Skip to content

FRM Part I · FRM Exam Part I · Machine Learning and Prediction

An analyst runs PCA on three unstandardized variables whose variances are 100, 4 and 1, with small covariances between them. The analyst notices the first principal component is almost identical to the first variable. What is the most appropriate explanation and remedy?

The first variable dominates because PCA is scale-sensitive and its variance of 100 is far larger than the others. The usual remedy is to standardize the variables to unit variance, effectively using the correlation matrix, before extracting components.

  1. APCA is sensitive to scale, so the high-variance variable dominates; standardize the variables before applying PCACorrect
  2. BThe first variable is the only one that contains information, so the other two should be discarded without further analysis
  3. CPrincipal components are always aligned to the original variables; no remedy is needed
  4. DThe covariances are too small, so the analyst should add a constant to each variable to raise them

Explanation

PCA maximizes variance, so a variable measured on a much larger scale dominates the first component. Standardizing to unit variance (using the correlation matrix) puts the variables on equal footing. Adding constants does not change variances or covariances, and low variance does not imply no information.

Did you get it right without looking?

One question tells you little. A timed set on Machine Learning and Prediction shows your real accuracy, how long you take and where you lose marks.

Practise Machine Learning and PredictionFree diagnostic mock

More Machine Learning and Prediction questions