experiments; and (iv) seed sensitivity analysis confirming reproducibility (mean CV 1.4%). A Kruskal-Wallis factorial analysis reveals that dataset choice dominates performance variance ($\varepsilon^2 = 0.73$), while kernel type accounts for only 9%. Spectral analysis offers a mechanistic explanation: current quantum feature maps produce eigenspectra that are either too flat or too concentrated, missing the intermediate profile of the best classical kernel, the radial basis function (RBF). Quantum kernel training (QKT) via kernel-target alignment yields the single competitive result -- balanced accuracy 0.968 on breast cancer -- but with ~2,000x computational overhead. Our findings provide actionable guidelines for quantum kernel research. The complete benchmark suite is publicly available to facilitate reproduction and extension.

We study post-training interpretability for Support Vector Machines (SVMs) built from truncated orthogonal polynomial kernels. Since the associated reproducing kernel Hilbert space is finite-dimensional and admits an explicit tensor-product orthonormal basis, the fitted decision function can be expanded exactly in intrinsic RKHS coordinates. This leads to Orthogonal Representation Contribution Analysis (ORCA), a diagnostic framework based on normalized Orthogonal Kernel Contribution (OKC) indices. These indices quantify how the squared RKHS norm of the classifier is distributed across interaction orders, total polynomial degrees, marginal coordinate effects, and pairwise contributions. The methodology is fully post-training and requires neither surrogate models nor retraining. We illustrate its diagnostic value on a synthetic double-spiral problem and on a real five-dimensional echocardiogram dataset. The results show that the proposed indices reveal structural aspects of model complexity that are not captured by predictive accuracy alone.

Existing support vector machines(SVM) models are sensitive to noise and lack sparsity, which limits their performance. To address these issues, we combine the elastic net loss with a robust loss framework to construct a sparse $\varepsilon$-insensitive bounded asymmetric elastic net loss, and integrate it with SVM to build $\varepsilon$ Insensitive Zone Bounded Asymmetric Elastic Net Loss-based SVM($\varepsilon$-BAEN-SVM). $\varepsilon$-BAEN-SVM is both sparse and robust. Sparsity is proven by showing that samples inside the $\varepsilon$-insensitive band are not support vectors. Robustness is theoretically guaranteed because the influence function is bounded. To solve the non-convex optimization problem, we design a half-quadratic algorithm based on clipping dual coordinate descent. It transforms the problem into a series of weighted subproblems, improving computational efficiency via the $\varepsilon$ parameter. Experiments on simulated and real datasets show that $\varepsilon$-BAEN-SVM outperforms traditional and existing robust SVMs. It balances sparsity and robustness well in noisy environments. Statistical tests confirm its superiority. Under the Gaussian kernel, it achieves better accuracy and noise insensitivity, validating its effectiveness and practical value.

Robust Support Vector Machines (R-SVMs) address feature noise by adopting a worst-case robust formulation that explicitly incorporates uncertainty sets into training. While this robustness improves reliability, it also leads to increased computational cost. In this work, we develop safe sample screening rules for R-SVMs that reduce the training complexity without affecting the optimal solution. To the best of our knowledge, this is the first study to apply safe screening techniques to worst-case robust models in supervised machine learning. Our approach safely identifies training samples whose uncertainty sets are guaranteed to lie entirely on either side of the margin hyperplane, thereby reducing the problem size and accelerating optimization. Owing to the nonstandard structure of R-SVMs, the proposed screening rules are derived from the Lagrangian duality rather than the Fenchel-Rockafellar duality commonly used in recent methods. Based on this analysis, we first establish an ideal screening rule, and then derive a practical rule by adapting GAP-based safe regions to the robust setting. Experiments demonstrate that the proposed method significantly reduces training time while preserving classification accuracy.

Support Vector Machines (SVMs) rely heavily on the choice of the kernel function to map data into high-dimensional feature spaces. While the Gaussian Radial Basis Function (RBF) is the industry standard, its exponential decay makes it highly susceptible to structural noise and outliers, often leading to severe overfitting in complex datasets. In this paper, we propose a novel class of non-stationary kernels derived from the fundamental solution of the generalized time-space fractional diffusion-wave equation. By leveraging a structure-preserving transmutation method over Weighted Sobolev Spaces, we introduce the Amnesia-Weighted Fox Kernel, an exact analytical Mercer kernel governed by the Fox H-function. Unlike standard kernels, our formulation incorporates an aging weight function (the "Amnesia Effect") to penalize distant outliers and a fractional asymptotic power-law decay to allow for robust, heavy-tailed feature mapping (analogous to Lévy flights). Numerical experiments on both synthetic datasets and real-world high-dimensional radar data (Ionosphere) demonstrate that the proposed Amnesia-Weighted Fox Kernel consistently outperforms the standard Gaussian RBF baseline, reducing the classification error rate by approximately 50% while maintaining structural robustness against outliers.

In this paper, we propose a novel bounded asymmetric elastic net ($L_{baen}$) loss function and combine it with the support vector machine (SVM), resulting in the BAEN-SVM. The $L_{baen}$ is bounded and asymmetric and can degrade to the asymmetric elastic net hinge loss, pinball loss, and asymmetric least squares loss. BAEN-SVM not only effectively handles noise-contaminated data but also addresses the geometric irrationalities in the traditional SVM. By proving the violation tolerance upper bound (VTUB) of BAEN-SVM, we show that the model is geometrically well-defined. Furthermore, we derive that the influence function of BAEN-SVM is bounded, providing a theoretical guarantee of its robustness to noise. The Fisher consistency of the model further ensures its generalization capability. Since the $L_{\text{baen}}$ loss is non-convex, we designed a clipping dual coordinate descent-based half-quadratic algorithm to solve the non-convex optimization problem efficiently. Experimental results on artificial and benchmark datasets indicate that the proposed method outperforms classical and advanced SVMs, particularly in noisy environments.

Unsupervised anomaly detection (UAD) aims to detect anomalies without labeled data, a necessity in many machine learning applications where anomalous samples are rare or not available. Most state-of-the-art methods fall into two categories: reconstruction-based approaches, which often reconstruct anomalies too well, and decoupled representation learning with density estimators, which can suffer from suboptimal feature spaces. While some recent methods attempt to couple feature learning and anomaly detection, they often rely on surrogate objectives, restrict kernel choices, or introduce approximations that limit their expressiveness and robustness. To address this challenge, we propose a novel method that couples representation learning the exact One-Class SVM (OCSVM) optimization problem, through a custom loss formulation that directly aligns latent features with the OCSVM decision boundary. The model is evaluated on two tasks: a benchmark based on MNIST-C, and a challenging brain MRI lesion detection task. Unlike most methods that focus on large, hyperintense lesions at the image level, our approach succeeds to target small, non-hyperintense lesions, while we evaluate voxel-wise metrics, addressing a more clinically relevant scenario. Both experiments evaluate a form of robustness to domain shifts, including corruption types in MNIST-C and texture or population age variations in MRI. Results demonstrate performance and robustness of our proposed model, highlighting its potential for general UAD and real-world medical imaging applications. The source code is available at https://github.com/Nicolas-Pinon/uad\_ocsvm\_guided\_repr\_learning.

Kernel selection for regression of physical observables is often heuristic. We investigate a physics-informed strategy in which functional forms and spectral structures associated with Green's functions motivate kernel selection without requiring an exact identification between a machine-learning kernel and a physical propagator. The principal construction is a Jackson-damped Chebyshev kernel inspired by the kernel polynomial method (KPM); its explicit feature map yields a positive-semidefinite Gram matrix by construction and provides an inspectable spectral prior for structured observables. We evaluate standard and custom SVR models on copper-conductivity proxies, local Dirac-like band dispersion, quartic-oscillator energy levels, photonic-crystal transmission, and Fibonacci-chain transmission using repeated nested validation, learning curves, random-forest and multilayer-perceptron baselines, and low-rank Nyström tests where relevant. The framework is intended for finite-data regression of precomputed observables while boundary conditions remain part of the physical model that generates those observables.

Quantum Support Vector Machine is a kernel-based approach to classification problems. We study the applicability of quantum kernels to financial data, specifically our self-curated Dhaka Stock Exchange (DSEx) Broad Index dataset. To the best of our knowledge, this is the first systematic study of quantum kernels applied to this dataset. Working within the empirical quantum advantage (EQA) framework of Krunic et al., we benchmark several quantum kernels against a classical RBF-kernel SVM baseline, propose the best-performing kernel for this dataset, and relate the observations to the Phase Space Terrain Ruggedness Index metric. We estimate the resources needed to carry out these investigations on a larger scale for future practitioners.