Dimension Reduction

Sanjiv R. Das

NCAA dataset

A Matrix Reduction

Suppose we reduce the $k=11$ dimensional feature space $X$ to reduced factor space $R$ with $k=3$. We translate with a matrix $L$.

$$ R = X \cdot L $$

where $F$ is $(64 \times 3)$, $X$ is $(64 \times 11)$, and $L$ is $(11 \times 3)$.

Where does matrix L come from?

$$ \lambda l = C \cdot l $$

Principal Components Analysis (PCA)

Treasury Rates Dataset

Clearly, all interest rates are driven by one major component!