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The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…
The 3D depth estimation and relative pose estimation problem within a decentralized architecture is a challenging problem that arises in missions that require coordination among multiple vision-controlled robots. The depth estimation…
With the recent development of technology, wireless sensor networks (WSN) are becoming an important part of many applications. Knowing the exact location of each sensor in the network is very important issue. Therefore, the localization…
Robot localization is an inverse problem of finding a robot's pose using a map and sensor measurements. In recent years, Invertible Neural Networks (INNs) have successfully solved ambiguous inverse problems in various fields. This paper…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
This work deals with a practical everyday problem: stable object placement on flat surfaces starting from unknown initial poses. Common object-placing approaches require either complete scene specifications or extrinsic sensor measurements,…
Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
An unknown-position sensor can be localized if there are three or more anchors making time-of-arrival (TOA) measurements of a signal from it. However, the location errors can be very large due to the fact that some of the measurements are…
Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordant barrier. We give a suitable generalization of…
Image registration is a process of aligning two or more images of same objects using geometric transformation. Most of the existing approaches work on the assumption of location invariance. These approaches require object-centric images to…
Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…
We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM,…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
Accurate localization in diverse environments is a fundamental challenge in computer vision and robotics. The task involves determining a sensor's precise position and orientation, typically a camera, within a given space. Traditional…
This paper studies the problem of determining the sensor locations in a large sensor network using relative distance (range) measurements only. Our work follows from a seminal paper by Khan et al. [1] where a distributed algorithm, known as…
We consider the problem of localizing wireless devices in an ad-hoc network embedded in a d-dimensional Euclidean space. Obtaining a good estimation of where wireless devices are located is crucial in wireless network applications including…
Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice,…