Related papers: Low frame coherence via zero-mean tensor embedding…

Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…

Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…

Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…

We introduce a notion of embedding codimension of an arbitrary local ring, establish some general properties, and study in detail the case of arc spaces of schemes of finite type over a field. Viewing the embedding codimension as a measure…

We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…

We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…

Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…

In this paper we consider the existence and regularity problem for Coulomb frames in the normal bundle of two-dimensional surfaces with higher codimension in Euclidean spaces. While the case of two codimensions can be approached directly by…

Low-dimensional representations, or embeddings, of a graph's nodes facilitate several practical data science and data engineering tasks. As such embeddings rely, explicitly or implicitly, on a similarity measure among nodes, they require…

Two-uniform frames and their use for the coding of vectors are the main subject of this paper. These frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest possible error when up to two…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…

The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…

We determine the minimal equivariant embedding dimension of orthgonal groups acting on real flag manifolds and unitary groups acting on complex flag manifolds. The minimal embedding dimension is achieved at isospectral model.

So far there has not been paid attention to frames that are balanced, i.e. those frames which sum is zero. In this paper we consider balanced frames, and in particular balanced unit norm tight frames, in finite dimensional Hilbert spaces.…

Goemans showed that any $n$ points $x_1, \dotsc x_n$ in $d$-dimensions satisfying $\ell_2^2$ triangle inequalities can be embedded into $\ell_{1}$, with worst-case distortion at most $\sqrt{d}$. We extend this to the case when the points…

Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…

We introduce Mercator, a reliable embedding method to map real complex networks into their hyperbolic latent geometry. The method assumes that the structure of networks is well described by the Popularity$\times$Similarity…

This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rather than approximate the extrinsic geometry, we construct a…

In this paper we study {\em terminal embeddings}, in which one is given a finite metric $(X,d_X)$ (or a graph $G=(V,E)$) and a subset $K \subseteq X$ of its points are designated as {\em terminals}. The objective is to embed the metric into…