# A Summary Of The Kernel Matrix, And How To Learn It Effectively Using Semidefinite Programming

arXiv: https://arxiv.org/abs/1709.06557 · HTML: https://mlsanity.com/paper/1709.06557/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2017.

## Built on by (most cited first, 2 of 2)

- [Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr"om Method, and Use of Kernels in Machine Learning: Tutorial and Survey](https://mlsanity.com/paper/2106.08443/) (2021)
- [Unified Framework for Spectral Dimensionality Reduction, Maximum Variance Unfolding, and Kernel Learning By Semidefinite Programming: Tutorial and Survey](https://mlsanity.com/paper/2106.15379/) (2021)

## Abstract (arXiv)

Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between object pairs specifies their distance in the embedding space. Applying kernel methods to partially labeled datasets is a classical challenge in this regard, requiring that the distances between unlabeled pairs must somehow be learnt using the labeled data. In this independent study, I will summarize the work of G. Lanckriet et al.'s work on "Learning the Kernel Matrix with Semidefinite Programming" used in support vector machines (SVM) algorithms for the transduction problem. Throughout the report, I have provide alternative explanations / derivations / analysis related to this work which is designed to ease the understanding of the original article.