Cross-entropy approach to data visualization based on the neural gas network

A new approach to mapping high dimensional data into a low dimensional space embedding is presented. The aim of this approach is to project simultaneously the input data and the codebook vectors into a low dimensional output space, preserving the local neighborhood. The neural gas algorithm is used to obtain codebook vectors. A cost function based on the cross entropy (CE) between input and output probabilities is minimized by using a Newton-Raphson method. The new approach is compared with multidimensional scaling (MDS) using a benchmark data set and three high dimensional real world data sets. In comparison with MDS, our method delivers a clear visualization of both data points and codebooks, and better CE and topology preservation measurements.