3. Feature redundancy#
FastCan can effectively skip the linearly redundant features.
Here a feature \(x_r\in \mathbb{R}^{N\times 1}\) is linearly
redundant to a set of features \(X\in \mathbb{R}^{N\times n}\) means that
\(x_r\) can be obtained from an affine transformation of \(X\), given by
where \(a\in \mathbb{R}^{n\times 1}\) and \(b\in \mathbb{R}^{N\times 1}\). In other words, the feature can be acquired by a linear transformation of \(X\), i.e. \(Xa\), and a translation, i.e. \(+b\).
This capability of FastCan is benefited from the
Modified Gram-Schmidt,
which gives large rounding-errors when linearly redundant features appears.
References
“Canonical-correlation-based fast feature selection for structural health monitoring” Zhang, S., Wang, T., Worden, K., Sun L., & Cross, E. J. Mechanical Systems and Signal Processing, 223, 111895 (2025).
Examples
See Performance on redundant features for an example of feature selection on datasets with redundant features.