This paper proposes an incremental learning strategy for neural word embedding methods, such as SkipGrams and Global Vectors. Since our method iteratively generates embedding vectors one dimension at a time, obtained vectors equip a unique property. Namely, any right-truncated vector matches the solution of the corresponding lower-dimensional embedding. Therefore, a single embedding vector can ...

We will show how to obtain embeddings into `p with small dimension where all but an -fraction of the embedded distances have small distortion. This result has various applications in networking. The embedding is achieved by randomly choosing a small set of beacons, constructing a good embedding for these nodes (using, e.g., Borgain’s embedding), and then extending this embedding to the remainin...

Predicting future behavior of chaotic time series system is a challenging area in the literature of nonlinear systems. The prediction's accuracy of chaotic time series is extremely dependent on the model and the learning algorithm. On the other hand the cyclic solar activity as one of the natural chaotic systems has significant effects on earth, climate, satellites and space missions. Several m...

The strong isometric dimension of a reflexive graph is related to its injective hull: both deal with embedding reflexive graphs in the strong product of paths. We give several upper and lower bounds for the strong isometric dimension of general graphs; the exact strong isometric dimension for cycles and hypercubes; and the isometric dimension for trees is found to within a factor of two.

We give an overview of immersion in order to present the idea of embedding, then discuss Whitney’s work on his weak immersion and strong embedding theorems as the main theorems of the talk, drawing briefly on notions of transversality as presented by the previous speaker, rigorously proving a weaker form of Whitney’s embedding theorem, and sketching out a result of a linear bound for the minimu...

The network distance estimation schemes based on Euclidean embedding have been shown to provide reasonably good overall accuracy. While some recent studies have revealed that triangle inequality violations (TIVs) inherent in network distances among Internet hosts fundamentally limit their accuracy, these Euclidean embedding methods are nonetheless appealing and useful for many applications due ...

We present a new technique for the embedding of large cube-connected cycles networks (CCC) into smaller ones, a problem that arises when algorithms designed for an architecture of an ideal size are to be executed on an existing architecture of a xed size. Using the new embedding strategy, we show that the CCC of dimension l can be embedded into the CCC of dimension k with dilation 1 and optimum...

This paper is considered with the problem of embedding complete binary trees into 3-dimensional meshes using dimension-ordered routing with the primary concern of minimizing the link congestion. The authors showed that a complete binary tree with 2 1 nodes can be embedded into a 3-dimensional mesh with optimum size, 2 nodes, if the link congestion is two [7]. (More precisely, the link congestio...

Learning distributed representations for nodes in graphs has become an important problem that underpins a wide spectrum of applications. Existing methods to this problem learn representations by optimizing a softmax objective while constraining the dimension of embedding vectors. We argue that the generalization performance of these methods are probably not due to the dimensionality constraint ...

The dot in (1) denotes the usual scalar product of R. The notion embedding means, that w is locally an immersion and globally a homeomorphism of M onto the subspace u(M) of R*. If an embedding w : M -• R satisfies (1) on the whole M, we speak of an isometric embedding. If w is an immersion and a solution of (1) in a (possibly small) neighbourhood of any point of M, we speak of a local isometric...