How many components

Topic: Principal component analysis · more questions on this topic
‹ Principal components through the singular values A low-variance predictor ›

A sample covariance matrix has eigenvalues 5.87, 1.81 and 1.32. Find the proportion of variance explained by each component and the cumulative proportions. How many components are needed to reach 80\%?

Worked answer (click to show)

Use the cumulative explained variance for the requested threshold. The individual percentages alone do not say how many components must be retained.

The total is 5.87+1.81+1.32=9.00. The proportions are 0.652, 0.201 and 0.147, and the cumulative proportions are 65.2\%, 85.3\% and 100\%. Two components are needed to reach 80\%.