Performing PCA in Python

In this exercise, we will use Python to perform PCA on a given data matrix.

Steps

1. Determine the standardized data matrix Z.
2. Deduce the correlation matrix RX.
3. Determine the spectrum of RX.
4. Deduce the principle components matrix CX.
5. Decide how many principle components we should retain. Justify your decision.
6. Say whether we were able to predict the result of PCA earlier.

Implementation

The exercise was implemented using the numpy and scikit-learn libraries in Python.

Conclusion

In this exercise, we have learned how to perform PCA in Python and how to determine the optimal number of principal components to retain.