@@ -7,10 +7,15 @@ Unsupervised feature selection
77==============================
88
99We can use :class: `FastCan ` to do unsupervised feature selection.
10- The unsupervised application of :class: `FastCan ` tries to select features, which
11- maximize the sum of the squared canonical correlation (SSC) with the principal
12- components (PCs) acquired from PCA (principal component analysis) of the feature
13- matrix :math: `X`. See the example below.
10+ The basic idea of unsupervised feature selection is to use the learned features,
11+ like PCA (principal component analysis), or the hand-crafted features, like Fourier
12+ transform, as the targets and to select the features which are most correlated with
13+ the targets.
14+
15+ In PCA cases, the unsupervised application of :class: `FastCan ` tries to select
16+ features, which maximize the sum of the squared canonical correlation (SSC) with
17+ the principal components (PCs) acquired from PCA of the feature matrix :math: `X` [1 ]_.
18+ See the example below.
1419
1520 >>> from sklearn.decomposition import PCA
1621 >>> from sklearn import datasets
@@ -29,10 +34,22 @@ matrix :math:`X`. See the example below.
2934 Because :class: `FastCan ` selects features in a greedy manner, which may lead to
3035 suboptimal results.
3136
37+ However, PCA does not take nonlinearity into consideration.
38+ To solve the problem, targets (learned features) can be generated by manifold
39+ learning [2 ]_.
40+ Then, use :class: `FastCan ` to select features, which is the same as the above.
41+
42+
3243.. rubric :: References
3344
34- * `"Automatic Selection of Optimal Structures for Population-Based
35- Structural Health Monitoring" <https://doi.org/10.1007/978-3-031-34946-1_10> `_
36- Wang, T., Worden, K., Wagg, D.J., Cross, E.J., Maguire, A.E., Lin, W.
37- In: Conference Proceedings of the Society for Experimental Mechanics Series.
38- Springer, Cham. (2023).
45+ .. [1 ] `"Automatic Selection of Optimal Structures for Population-Based
46+ Structural Health Monitoring" <https://doi.org/10.1007/978-3-031-34946-1_10> `_
47+ Wang, T., Worden, K., Wagg, D.J., Cross, E.J., Maguire, A.E., & Lin, W.
48+ In: Conference Proceedings of the Society for Experimental Mechanics Series.
49+ Springer, Cham. (2023).
50+
51+ .. [2 ] `"Manifold learning-based unsupervised feature selection for structural health
52+ monitoring" <https://mrforum.com/wp-content/uploads/open_access/9781644903513/9.pdf> `_
53+ Wang, T., & Sun, L.
54+ Materials Research Proceedings, 50, 82-89, (2025).
55+
0 commit comments