Are PCA features uncorrelated?
Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The resulting vectors are an uncorrelated orthogonal basis set.
When to use a principal component analysis ( PCA )?
Assess how many principal components are needed; Interpret principal component scores and describe a subject with a high or low score; Determine when a principal component analysis should be based on the variance-covariance matrix or the correlation matrix; Use principal component scores in further analyses.
How are principal components different from factor analysis?
There are two approaches to factor extraction which stems from different approaches to variance partitioning: a) principal components analysis and b) common factor analysis. Unlike factor analysis, principal components analysis or PCA makes the assumption that there is no unique variance, the total variance is equal to common variance.
When to standardize variables in principal components analysis?
If the variables have different units of measurement, (i.e., pounds, feet, gallons, etc), or if we wish each variable to receive equal weight in the analysis, then the variables should be standardized before conducting a principal components analysis. To standardize a variable, subtract the mean and divide by the standard deviation:
How is the variance of a principal component determined?
The variance for the i th principal component is equal to the i th eigenvalue. Moreover, the principal components are uncorrelated with one another. The variance-covariance matrix may be written as a function of the eigenvalues and their corresponding eigenvectors. This is determined by the Spectral Decomposition Theorem.