Geometrical description of denormalized thermodynamic manifold

In view of differential geometry, the state space of thermodynamic parameters is investigated. Here the geometrical structures of the denormalized thermodynamic manifold are considered. The relation of their geometrical metrics is obtained. Moreover an example is used to illustrate our conclusions.

Adaptive Graph Embedding With Consistency and Specificity for Domain Adaptation

Domain adaptation(DA) aims to find a subspace,where the discrepancies between the source and target domains are reduced. Based on this subspace, the classifier trained by the labeled source samples can classify unlabeled target samples well.Existing approaches leverage Graph Embedding Learning to explore such a subspace. Unfortunately, due to 1) the interaction of the consistency and specificity between samples, and 2) the joint impact of the degenerated features and incorrect labels in the samples, the existing approaches might assign unsuitable similarity, which restricts their performance. In this paper, we propose an approach called adaptive graph embedding with consistency and specificity(AGE-CS) to cope with these issues. AGE-CS consists of two methods, i.e., graph embedding with consistency and specificity(GECS), and adaptive graph embedding(AGE).GECS jointly learns the similarity of samples under the geometric distance and semantic similarity metrics, while AGE adaptively adjusts the relative importance between the geometric distance and semantic similarity during the iterations. By AGE-CS,the neighborhood samples with the same label are rewarded,while the neighborhood samples with different labels are punished. As a result, compact structures are preserved, and advanced performance is achieved. Extensive experiments on five benchmark datasets demonstrate that the proposed method performs better than other Graph Embedding methods.