FPCA

[aroarmath]

Hi! I am exploring the library to work with functional principal components. I have seen how to calculate them, but I can't find the way to express the data based on two of the components for example. Could you help me?

[vnmabus]

Hello there! The transform method of the FPCA class gives the coefficients of each curve (with the mean subtracted) in the basis of the principal components.

You can recover a smoothed version of the original curve expressing the linear combination manually (we should probably add a method for this in the future):

import skfda

X, y = skfda.datasets.fetch_weather(return_X_y=True)
X = X.coordinates[0]

fpca = skfda.preprocessing.dim_reduction.feature_extraction.FPCA(n_components=5)
transf = fpca.fit_transform(X)

fig = X[0].plot()
(fpca.mean_ + (fpca.components_ * transf[0]).sum()).plot(fig=fig).show()

[vnmabus]

Well, once you transform your data you have a vector of n_components features. You can use the scatter function in Matplotlib to represent the two first coefficients in a scatterplot, or use another visualization method for multivariate data. See https://stackoverflow.com/questions/39216897/plot-pca-loadings-and-loading-in-biplot-in-sklearn-like-rs-autoplot for an example in scikit-learn which should be similar.

[aroarmath]

And if we have functional data, could we have this kind of representation? Because de n_componentes obtained from a fpca method has not the same type of a multivariate method.

[aroarmath]

Sorry, yesterday I uploaded a multivariate example, but this one is for functional data
https://www.google.com/url?sa=t&source=web&rct=j&url=https://dialnet.unirioja.es/descarga/articulo/6765740.pdf&ved=2ahUKEwixrtXiiIXyAhW86uAKHW_dDMkQFjAKegQIBxAC&usg=AOvVaw2QDUrdtHpwZuFV7RBQ6Eqx

[vnmabus]

You mean the "Análisis de correspondencias" graph? Isn't it a scatterplot of the coefficients of the first two principal components?
An example of the thing I was proposing is the following:

import skfda
import matplotlib.pyplot as plt

X, y = skfda.datasets.fetch_weather(return_X_y=True)
X = X.coordinates[0]

fpca = skfda.preprocessing.dim_reduction.feature_extraction.FPCA(n_components=2)
transf = fpca.fit_transform(X)

plt.scatter(transf[:, 0], transf[:, 1])
for i, txt in enumerate(X.sample_names):
    plt.annotate(txt, (transf[i, 0], transf[i, 1]))
plt.show()

[aroarmath]

It was really helpfull, thanks for all coments 😊😊😊