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Geometric aspects of least squares smoothing

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1 Author(s)
Hauser, A.A. ; Sperry Gyroscope Co., Great Neck, N.Y.

An understanding of the operation of a least squares smoother is enhanced by establishing an m-dimensional space in which inputs and outputs are vectors and the smoother is a transformation. The concept of transmission and rejection manifold as established by Zadeh is introduced and the manner in which signal and noise are separated is illustrated geometrically. An explicit pictorial representation of the process is given for the three dimensional case.

Published in:

Proceedings of the IRE  (Volume:42 ,  Issue: 4 )