Data Dimension Reduction and Network Sparsification Based on Minimal Algorithmic Information Loss

We introduce a family of unsupervised, domain-free, and (asymptotically) model-independent algorithms based on the principles of algorithmic information theory designed to minimize the loss of algorithmic information. The method coarse-grains data in an algorithmic fashion by collapsing regions that can be procedurally regenerated from the compressed version. We show that the method can preserve the salient properties of objects and structures in the process of data dimension reduction and denoising. Using suboptimal approximations of efficient (polynomial) estimations to algorithmic complexity by recent numerical methods of algorithmic probability we demonstrate how these algorithms can preserve structure properties, outperforming other algorithms in e.g. the area of network dimension reduction. As a case study, we report that the method preserves all the graph-theoretic indices measured on a well-known set of synthetic and real-world networks of very different nature, ranging from degree distribution and clustering coefficient to edge betweenness and degree and eigenvector centralities, achieving equal or significantly better results than other data reduction and some of the leading network sparsification methods.