Minimal Algorithmic Information Loss Methods for Dimension Reduction, Feature Selection and Network Sparsification

We introduce a family of unsupervised, domain-free, and (asymptotically) model-independent algorithms based on the principles of algorithmic probability and information theory designed to minimize the loss of algorithmic information, including a lossless-compression-based lossy compression algorithm. The methods can select and coarse-grain data in an algorithmic-complexity fashion (without the use of popular compression algorithms) by collapsing regions that may procedurally be regenerated from a computable candidate model. We show that the method can preserve the salient properties of objects and perform dimension reduction, denoising, feature selection, and network sparsification. As validation case, we demonstrate 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. The methods (InfoRank, MILS) can also be applied to applications such as image segmentation based on algorithmic probability.Comment: 23 pages in double column including Appendix, online implementation at http://complexitycalculator.com/MILS