I am interested in clustering daily gridded data.
Because of the many dimensions (gridpoints), I first perform PCA to reduce the dimensionality and keep the n-first PCs that account for at least 85% of the variation of the actual data. Then I use these n PCs as inputs to k-Means clustering.
My question is if I should use the standardized (mean=0, std=1) PCs as inputs to the k_Means clustering, or adjust the PCs based on the % of total variation that each PC accounts for. The adjustment can be something like PC[i] * Variation[i] /sum(Variation)
The 1st option results in PCs with the same variance, thus the clustering is unbiased. The 2nd option will end up with a bias towards the PCs that explain most of the variation.
Based on my understanding it is better to work with unbiased data. Nevertheless, in the case of PCA, the PCs are by default of varying importance. Would this support the use of the adjusted PCs?