What is the process that can be used opposite to that of dimensionality reduction?

Hi, I want to know, how to retrieve the original data after the dimensionality reduction has been done?, that is the opposite of this dimensionality reduction. So that we check whether the retrieved data is same.Is there other toolbox or the same toolbox can be used. Thank you.

Answer 1

[Nath]

I assume your dimension-reduction model matricially writes Y= X*B + Z With observable data Y, unknown factors X and weights B, and error term Z. The data fitered by your model writes Yfilter= X*B, so you can compare each column of Y to the corresponding column of X*B

[RUPESH]

Thanks for your response, but my question was to know that : If let X is the data set used and Y is the reduced dataset of intrinsic dim. 'd'. Then how can we retrieve the X from Y.?? Waiting for reply.. Thanks.