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From basis functions to basis fields: vector field approximation from sparse data.

F A Mussa-Ivaldi1

  • 1Department of Brain and Cognitive Sciences, Massachussetts Institute of Technology, Cambridge 02139.

Biological Cybernetics
|January 1, 1992
PubMed
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Living organisms process sensory information using vector-valued mappings, not just real-valued functions. This study introduces "basis fields" for efficient and coordinate-invariant vector-field representation in computational models.

Area of Science:

  • Computational neuroscience
  • Machine learning
  • Vector field analysis

Background:

  • Learning problems often involve reconstructing real-valued functions from sparse data.
  • Biological systems process sensory information using complex vector-valued mappings, such as optical flow and force fields.
  • Existing methods for vector-valued mappings can be dependent on coordinate systems.

Purpose of the Study:

  • To explore vector-field processing from a computational viewpoint.
  • To introduce a novel representation for vector patterns using "basis fields".
  • To demonstrate the advantages of basis fields over component-based representations.

Main Methods:

  • Proposed a representation of vector patterns using linear combinations of "basis fields".

Related Experiment Videos

  • Analyzed the properties of these basis fields in representing vector-valued mappings.
  • Investigated the invariance of this representation under coordinate transformations.

    • Main Results:

    • A variety of vector patterns can be efficiently represented by basis fields.
    • Basis fields provide a coordinate-invariant representation, unlike component-based methods.
    • This approach offers a potentially superior alternative for specific vector-field processing tasks.

    Conclusions:

    • Basis fields offer an efficient and robust method for representing vector-valued mappings.
    • This representation is invariant to coordinate changes, a significant advantage for biological and computational systems.
    • The concept of basis fields advances the computational understanding of how organisms process complex sensory information.