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This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric.…
We investigate the construction of prefix-free and fix-free codes with specified codeword compositions. We present a polynomial time algorithm which constructs a fix-free code with the same codeword compositions as a given code for a…
The Fermat distance has been recently established as a useful tool for machine learning tasks when a natural distance is not directly available to the practitioner or to improve the results given by Euclidean distances by exploding the…
A novel class of derivative-free optimization algorithms is developed. The main idea is to utilize certain non-commutative maps in order to approximate the gradient of the objective function. Convergence properties of the novel algorithms…
In this paper, we analyze $m$-dimensional ($m$D) convolutional codes with finite support, viewed as a natural generalization of one-dimensional (1D) convolutional codes to higher dimensions. An $m$D convolutional code with finite support…
Convolutional networks are one of the most widely employed architectures in computer vision and machine learning. In order to leverage their ability to learn complex functions, large amounts of data are required for training. Training a…
Many state-of-the-art computer vision algorithms use large scale convolutional neural networks (CNNs) as basic building blocks. These CNNs are known for their huge number of parameters, high redundancy in weights, and tremendous computing…
Robots are notoriously difficult to design because of complex interdependencies between their physical structure, sensory and motor layouts, and behavior. Despite this, almost every detail of every robot built to date has been manually…
The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both…
We explore fairness from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We…
Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which…
The Chord algorithm is a popular, simple method for the succinct approximation of curves, which is widely used, under different names, in a variety of areas, such as, multiobjective and parametric optimization, computational geometry, and…
To operate reactively in uncertain environments, robots need to be able to quickly estimate the risk that they will collide with their environment. This ability is important for both planning (to ensure that plans maintain acceptable levels…
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
This paper investigates the concept of self-dual convolutional code. We derive the basic properties of this interesting class of codes and we show how some of the techniques to construct self-dual linear block codes generalize to self-dual…
We survey theoretical, algorithmic, and computational results at the intersection of distance geometry problems and mathematical programming, both with and without adjacencies as part of the input. While mathematical programming methods can…
Classical machine learning approaches are sensitive to non-stationarity. Transfer learning can address non-stationarity by sharing knowledge from one system to another, however, in areas like machine prognostics and defense, data is…
This paper presents the generalization of weighted distances to modules and their computation through the chamfer algorithm on general point lattices. The first part is dedicated to formalization of definitions and properties (distance,…
Maximum-distance separable (MDS) convolutional codes form an optimal family of convolutional codes, the study of which is of great importance. There are very few general algebraic constructions of MDS convolutional codes. In this paper, we…