Nonparametric time dependent principal components analysis

Principal Component Analysis (PCA) is a popular data reduction technique widely used in data mining. It is common to ignore any existing time component of the data when performing PCA. One way of incorporating this dimension is to perform PCA for the data at each such point. The disadvantage of this approach is that there may not be enough data at each time point. We overcome this by using a smoothed covariance or correlation matrix and by the choice of bandwidth we control the amount of neighbouring data contributing to the calculation. Permutations are used to construct reference bands to test whether there is a time effect. If there is a time effect then performing PCA as a data reduction technique is inappropriate. Nonetheless the smoothed loadings of the principal components deemed to account for most of the variation in the data may give one insight into the structure of the data. The techniques are illustrated using aircraft development data.