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2011•AUSTRALIAN JOURNAL OF BASIC AND APPLIED SCIENCESRequires access

Exploring reproducing kernel hilbert space and its application to survival data.

Nur'azah Abdul Manaf, Gafurjan Ismailovich Ibragimov, Mohd Rizam Abu Bakar, Bader Ahmad I. Aljawadi

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Abstract

In this paper, we will construct a kernel K(x,y) and verify that it is a reproducing kernel in Hilbert space (RKHS). The basic facts and important properties of an RKHS will be reviewed. Diagonal matrices will be used in the construction of the reproducing kernel. We will construct a reproducing kernel and extend the kernel Cox regression model for the survival data of HIV patients by estimating the risk or loss function. The results from analysis indicate that the kernel method is efficient and helpful in predicting the risk or survival of patients.

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What this paper is about

In this paper, we will construct a kernel K(x,y) and verify that it is a reproducing kernel in Hilbert space (RKHS). The basic facts and important properties of an RKHS will be reviewed. Diagonal matrices will be used in the construction of the reproducing kernel. We will construct a reproducing kernel and extend the kernel Cox regression model for the survival data of HIV patients by estimating the risk or loss function. The results from analysis indicate that the kernel method is efficient and helpful in predicting the risk or survival of patients.

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Available abstract

In this paper, we will construct a kernel K(x,y) and verify that it is a reproducing kernel in Hilbert space (RKHS). The basic facts and important properties of an RKHS will be reviewed. Diagonal matrices will be used in the construction of the reproducing kernel. We will construct a reproducing kernel and extend the kernel Cox regression model for the survival data of HIV patients by estimating the risk or loss function. The results from analysis indicate that the kernel method is efficient and helpful in predicting the risk or survival of patients.

Key concepts: Reproducing kernel Hilbert space, Kernel (algebra), Kernel embedding of distributions, Kernel principal component analysis, Variable kernel density estimation, Mathematics, Representer theorem, Construct (python library)

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