The Bregman chord divergence

Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of testing one by one the entries of an ever-expanding dictionary of {\em ad hoc} distances, one rather prefers to consider parametric classes of distances that are exhaustively characterized by axioms derived from first principles. Bregman divergences are such a class. However fine-tuning a Bregman divergence is delicate since it requires to smoothly adjust a functional generator. In this work, we propose an extension of Bregman divergences called the Bregman chord divergences. This new class of distances does not require gradient calculations, uses two scalar parameters that can be easily tailored in applications, and generalizes asymptotically Bregman divergences.Comment: 10 page

Glosarium Matematika

273 p.; 24 cm

Indoor localization utilizing existing infrastructure in smart homes : a thesis by publications presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Computer and Electronics Engineering, Massey University, Albany, New Zealand

Listed in 2019 Dean's List of Exceptional ThesesIndoor positioning system (IPS) have received significant interest from the research community over the past decade. However, this has not eventuated into widespread adoption of IPS and few commercial solutions exist. Integration into Smart Homes could allow for secondary services including location-based services, targeted user experiences and intrusion detection, to be enabled using the existing underlying infrastructure. Since New Zealand has an aging population, we must ensure that the elderly are well looked after. An IPS solution could detect whether a person has been immobile for an extended period and alert medical personnel. A major shortcoming of existing IPS is their reliance on end-users to undertake a significant infrastructure investment to facilitate the localization tasks. An IPS that does not require extensive installation and calibration procedures, could potentially see significant uptake from end users. In order to expedite the widespread adoption of IPS technology, this thesis focuses on four major areas of improvement, namely: infrastructure reuse, reduced node density, algorithm improvement and reduced end user calibration requirements. The work presented demonstrates the feasibility of utilizing existing wireless and lighting infrastructure for positioning and implements novel spring-relaxation and potential fields-based localization approaches that allow for robust target tracking, with minimal calibration requirements. The developed novel localization algorithms are benchmarked against the existing state of the art and show superior performance

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282