Traditional distance metric learning with side information usually formulates the objectives using the covariance matrices of the data point pairs in the two constraint sets of must-links and cannotlinks. Because the covariance matrix computes the sum of the squared l2-norm distances, it is prone to both outlier samples and outlier features. To develop a robust distance metric learning method, ...

We consider the problem of placing n points, each one inside its own, prespecified disk, with the objective of maximizing the distance between the closest pair of them. The disks can overlap and have different sizes. The problem is NP-hard and does not admit a PTAS. In the L∞ metric, we give a 2-approximation algorithm running in O(n √ n log n) time. In the L2 metric, we give a quadratic time a...

We study the 3D shape similarity between closed surfaces. We represent a curved or polyhedral 3D object of genus zero using a mesh representation that has nearly uniform distribution with known connectivity among mesh nodes. We define a shape similarity metric based on the L2 distance between the local curvature distributions over the mesh representations of the two objects. For both convex and...

Some asymptotic properties of point estimation with n-dimensional fuzzy data with respect to a special L2-metric ρ are investigated in this paper. It is shown that the collection of all n-dimensional fuzzy data endowed with the ρ-metric is a complete and separable space. Some criterions for point estimation in such fuzzy environments are proposed and the sample mean and variance and covariance ...

There are several characterizations of coarse embeddability of a discrete metric space into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces Lp(μ), we get their coarse embeddability into a Hilbert space for 0 < p < 2. This together with a theorem by Banach and Mazur yields that coarse embeddability into l2 and into L...

LeBrun constructed a scalar-flat Kähler metric on the total space of Chern class −n line bundle O(−n) → CP1. We study moduli spaces of ASD connections on it. It is known that the natural L2-metrics on them are kählerian. We study them when the metric is complete. We give an algorithm to compute their Betti numbers. On the way of the proof, we also show that their homology groups have no torsion...

We investigate the efficiency of approximation by linear combinations of ridge functions in the metric of L2(B ) with Bd the unit ball in Rd. If Xn is an n-dimensional linear space of univariate functions in L2(I), I = [−1, 1], and Ω is a subset of the unit sphere Sd−1 in Rd of cardinality m, then the space Yn := span{r(x · ξ) : r ∈ Xn, ω ∈ Ω} is a linear space of ridge functions of dimension ≤...

Finding large numbers of target items for phonetic and phonological experiments can be a time-consuming and error-prone task. Using freely available tools and data, we have generated a bilingual corpus with the specific aim of investigating the processing and perception of stress in second-language (L2) words. Normalized Levenshtein distances between orthographic and phonemic transcriptions of ...

Given a function ψ in L2(Rd), the affine (wavelet) system generated by ψ, associated to an invertible matrix a and a lattice Γ, is the collection of functions {| det a|j/2ψ(ajx−γ) : j ∈ Z, γ ∈ Γ}. In this article we prove that the set of functions generating affine systems that are a Riesz basis of L2(Rd) is dense in L2(Rd). We also prove that a stronger result is true for affine systems that a...