We have applied the concept of fractional distance measures, proposed by Aggarwal et al. [1], to content-based image retrieval. Our experiments show that retrieval performances of these measures consistently outperform the more usual Manhattan and Euclidean distance metrics when used with a wide range of high-dimensional visual features. We used the parameters learnt from a Corel dataset on a v...

Finding the nearest neighbor among a large collection of high dimensional vectors can be a computationally demanding task. In this paper, we pursue fast vector matching by representing vectors in IRn with lower dimensional projections in IR, m ≤ n. The key to creating and using the representative vectors is a lower bound on the Euclidean distance between arbitrary vectors in IRn based on the su...

We introduce a gradient operator that generalizes the Euclidean and Riemannian gradients. This operator acts on sections of vector bundles and is determined by three geometric data: a Riemannian metric on the base manifold, a Riemannian metric and a covariant derivative on the vector bundle. Under the assumption that the covariant derivative is compatible with the metric of the vector bundle, w...

We consider magnetization dynamics under the influence of a spin-polarized current, given in terms of a spin-velocity field v, governed by the following modification of the Landau– Lifshitz–Gilbert equation ∂m ∂t + v · ∇m = m × (α ∂m ∂t + β v · ∇m − Δm), called the Landau– Lifshitz–Slonczewski equation. We focus on the situation of magnetizations defined on the entire Euclidean space m(t) : R3 ...

We show that the survivable bottleneck Steiner tree problem in normed planes can be solved in polynomial time when the number of Steiner points is constant. This is a fundamental problem in wireless ad-hoc network design where the objective is to design networks with efficient routing topologies. Our result holds for a general definition of survivability and for any norm whose ball is specified...

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9, 17], and tensor clustering [8, 32]. Like k-means, these more general problems also suffer from the NP-hardness of the associated optimization. Researchers have developed approximat...

We present LEAR (Lexical Entailment Attract-Repel), a novel post-processing method that transforms any input word vector space to emphasise the asymmetric relation of lexical entailment (LE), also known as the IS-A or hyponymy-hypernymy relation. By injecting external linguistic constraints (e.g., WordNet links) into the initial vector space, the LE specialisation procedure brings true hyponymy...

Based on the theory of Fermat reals we introduce new topologies on spaces of Colombeau generalized points and derive some of their fundamental properties. In particular, we obtain metric topologies on the space of near-standard generalized points that induce the standard Euclidean topology on the reals. We also give a new description of the sharp topology in terms of the natural extension of th...

1. Problem Definition Hash tag prediction is different from normal texts classification. Here we don’t know how many clusters we need to find. In addition, the tag set changes so frequently that it is almost impossible to effectively carry out classification or clustering, since a new tag would force us to establish a new class and a new classification rule. Our intuition is: if we can measure ...

We consider a generalization of the concept of d-flattenability of graphs introduced for the l2 norm by Belk and Connelly to general lp norms, with integer P , 1 ≤ p < ∞, though many of our results work for l∞ as well. The following results are shown for graphs G, using notions of genericity, rigidity, and generic d-dimensional rigidity matroid introduced by Kitson for frameworks in general lp ...