|
|
| |
| Regularized Principal Component Analysis |
| |
Citation： |
Yonathan AFLALO,Ron KIMMEL.Regularized Principal Component Analysis[J].Chinese Annals of Mathematics B,2017,38(1):1~12 |
| Page view： 698
Net amount： 583 |
Authors： |
Yonathan AFLALO; Ron KIMMEL |
Foundation： |
This work was supported by the ERC Advanced Grant
267414. |
|
|
| Abstract： |
Given a set of signals, a classical construction of an optimal
truncatable basis for optimally representing the signals,
is the principal component analysis (PCA for short) approach.
When the information about the signals one would like to represent
is a more general property, like smoothness,
a different basis should be considered.
One example is the Fourier basis which is optimal for representation
smooth functions sampled
on regular grid.
It is derived as the eigenfunctions of the circulant Laplacian
operator. In this paper, based on the optimality of the
eigenfunctions of the Laplace-Beltrami operator (LBO for short), the
construction of PCA for geometric structures is regularized.
By assuming smoothness of a given data, one could exploit the
intrinsic geometric structure to regularize the
construction of a basis by which the observed data is represented.
The LBO can be decomposed to provide a representation space
optimized for both internal structure and external observations. The
proposed model takes the best from both the intrinsic and the
extrinsic structures of the data and
provides an optimal smooth representation of shapes and forms. |
Keywords： |
Laplace-Beltrami operator, Principal component analysis, Isometry |
Classification： |
62H25, 54C56 |
|
|
Download PDF Full-Text
|
|
|
|
