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3 | 3 | in order to compress data or visualise trends in the dataset. In the archetypal |
4 | 4 | method for this dimensionality reduction, principal components analysis (PCA), |
5 | 5 | features are transformed into the latent space which best preserves the |
6 | | -variance of the original data. This module provides the Principal Covariates |
7 | | -Regression (PCovR), as introduced by [deJong1992]_, is a modification to PCA |
| 6 | +variance of the original data. |
| 7 | +
|
| 8 | +This module provides the Principal Covariates |
| 9 | +Regression (PCovR), as introduced by [deJong1992]_, which is a modification to PCA |
8 | 10 | that incorporates target information, such that the resulting embedding could |
9 | 11 | be tuned using a mixing parameter α to improve performance in regression tasks |
10 | 12 | (:math:`\alpha = 0` corresponding to linear regression and :math:`\alpha = 1` |
11 | | -corresponding to PCA). [Helfrecht2020]_ introduced the non-linear version, |
| 13 | +corresponding to PCA). Also provided is Principal Covariates Classification (PCovC), |
| 14 | +proposed in [Jorgensen2025]_, which adapts PCovR for use in classification tasks by |
| 15 | +leveraging the evidence :math:`\mathbf{Z}` as an approximation of :math:`\mathbf{Y}`. |
| 16 | +
|
| 17 | +[Helfrecht2020]_ introduced the non-linear version of PCovR, |
12 | 18 | Kernel Principal Covariates Regression (KPCovR), where the mixing parameter α |
13 | 19 | now interpolates between kernel ridge regression (:math:`\alpha = 0`) and |
14 | 20 | kernel principal components analysis (KPCA, :math:`\alpha = 1`). |
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20 | 26 | a low-dimensional projection of the feature vectors that simultaneously minimises |
21 | 27 | information loss and error in predicting the target properties using only the |
22 | 28 | latent space vectors :math:`\mathbf{T}`. |
23 | | -* :ref:`KPCovR-api` the Kernel Principal Covariates Regression |
24 | | - a kernel-based variation on the |
| 29 | +* :ref:`PCovC-api` the Principal Covariates Classification. Adapts PCovR for |
| 30 | + classification tasks, proposed in [Jorgensen2025]_. |
| 31 | +* :ref:`KPCovR-api` the Kernel Principal Covariates Regression. |
| 32 | + A kernel-based variation on the |
25 | 33 | original PCovR method, proposed in [Helfrecht2020]_. |
26 | 34 | """ |
27 | 35 |
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