Semidefinite Relaxation for Hyperbolic SVMs: A Polynomial Approach | HackerNoon

Table of Links

Abstract and 1. Introduction

2. Related Works

3. Convex Relaxation Techniques for Hyperbolic SVMs

   3.1 Preliminaries

   3.2 Original Formulation of the HSVM

   3.3 Semidefinite Formulation

   3.4 Moment-Sum-of-Squares Relaxation

4. Experiments

   4.1 Synthetic Dataset

   4.2 Real Dataset

5. Discussions, Acknowledgements, and References

A. Proofs

B. Solution Extraction in Relaxed Formulation

C. On Moment Sum-of-Squares Relaxation Hierarchy

D. Platt Scaling [31]

E. Detailed Experimental Results

F. Robust Hyperbolic Support Vector Machine

3.3 Semidefinite Formulation

Note that Equation (7) is a non-convex quadratically-constrained quadratic programming (QCQP) problem, we can apply a semidefinite relaxation (SDP) [8]. The SDP formulation is given by

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Authors:

(1) Sheng Yang, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA ([email protected]);

(2) Peihan Liu, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA ([email protected]);

(3) Cengiz Pehlevan, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, Center for Brain Science, Harvard University, Cambridge, MA, and Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University, Cambridge, MA ([email protected]).

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This paper is available on arxiv under CC by-SA 4.0 Deed (Attribution-Sharealike 4.0 International) license.

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