Lipschitz embeddings of random sequences

Metric Embeddings and Lipschitz Extensions

Quantitative Bi-Lipschitz embeddings of manifolds

The goal of this write up is to provide a more detailed proof of the collapsing result already contained in [2]. While reading this paper the author struggled to understand many details of the proofs, particularly where the details of an argument were spread over several papers or simply assumed obvious. Nothing new is proven in this write up, but results are explicated and an attempt is made t...

Bouligand Dimension and Almost Lipschitz Embeddings

In this paper we present some new properties of the metric dimension defined by Bouligand in 1928 and prove the following new projection theorem: Let dimb(A − A) denote the Bouligand dimension of the set A − A of differences between elements of A. Given any compact set A ⊆ R such that dimb(A−A) < m, then almost every orthogonal projection P of A of rank m is injective on A and P |A has Lipschit...

Energy-aware adaptive bi-Lipschitz embeddings

We propose a dimensionality reducing matrix design based on training data with constraints on its Frobenius norm and number of rows. Our design criteria is aimed at preserving the distances between the data points in the dimensionality reduced space as much as possible relative to their distances in original data space. This approach can be considered as a deterministic Bi-Lipschitz embedding o...

FURTHER RESULTS OF CONVERGENCE OF UNCERTAIN RANDOM SEQUENCES

Convergence is an issue being widely concerned about. Thus, in this paper, we mainly put forward two types of concepts of convergence in mean and convergence in distribution for the sequence of uncertain random variables. Then some of theorems are proved to show the relations among the three convergence concepts that are convergence in mean, convergence in measure and convergence in distributio...