Comparison-based centrality measures

Recently, learning only from ordinal information of the type “item x is closer to item y than to item z” has received increasing attention in the machine learning community. Such triplet comparisons are particularly well suited for learning from crowdsourced human intelligence tasks, in which workers make statements about the relative distances in a triplet of items. In this paper, we systematically investigate comparison-based centrality measures on triplets and theoretically analyze their underlying Euclidean notion of centrality. Two such measures already appear in the literature under opposing approaches, and we propose a third measure, which is a natural compromise between these two. We further discuss their relation to statistical depth functions, which comprise desirable properties for centrality measures, and conclude with experiments on real and synthetic datasets for medoid estimation and outlier detection.

Depth classification based on affine-invariant, weighted and kernel-based spatial depth functions

Several multivariate depth functions have been proposed in the literature, of which some satisfy all the conditions for statistical depth functions while some do not. Spatial depth is known to be invariant to spherical and shift transformations. In this paper, the possibility of using different versions of spatial depth in classification is considered. The covariance-adjusted, weighted, and kernel-based versions of spatial depth functions are presented to classify multivariate outcomes. We extend the maximal depth classification notions for the covariance-adjusted, weighted, and kernel-based spatial depth versions. The classifiers' performance is considered and compared with some existing classification methods using simulated and real datasets.