Generalized RBF kernel for incomplete data

TL;DR

This paper introduces genRBF, a generalized Gaussian kernel for incomplete data that models uncertainty using data distribution, enabling effective embedding and classification even with many missing features.

Contribution

The paper proposes genRBF, a novel kernel for incomplete data that incorporates data distribution and uncertainty, improving classification performance.

Findings

GenRBF kernel outperforms state-of-the-art methods on incomplete data.

The kernel is easy to implement and compatible with existing kernel methods.

Improved results are especially notable with many missing features.

Abstract

We construct $\bf genRBF$ kernel, which generalizes the classical Gaussian RBF kernel to the case of incomplete data. We model the uncertainty contained in missing attributes making use of data distribution and associate every point with a conditional probability density function. This allows to embed incomplete data into the function space and to define a kernel between two missing data points based on scalar product in $L_2$. Experiments show that introduced kernel applied to SVM classifier gives better results than other state-of-the-art methods, especially in the case when large number of features is missing. Moreover, it is easy to implement and can be used together with any kernel approaches with no additional modifications.