Bi-stochastic kernels via asymmetric affinity functions

TL;DR

This paper introduces a simple method to construct bi-stochastic kernels from asymmetric affinity functions, enabling efficient out-of-sample extensions for large datasets.

Contribution

It presents a novel, straightforward approach to create bi-stochastic kernels from asymmetric affinity functions, avoiding iterative or optimization-based methods.

Findings

Provides a simple construction method for bi-stochastic kernels

Enables out-of-sample extensions for large datasets

Offers an alternative to iterative or optimization-based approaches

Abstract

In this short letter we present the construction of a bi-stochastic kernel p for an arbitrary data set X that is derived from an asymmetric affinity function {\alpha}. The affinity function {\alpha} measures the similarity between points in X and some reference set Y. Unlike other methods that construct bi-stochastic kernels via some convergent iteration process or through solving an optimization problem, the construction presented here is quite simple. Furthermore, it can be viewed through the lens of out of sample extensions, making it useful for massive data sets.