Unsupervised nearest neighbors with kernels

Abstract

In this paper we introduce an extension of unsupervised nearest neighbors for embedding patterns into continuous latent spaces of arbitrary dimensionality with stochastic sampling. Distances in data space are employed as standard deviation for Gaussian sampling in latent space. Neighborhoods are preserved with the nearest neighbor data space reconstruction error. Similar to the previous unsupervised nearest neighbors (UNN) variants this approach is an iterative method that constructs a latent embedding by selecting the position with the lowest error. Further, we introduce kernel functions for computing the data space reconstruction error in a feature space that allows to better handle non-linearities. Experimental studies show that kernel unsupervised nearest neighbors (KUNN) is an efficient method for embedding high-dimensional patterns. © 2012 Springer-Verlag.