Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2014-22

Stefan P. Müller


Induced Markov Chains for the Encoding of Graph-based Data



Abstract: Graph-based data occurs in various applications, e.g. finite-element simulations and computer-generated imagery. There are several techniques to compress these data sets with prediction methods and encoding of the residual. The focus of these methods is almost always on the prediction rather than on encoding. We present a new encoding scheme based on induced Markov chains (iMc) reflecting the underlying distribution of graph-based data. For this purpose, we define transition probabilities between the occurring values that are dependent on the topology of the graph. The basic idea is to transform a topological relation into a value-based one. The transition probabilities along with an initial distribution can be interpreted as a Markov chain, the so-called iMc. The topology combined with the transition probabilities can be used as side information for an encoder. Additionally we combine the iMc encoding scheme with tree and time differences as prediction methods, since some correlations cannot be entirely removed neither by the prediction methods, nor by the iMc by its own.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), P-2014-22