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:

skfda.preprocessing.dim_reduction.variable_selection.MaximaHunting([...])	Maxima Hunting variable selection.
skfda.preprocessing.dim_reduction.variable_selection.RecursiveMaximaHunting(*)	Recursive Maxima Hunting variable selection.
skfda.preprocessing.dim_reduction.variable_selection.RKHSVariableSelection([...])	Reproducing kernel variable selection.
skfda.preprocessing.dim_reduction.variable_selection.MinimumRedundancyMaximumRelevance()	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.

skfda.preprocessing.dim_reduction.FPCA([...])	Principal component analysis.
skfda.preprocessing.dim_reduction.FPLS([...])	Functional Partial Least Squares Regression.

Difussion methods

Diffusion methods, such as functional difussion maps, try to find a natural less-dimensional manifold in which the data lives, trying to preserve the local neigborhood of the observations in the reduced space.

skfda.preprocessing.dim_reduction.DiffusionMap(*)

Functional diffusion maps.