Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Related Works


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


Experiments
4.1 Synthetic Dataset
4.2 Real Dataset


Discussions, Acknowledgements, and References Related Works Related Works Related Works 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 Convex Relaxation Techniques for Hyperbolic SVMs 3.1 Preliminaries 3.1 Preliminaries 3.2 Original Formulation of the HSVM 3.2 Original Formulation of the HSVM 3.3 Semidefinite Formulation 3.3 Semidefinite Formulation 3.4 Moment-Sum-of-Squares Relaxation 3.4 Moment-Sum-of-Squares Relaxation Experiments
4.1 Synthetic Dataset
4.2 Real Dataset Experiments Experiments 4.1 Synthetic Dataset 4.1 Synthetic Dataset 4.2 Real Dataset 4.2 Real Dataset Discussions, Acknowledgements, and References Discussions, Acknowledgements, and References Discussions, Acknowledgements, and References A. Proofs A. Proofs B. Solution Extraction in Relaxed Formulation B. Solution Extraction in Relaxed Formulation C. On Moment Sum-of-Squares Relaxation Hierarchy C. On Moment Sum-of-Squares Relaxation Hierarchy D. Platt Scaling [31] D. Platt Scaling [31] E. Detailed Experimental Results E. Detailed Experimental Results F. Robust Hyperbolic Support Vector Machine 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 Authors:
(1) Sheng Yang, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA (shengyang@g.harvard.edu);
(2) Peihan Liu, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA (peihanliu@fas.harvard.edu);
(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 (cpehlevan@seas.harvard.edu). Authors: Authors: (1) Sheng Yang, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA (shengyang@g.harvard.edu); (2) Peihan Liu, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA (peihanliu@fas.harvard.edu); (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 (cpehlevan@seas.harvard.edu). This paper is available on arxiv under CC by-SA 4.0 Deed (Attribution-Sharealike 4.0 International) license. This paper is available on arxiv under CC by-SA 4.0 Deed (Attribution-Sharealike 4.0 International) license. available on arxiv available on arxiv

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

Moment

Semidefinite Relaxation for Hyperbolic SVMs: A Polynomial Approach

About Author

Comments

TOPICS

THIS ARTICLE WAS FEATURED IN

Related Stories

A Comparative Performance Analysis of SymTax on Five Citation Recommendation Datasets

Beyond Euclidean Space: Optimizing Hierarchical Data in Hyperbolic HSVMs

Beyond Euclidean Space: Optimizing Hierarchical Data in Hyperbolic HSVMs

Darwin's Hybrid Intelligence to Align AI & Human Goals for Startups & VCs

100+ Free Pluralsight Courses to learn Python, Java, and Spring Boot

100 Days of AI Day 1: From Newsletter to Podcast, Leveraging AI for Audio Transformation

A Comparative Performance Analysis of SymTax on Five Citation Recommendation Datasets

Beyond Euclidean Space: Optimizing Hierarchical Data in Hyperbolic HSVMs

Beyond Euclidean Space: Optimizing Hierarchical Data in Hyperbolic HSVMs

Darwin's Hybrid Intelligence to Align AI & Human Goals for Startups & VCs

100+ Free Pluralsight Courses to learn Python, Java, and Spring Boot

100 Days of AI Day 1: From Newsletter to Podcast, Leveraging AI for Audio Transformation

Light-Mode

Classic

Newspaper

Minty

Dark-Mode

Neon Noir

Minty

HN StartUps