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 B Solution Extraction in Relaxed Formulation B.1 Semidefinite Relaxation Typically the top eigendirection is selected as the best candidate. B.2 Moment-Sum-of-Squares Relaxation In moment-sum-of-squares relaxation, the decision variable is the truncated multi-sequence z, but we could decode the solution from the moment matrix 𝑀𝜅[z] it generates. We are able to extract the part in TMS that corresponds to w = [𝑤0, 𝑤1, ..., 𝑤𝑑], by reading off these entries from the moment matrix, which is already a good enough solution. 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 [3] a method mentioned in slide 14 of https://web.stanford.edu/class/ee364b/lectures/sdp-relax_slides.pdf

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Extracting Solutions from SDP Relaxations via Rank-One Approximation

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