Geometric Mixture Classifier (GMC): A Discriminative Per-Class Mixture of Hyperplanes

• URL: http://arxiv.org/abs/2509.16769v1
• Date: Sat, 20 Sep 2025 18:32:05 GMT
• Title: Geometric Mixture Classifier (GMC): A Discriminative Per-Class Mixture of Hyperplanes
• Authors: Prasanth K K, Shubham Sharma,
• Abstract summary: Many real world categories are multimodal, with single classes occupying disjoint regions in feature space. Classical linear models (logistic regression, linear SVM) use a single global hyperplane and perform poorly on such data.<n>We propose the Geometric Mixture (GMC), a discriminative model that represents each class as a mixture of hyperplanes.
• Score: 1.4557098800700885
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many real world categories are multimodal, with single classes occupying disjoint regions in feature space. Classical linear models (logistic regression, linear SVM) use a single global hyperplane and perform poorly on such data, while high-capacity methods (kernel SVMs, deep nets) fit multimodal structure but at the expense of interpretability, heavier tuning, and higher computational cost. We propose the Geometric Mixture Classifier (GMC), a discriminative model that represents each class as a mixture of hyperplanes. Within each class, GMC combines plane scores via a temperature-controlled soft-OR (log-sum-exp), smoothly approximating the max; across classes, standard softmax yields probabilistic posteriors. GMC optionally uses Random Fourier Features (RFF) for nonlinear mappings while keeping inference linear in the number of planes and features. Our practical training recipe: geometry-aware k-means initialization, silhouette-based plane budgeting, alpha annealing, usage-aware L2 regularization, label smoothing, and early stopping, makes GMC plug-and-play. Across synthetic multimodal datasets (moons, circles, blobs, spirals) and tabular/image benchmarks (iris, wine, WDBC, digits), GMC consistently outperforms linear baselines and k-NN, is competitive with RBF-SVM, Random Forests, and small MLPs, and provides geometric introspection via per-plane and class responsibility visualizations. Inference scales linearly in planes and features, making GMC CPU-friendly, with single-digit microsecond latency per example, often faster than RBF-SVM and compact MLPs. Post-hoc temperature scaling reduces ECE from about 0.06 to 0.02. GMC thus strikes a favorable balance of accuracy, interpretability, and efficiency: it is more expressive than linear models and lighter, more transparent, and faster than kernel or deep models.

Related papers

• GP-FL: Model-Based Hessian Estimation for Second-Order Over-the-Air Federated Learning [52.295563400314094]
  Second-order methods are widely adopted to improve the convergence rate of learning algorithms.<n>This paper introduces a novel second-order FL framework tailored for wireless channels.
  arXiv  Detail & Related papers  (2024-12-05T04:27:41Z)
• Optimal Mixed Integer Linear Optimization Trained Multivariate Classification Trees [0.0]
  We propose two cut-based mixed integer linear optimization (MILO) formulations for designing optimal binary classification trees. Our models leverage on-the-fly identification of minimal infeasible subsystems (MISs) from which we derive cutting planes that hold the form of packing constraints.
  arXiv  Detail & Related papers  (2024-08-02T14:37:28Z)
• MC-GTA: Metric-Constrained Model-Based Clustering using Goodness-of-fit Tests with Autocorrelations [6.172236465839398]
  Existing clustering algorithms overlook the rich correlation between feature similarity and metric distance. We show that MC-GTA successfully incorporates metric autocorrelation. It outperforms strong baselines by large margins.
  arXiv  Detail & Related papers  (2024-05-28T17:35:05Z)
• Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networks [64.39488944424095]
  We present the first machine learning approach to generate low-discrepancy point sets named Message-Passing Monte Carlo points. MPMC points are empirically shown to be either optimal or near-optimal with respect to the discrepancy for low dimension and small number of points.
  arXiv  Detail & Related papers  (2024-05-23T21:17:20Z)
• Minimally Supervised Learning using Topological Projections in Self-Organizing Maps [55.31182147885694]
  We introduce a semi-supervised learning approach based on topological projections in self-organizing maps (SOMs) Our proposed method first trains SOMs on unlabeled data and then a minimal number of available labeled data points are assigned to key best matching units (BMU) Our results indicate that the proposed minimally supervised model significantly outperforms traditional regression techniques.
  arXiv  Detail & Related papers  (2024-01-12T22:51:48Z)
• An extended asymmetric sigmoid with Perceptron (SIGTRON) for imbalanced linear classification [0.0]
  This article presents a new parameterized sigmoid called SIGTRON, and its companion convex model called SIGTRON-imbalanced classification (SIC) model. In contrast to the conventional $pi$-weighted cost-sensitive learning model, the SIC model does not have an external $pi$-weight on the loss function. We show that the proposed SIC model is more adaptive to variations of the dataset.
  arXiv  Detail & Related papers  (2023-12-26T13:14:17Z)
• Fully Linear Graph Convolutional Networks for Semi-Supervised Learning and Clustering [13.19688594704988]
  We show that FLGC is powerful to deal with both graph-structured data and regular data. We also show that FLGC acts as a natural generalization of classic linear models in the non-Euclidean domain.
  arXiv  Detail & Related papers  (2021-11-15T17:45:09Z)
• Unfolding Projection-free SDP Relaxation of Binary Graph Classifier via GDPA Linearization [59.87663954467815]
  Algorithm unfolding creates an interpretable and parsimonious neural network architecture by implementing each iteration of a model-based algorithm as a neural layer. In this paper, leveraging a recent linear algebraic theorem called Gershgorin disc perfect alignment (GDPA), we unroll a projection-free algorithm for semi-definite programming relaxation (SDR) of a binary graph. Experimental results show that our unrolled network outperformed pure model-based graph classifiers, and achieved comparable performance to pure data-driven networks but using far fewer parameters.
  arXiv  Detail & Related papers  (2021-09-10T07:01:15Z)
• Edge Federated Learning Via Unit-Modulus Over-The-Air Computation (Extended Version) [64.76619508293966]
  This paper proposes a unit-modulus over-the-air computation (UM-AirComp) framework to facilitate efficient edge federated learning. It uploads simultaneously local model parameters and updates global model parameters via analog beamforming. We demonstrate the implementation of UM-AirComp in a vehicle-to-everything autonomous driving simulation platform.
  arXiv  Detail & Related papers  (2021-01-28T15:10:22Z)
• Memory and Computation-Efficient Kernel SVM via Binary Embedding and Ternary Model Coefficients [18.52747917850984]
  Kernel approximation is widely used to scale up kernel SVM training and prediction. Memory and computation costs of kernel approximation models are still too high if we want to deploy them on memory-limited devices. We propose a novel memory and computation-efficient kernel SVM model by using both binary embedding and binary model coefficients.
  arXiv  Detail & Related papers  (2020-10-06T09:41:54Z)
• Multi-Objective Matrix Normalization for Fine-grained Visual Recognition [153.49014114484424]
  Bilinear pooling achieves great success in fine-grained visual recognition (FGVC) Recent methods have shown that the matrix power normalization can stabilize the second-order information in bilinear features. We propose an efficient Multi-Objective Matrix Normalization (MOMN) method that can simultaneously normalize a bilinear representation.
  arXiv  Detail & Related papers  (2020-03-30T08:40:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.