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Fast and Scalable Multi-Kernel Encoder Classifier

Cencheng Shen

TL;DR

This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques, and demonstrates superior running time compared to standard approaches such as support vector machines and two-layer neural network.

Abstract

This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding, and seamlessly integrates multiple kernels to enhance the learning process. Our theoretical analysis offers a population-level characterization of this approach using random variables. Empirically, our method demonstrates superior running time compared to standard approaches such as support vector machines and two-layer neural network, while achieving comparable classification accuracy across various simulated and real datasets.

Fast and Scalable Multi-Kernel Encoder Classifier

TL;DR

This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques, and demonstrates superior running time compared to standard approaches such as support vector machines and two-layer neural network.

Abstract

This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding, and seamlessly integrates multiple kernels to enhance the learning process. Our theoretical analysis offers a population-level characterization of this approach using random variables. Empirically, our method demonstrates superior running time compared to standard approaches such as support vector machines and two-layer neural network, while achieving comparable classification accuracy across various simulated and real datasets.
Paper Structure (9 sections, 6 theorems, 41 equations, 1 figure, 1 table)

This paper contains 9 sections, 6 theorems, 41 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Graph Encoder Embedding for Kernel
  3. Fast Multi-Kernel Encoder Classifier
  4. Population Theory
  5. Experiments
  6. Simulations
  7. Real Data
  8. Conclusion
  9. Proof

Key Result

theorem 1

Given the random variable pair $(X,Y)$ of finite moments. Let $U \in \mathbb{R}^{K \times p}$, where each row satisfies Under the above probabilistic assumption for the sample data $(\mathbf{X}, \mathbf{Y})$, the matrix $\mathbf{U}$ in Section sec2 satisfies: for the Frobenius matrix norm.

Figures (1)

  • Figure 1: The figure provides a comparison of classification errors and running times across six different simulations. These comparisons were conducted utilizing 20 Monte-Carlo replicates and a 5-fold evaluation.

Theorems & Definitions (9)

  • theorem 1
  • theorem 2
  • theorem 3
  • theorem 1
  • proof
  • theorem 2
  • proof
  • theorem 3
  • proof