Consider an i.i.d. sample from unknown density function supported on manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning distance between points, able to capture both geometry and underlying density. define such prove convergence, as size goes infinity, macroscopic one that we call Fermat it minimizes path functional, resembling principle optics. The proof...

One of the causes increasing maternal mortality rate in Indonesia is declining performance health services each Indonesian province. To overcome decline performance, namely by determining advance provinces that need to be prioritized for grouping 34 Indonesia. This study aims obtain best provincial results so it can prioritize right provinces. methods are suitable K-Means because simple and eas...

1 Similarity Metrics Many recommendation algorithms employ some form of similarity metric in the generation of ratings predictions. Similarity metrics are often associated with some form of distance measure. Definition 1.0.1. Let δ be a function δ : R × R → R. Let x,y, z ∈ R. Then δ is a distance measure if it satisfies the following four properties. (d1) δ(x,y) ≥ 0 (no negative distances). (d2...

In this paper, we use known bounds on the smallest eigenvalue of a symmetric matrix and Schoenberg’s Theorem to provide both necessary as well as sufficient trace inequalities that guarantee a matrix D is a Euclidean distance matrix, EDM. We also provide necessary and sufficient trace inequalities that guarantee a matrix D is an EDM generated by a regular figure.

It is a simple consequence of the maximum principle that a superharmonic function u on Rn(i. e. ∆u ≤ 0) which is 1 near infinity is identically 1 on Rn (throughout this paper, n ≥ 3). Geometrically this means that one can not conformally deform the Euclidean metric in a bounded region without decreasing the scalar curvature somewhere. In fact there is a much stronger result: one can not have an...

This paper proposes a grey interval relation TOPSIS for the decision making in which all of the attribute weights and attribute values are given by the interval grey numbers. The feature of our method different from other grey relation decision-making is that all of the subjective and objective weights are obtained by interval grey number and that decisionmaking is performed based on the relati...

Let A be a compact set in the right-half plane and Γ(A) the set in R 3 obtained by rotating A about the vertical axis. We investigate the support of the limit distribution of minimal energy point charges on Γ(A) that interact according to the Riesz potential 1/r, 0 < s < 1, where r is the Euclidean distance between points. Potential theory yields that this limit distribution coincides with the ...

This study investigated the effect of social skills on the facial movement asymmetry in facial expressions. Threedimensional facial landmark data of facial expressions (neutral, happy, and angry) were obtained from Japanese participants (n = 62). After the facial expression task, each participant completed KiSS-18 (Kikuchi’s Scale of Social Skills; Kikuchi, 2007). Through a generalized Procrust...