In this paper, first we introduce the notion of a nonabelian embedding tensor, which is generalization an tensor. Then Leibniz-Lie algebra, underlying algebraic structure and can also be viewed as Leibniz algebra. Next using derived bracket, construct differential graded Lie whose Maurer-Cartan elements are exactly tensors. Consequently, obtain algebra that governs deformations Finally, define ...

In the literature, although structural representations (e.g. graph) are more powerful than feature vectors in terms of representational abilities, many robust and efficient methods for classification (unsupervised and supervised) have been developed for feature vector representations. In this paper, we propose a graph embedding technique based on the constant shift embedding which transforms a ...

We consider the vector embedding problem. are given a finite set of items, with goal assigning representative to each one, possibly under some constraints (such as collection vectors being standardized, i.e., have zero mean and unit covariance). data indicating that pairs items similar, optionally, other dissimilar. For similar we want corresponding be near other, for dissimilar pairs, not meas...

Ordinal embedding aims at finding a low dimensional representation of objects from set constraints the form ”item j is closer to item i than k”. Typically, each object mapped onto point vector in metric space. We argue that mapping density instead provides some interesting advantages, including an inherent reflection uncertainty about itself and its relative location Indeed, this paper, we prop...

Constructing approximations that can accurately mimic the behavior of complex models at reduced computational costs is an important aspect uncertainty quantification. Despite their flexibility and efficiency, classical surrogate such as kriging or polynomial chaos expansions tend to struggle with highly nonlinear, localized, nonstationary models. We hereby propose a novel sequential adaptive mo...