Principle Component Analysis (PCA)

Let where we generally have . We also assume the data is normalized, that is . We wish to find the unit vector (direction) that captures the most information. Mathematically that corresponds to maximizing the following:

The above simplifies to:

When we know the Singular Value Decomposition (SVD) of , .

In general the weight vectors of are for where is the th column of in the SVD of .

Example

Go to Conduct PCA to see a worked example of conducting PCA on a given dataset.