After reading about both algorithms (Principal Component analysis and Linear Discriminant analysis), I started using them combined in a way which appeared intuitive to me.
I have a data set that I project in 3D using PCA, then I cluster the projected data (e.g. using k-means clustering) and take the biggest cluster as my valid data set and the rest is considered as outliers. Then I use LDA to project my original valid data (not the PCA-projected one) into a space where the separation between classes is maximized. This model is then used to classify any new Input data later. I might also need to keep the PCA model to filter the new input data as well but this is another issue.
My question is: Is it correct to use these algorithms in this way? Or would you suggest a different approach?