Dimensionality Reduction#
When dealing with data samples with high dimensionality, we often need to reduce the dimensions so we can better observe the data.
Variable selection#
One approach to reduce the dimensionality of the data is to select a subset of the original variables or features. This approach is called variable selection. In FDA, this means evaluating the function at a small number of points. These evaluations would be the selected features of the functional datum.
The variable selection transformers implemented in scikit-fda are the following:
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Maxima Hunting variable selection. |
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Recursive Maxima Hunting variable selection. |
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Reproducing kernel variable selection. |
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Minimum redundancy maximum relevance (mRMR) method. |
Feature extraction#
Other dimensionality reduction methods construct new features from existing ones. For example, in functional principal component analysis, we project the data samples into a smaller sample of functions that preserve most of the original variance. Similarly, in functional partial least squares, we project the data samples into a smaller sample of functions that preserve most of the covariance between the two data blocks.
Principal component analysis. |
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Functional Partial Least Squares Regression. |