ESSENTIAL STEPS OF PRINCIPAL COMPONENT ANALYSIS

	nxp DATA MATRIX

Covariance Matrix, S		Correlation Matrix, R

Get eigenvalues (l₁, l₂, …, l_p) and eigenvectors (a₁, a₂, …, a_p)

Proportion of total variation explained by the jth principal component is l_j/tr(S)		Proportion of total variation explained by the jth principal component is l_j/p

Rescale principal components (a_i^*= l_i^1/2 a_i)

		Correlation between ith variable and jth principal component is a_ji^*

Choose the number of principal components

Select a percentage of the total variation that could be explained (70%-90%) Retain just enough components to attain this level	Exclude principal components whose eigenvalues are less than tr(S)/p (for S) 1 (for R)		Plot variance of components vs component number (Scree plot) Select the components based on the “elbow” in the curve.

Produce various plots including principal component score i vs j, biplots to understand what is going on.