Weighted PCA

[hamster-on-wheels]

All observations form a matrix X where each row is one observation and each column is one feature.
Each observation also has a weight w_i, which means the observation has occurred for w_i times.
For example, a weight of 2 means the same observation actually occurs for twice.

Can I do weighted sparse PCA by the following method?

1. Center each column of X by weighted average with w_i as weights.
2. Form matrix Y by multiplying each row of X by square root of w_i.
3. Calculate (robust) sparse PCA of Y with ristretto, which provides matrices A and B.
4. The matrix X is approximately XBA^T, where A^T is transpose of A.

Thank you.