相关论文: Near-Delaunay Metrics

Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the…

Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…

We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling…

Consider an experiment with a finite set of design points representing permissible trial conditions. Suppose that each trial is associated with a cost that depends on the selected design point. In this paper, we study the problem of…

In scalable machine learning systems, model training is often parallelized over multiple nodes that run without tight synchronization. Most analysis results for the related asynchronous algorithms use an upper bound on the information…

This paper discusses a new family of bounds for use in similarity search, related to those used in metric indexing, but based on Ptolemy's inequality, rather than the metric axioms. Ptolemy's inequality holds for the well-known Euclidean…

The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…

The Assouad and quasi-Assouad dimensions of a metric space provide information about the extreme local geometric nature of the set. The Assouad dimension of a set has a measure theoretic analogue, which is also known as the upper regularity…

<incorrect proofs; does not consider an important case because of which the proofs are wrong. The paper was withdrawn from submission> One of the objectives of a Delaunay mesh refinement algorithm is to produce meshes with tetrahedral…

We compute the convex hull in $\mathbb{C}^2$ of an arbitrary finite subgroup of ${\mathbb{C}^*}^2$. The combinatorics are dictated by continued fractions in a natural way. This reproves a theorem of Smilansky, with a slightly stronger…

Deep metric learning (DML) aims to minimize empirical expected loss of the pairwise intra-/inter- class proximity violations in the embedding space. We relate DML to feasibility problem of finite chance constraints. We show that minimizer…

We consider the construction of a polyhedral Delaunay partition as a limit of the sequence of power diagrams (radical partitions). The dual Voronoi diagram is obtained as a limit of the sequence of weighted Delaunay partitions. The problem…

Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…

We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we…

The concept of image similarity is ambiguous, and images can be similar in one context and not in another. This ambiguity motivates the creation of metrics for specific contexts. This work explores the ability of deep perceptual similarity…

The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…

This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…

Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the…

In the past few years, the number of fine-art collections that are digitized and publicly available has been growing rapidly. With the availability of such large collections of digitized artworks comes the need to develop multimedia systems…

In this paper we give a brief introduction to criteria for metrisability of a manifold and to some aspects of non-metrisable manifolds. Bias towards work currently being done by the author and his colleagues at the University of Auckland…