Euclidean Distance Matrices: Essential theory, algorithms, and applications

Euclidean distance matrices (EDMs) are matrices of the squared distances between points. The definition is deceivingly simple; thanks to their many useful properties, they have found applications in psychometrics, crystallography, machine learning, wireless sensor networks, acoustics, and more. Despite the usefulness of EDMs, they seem to be insufficiently known in the signal processing community. Our goal is to rectify this mishap in a concise tutorial. We review the fundamental properties of EDMs, such as rank or (non)definiteness, and show how the various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, we demonstrate applications to microphone…

• NS
  National Science Foundation
• Q
  Qualcomm
• MR
  Microsoft Research
• SU
  Sveučilište u Zagrebu
• ÉP
  École Polytechnique Fédérale de Lausanne
• SN
  Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung