A comprehensive look at coding techniques on Riemannian manifolds

Masoud Faraki, Mehrtash T. Harandi, Fatih Porikli

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


Core to many learning pipelines is visual recognition such as image and video classification. In such applications, having a compact yet rich and informative representation plays a pivotal role. An underlying assumption in traditional coding schemes [e.g., sparse coding (SC)] is that the data geometrically comply with the Euclidean space. In other words, the data are presented to the algorithm in vector form and Euclidean axioms are fulfilled. This is of course restrictive in machine learning, computer vision, and signal processing, as shown by a large number of recent studies. This paper takes a further step and provides a comprehensive mathematical framework to perform coding in curved and non-Euclidean spaces, i.e., Riemannian manifolds. To this end, we start by the simplest form of coding, namely, bag of words. Then, inspired by the success of vector of locally aggregated descriptors in addressing computer vision problems, we will introduce its Riemannian extensions. Finally, we study Riemannian form of SC, locality-constrained linear coding, and collaborative coding. Through rigorous tests, we demonstrate the superior performance of our Riemannian coding schemes against the state-of-the-art methods on several visual classification tasks, including head pose classification, video-based face recognition, and dynamic scene recognition.

Original languageEnglish
Pages (from-to)5701-5712
Number of pages12
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number11
Publication statusPublished - Nov 2018
Externally publishedYes


  • Australia
  • Bag of words (BoW)
  • collaborative coding (CC)
  • Encoding
  • Geometry
  • Level measurement
  • locality-constrained linear coding (LLC)
  • Manifolds
  • Riemannian geometry
  • sparse coding (SC)
  • Task analysis
  • vector of locally aggregated descriptors (VLADs).

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