My data consist ~130 observations. Each observation has several thousand features (including many collinear or otherwise useless features) and a position along a single spatial dimension. Some sets of features vary linearly with the spatial axis and I have had success selecting the spatially sensitive features with a lasso GLM with a normal distribution and identity link function, using position as response and my features as predictors.
However, I have another set of features which I believe are highly dependent on spatial position, but in a non-monotonic, perhaps piecewise-linear way. Below is plotted the first principal component of these features vs spatial position.
My idea is to linearize the data and then perform the lasso GLM fitting as normal. If this is reasonable, what is the best way to linearize the data? If not, what is an alternative approach? Maybe creating three models, one for each domain? Thank you.