Related papers: Measures of scalability
Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case…
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…
We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. The diagram vector of a vector in R2 was previously defined using polar coordinates and was used to characterize…
Fr\'echet means, conceptually appealing, generalize the Euclidean expectation to general metric spaces. We explore how well Fr\'echet means can be estimated from independent and identically distributed samples and uncover a fundamental…
Improvements in the accuracy of shape measurements are essential to exploit the statistical power of planned imaging surveys that aim to constrain cosmological parameters using weak lensing by large-scale structure. Although a range of…
The estimation of depth in two-dimensional images has long been a challenging and extensively studied subject in computer vision. Recently, significant progress has been made with the emergence of Deep Learning-based approaches, which have…
Many networking applications require timely access to recent network measurements, which can be captured using a sliding window model. Maintaining such measurements is a challenging task due to the fast line speed and scarcity of fast…
Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Skewness measures can be used to measure the level of asymmetry of a distribution. Given the prevalence of statistical methods that assume underlying symmetry, and also the desire for symmetry in order to make meaningful judgements for…
We study the problem of deriving compressibility measures for Piecewise Linear Approximations (PLAs), i.e., error-bounded approximations of a set of two-dimensional increasing data points using a sequence of segments. Such approximations…
In information fusion, one is often confronted with the following problem: given a preexisting set of measurements about an unknown quantity, what new measurements should one collect in order to accomplish a given fusion task with optimal…
We show that, contrarily to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of "observable". Nonorthogonal repeatability, however, occurs…
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…
This paper is an exploration of the nuanced realm of reference frames within the framework of General Relativity. Our analysis exposes a violation of Earman's SP1 principle in scenarios involving fields that are dynamically uncoupled, a…
In this paper, we study the tedious link between the properties of sensibility and approximability of models of untyped {\lambda}-calculus. Approximability is known to be a slightly, but strictly stronger property that sensibility. However,…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
The internal calibration of a pinhole camera is given by five parameters that are combined into an upper-triangular $3\times 3$ calibration matrix. If the skew parameter is zero and the aspect ratio is equal to one, then the camera is said…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…