diff --git a/doc/unsupervised.rst b/doc/unsupervised.rst index 2840f98..68c9d73 100644 --- a/doc/unsupervised.rst +++ b/doc/unsupervised.rst @@ -7,10 +7,15 @@ Unsupervised feature selection ============================== We can use :class:`FastCan` to do unsupervised feature selection. -The unsupervised application of :class:`FastCan` tries to select features, which -maximize the sum of the squared canonical correlation (SSC) with the principal -components (PCs) acquired from PCA (principal component analysis) of the feature -matrix :math:`X`. See the example below. +The basic idea of unsupervised feature selection is to use the learned features, +like PCA (principal component analysis), or the hand-crafted features, like Fourier +transform, as the targets and to select the features which are most correlated with +the targets. + +In PCA cases, the unsupervised application of :class:`FastCan` tries to select +features, which maximize the sum of the squared canonical correlation (SSC) with +the principal components (PCs) acquired from PCA of the feature matrix :math:`X` [1]_. +See the example below. >>> from sklearn.decomposition import PCA >>> from sklearn import datasets @@ -29,10 +34,22 @@ matrix :math:`X`. See the example below. Because :class:`FastCan` selects features in a greedy manner, which may lead to suboptimal results. +However, PCA does not take nonlinearity into consideration. +To solve the problem, targets (learned features) can be generated by manifold +learning [2]_. +Then, use :class:`FastCan` to select features, which is the same as the above. + + .. rubric:: References -* `"Automatic Selection of Optimal Structures for Population-Based - Structural Health Monitoring" `_ - Wang, T., Worden, K., Wagg, D.J., Cross, E.J., Maguire, A.E., Lin, W. - In: Conference Proceedings of the Society for Experimental Mechanics Series. - Springer, Cham. (2023). \ No newline at end of file +.. [1] `"Automatic Selection of Optimal Structures for Population-Based + Structural Health Monitoring" `_ + Wang, T., Worden, K., Wagg, D.J., Cross, E.J., Maguire, A.E., & Lin, W. + In: Conference Proceedings of the Society for Experimental Mechanics Series. + Springer, Cham. (2023). + +.. [2] `"Manifold learning-based unsupervised feature selection for structural health + monitoring" `_ + Wang, T., & Sun, L. + Materials Research Proceedings, 50, 82-89, (2025). +