Algorithms for learning Bayesian networks from data have two components: a scoring metric and a search procedure. The scoring metric computes a score reeecting the goodness-of-t of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et al. (1994) introduced a Bayesian metric, called the BDe metric, that computes the relative posterior...

Okumura gave a necessary and sufficient condition for an oriented real hypersurface of a Kähler manifold to be a contact metric manifold with respect to the naturally induced almost contact metric structure. In this paper, we discuss an oriented hypersurface of a quasi Kähler manifold and give a necessary and sufficient condition for such a hypersurface to be a quasi contact metric manifold wit...

A dilatation structure encodes the approximate self-similarity of a metric space. A metric space (X, d) which admits a strong dilatation structure (definition 2.2) has a metric tangent space at any point x ∈ X (theorem 4.1), and any such metric tangent space has an algebraic structure of a conical group (theorem 4.2). Particular examples of conical groups are Carnot groups: these are simply con...

This paper demonstrates a method of using non-metric visual information derived from an uncalibrated active vision system to navigate an autonomous vehicle through freespace regions detected in a cluttered environment. The structure of 3-space is recovered modulo an affine transformation using an uncalibrated active stereo head carried by the vehicle. The plane at infinity, necessary for recove...

We study the problem of clustering discrete probability distributions with respect to the Kullback-Leibler (KL) divergence. This problem arises naturally in many applications. Our goal is to pick k distributions as “representatives” such that the average or maximum KLdivergence between an input distribution and the closest representative distribution is minimized. Unfortunately, no polynomial-t...

In this paper we study a Riemanian metric on the tangent bundle T (M) of a Riemannian manifoldM which generalizes Sasakian metric and Cheeger–Gromoll metric along a compatible almost complex structure which together with the metric confers to T (M) a structure of locally conformal almost Kählerian manifold. This is the natural generalization of the well known almost Kählerian structure on T (M)...

A dilatation structure on a metric space, introduced in [3], is a notion in between a group and a differential structure, accounting for the approximate self-similarity of the metric space. The basic objects of a dilatation structure are dilatations (or contractions). The axioms of a dilatation structure set the rules of interaction between different dilatations. A metric space (X, d) which adm...

The present experiments investigated two characteristics of subjects' multidimensional representations: their dimensional organization and metric structure, for both analyzable and integral stimuli. In Experiment 1, subjects judged the dissimilarity between all pairs of stimuli differing in brightness and size (analyzable stimuli), while in Experiment 2, subjects made dissimilarity judgments fo...

Algorithms for learning Bayesian networks from data have two components: a scoring metric and a search procedure. The scoring metric computes a score re ecting the goodness-oft of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et al. (1995) introduce a Bayesian metric, called the BDe metric, that computes the relative posterior p...