Developments in the theory of randomized shortest paths with a comparison of graph node distances

There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into account the global structure of the graph. In this article, we develop the theory of one family of graph node distances, known as the randomized shortest path dissimilarity, which has its foundation in statistical physics. We show that the randomized shortest path dissimilarity can be easily computed in closed form for all pairs of nodes of a graph. Moreover, we come up with a new definition of a distance measure that we call the free energy distance. The free energy distance can be seen as an upgrade of the randomized shortest path dissimilarity as it defines a metric, in addition to which it satisfies the graph-geodetic property. The derivation and computation of the free energy distance are also straightforward. We then make a comparison between a set of generalized distances that interpolate between the shortest path distance and the commute time, or resistance distance. This comparison focuses on the applicability of the distances in graph node clustering and classification. The comparison, in general, shows that the parametrized distances perform well in the tasks. In particular, we see that the results obtained with the free energy distance are among the best in all the experiments.Comment: 30 pages, 4 figures, 3 table

Dissimilarity-based representation for radiomics applications

Radiomics is a term which refers to the analysis of the large amount of quantitative tumor features extracted from medical images to find useful predictive, diagnostic or prognostic information. Many recent studies have proved that radiomics can offer a lot of useful information that physicians cannot extract from the medical images and can be associated with other information like gene or protein data. However, most of the classification studies in radiomics report the use of feature selection methods without identifying the machine learning challenges behind radiomics. In this paper, we first show that the radiomics problem should be viewed as an high dimensional, low sample size, multi view learning problem, then we compare different solutions proposed in multi view learning for classifying radiomics data. Our experiments, conducted on several real world multi view datasets, show that the intermediate integration methods work significantly better than filter and embedded feature selection methods commonly used in radiomics.Comment: conference, 6 pages, 2 figure