Principal component analysis
One of the most commonly used methods of dimensionality reduction is Principal Component Analysis (PCA). Conceptually, PCA computes the axes along which the variation in the data is greatest. You may recall that in Chapter 3, Finding Patterns in the Noise – Clustering and Unsupervised Learning, we calculated the eigenvalues of the adjacency matrix of a dataset to perform spectral clustering. In PCA, we also want to find the eigenvalue of the dataset, but here, instead of any adjacency matrix, we will use the covariance matrix of the data, which is the relative variation within and between columns. The covariance for columns xi and xj in the data matrix X is given by:
This is the average product of the offsets from the ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Read now
Unlock full access