Boost Your Data Analysis: Handy pandas Tricks and PCA on the DAX30 Index

1. A pandas trick

apply() and applymap() are functions for DataFrame objects, while map() works on Series. apply() operates on a whole column or row, applymap() works element‑wise on every cell, and map() also applies a function element‑wise to each Series value.

2. PCA decomposition of the German DAX30 index

The DAX30 consists of thirty stocks; performing principal component analysis (PCA) helps identify the most important stocks. PCA finds the components that explain the most variance, involving matrix decomposition such as SVD.

Here is some code:

These plots show the contribution of the top ten stocks to the DAX30 index.

Using only the first component or the first five components yields surprisingly good results, effectively reducing dimensionality. Further visualizations illustrate the PCA effect.

We plot the PCA‑transformed values against the original values in a scatter plot.

The overall effect is good, though there are some issues at the edges and middle; segmenting the PCA in the middle could improve results.