Since I consider Unsupervised learning, I don't have any ground truth to compare with, during the validation phase. So, is there any standard method to deal with it?
Additional informations:
I realize this comes very late, but perhaps it is still useful for anyone looking into the same subject and coming across this question. I don't believe there is a standard method, as you ask. However, I worked on this about two years ago for my MSc thesis in Statistical Science: https://www.universiteitleiden.nl/binaries/content/assets/science/mi/scripties/statscience/2017-2018/2018_08_27_masterthesis_debakker.pdf. I think Chapter 2.4 (page 18-30) might be of interest with regard to your question and the following is about/in that chapter.
I worked out a v-fold cross-validation scheme to optimize a generic value for k, the number of clusters to look for in a data set. I reviewed and used/adapted several existing validation indices to measure "goodness of fit" of a clustering; many exist since, as you pointed out, there is no ground thruth in unsupervised learning, so there is no standard way to measure how well a clustering looking for a certain k number of clusters is doing. See also the literature study in my thesis, if you want an overview (note it's two years old by now and I have not followed the literature since). A personal favourite is Prediction Strength by Tibshirani and Walther (https://doi.org/10.1198/106186005X59243). In principle, any such cluster number validation index could in theory be implemented in the framework I designed (see image below, from thesis page 30).
Subsequently I applied this method to a data set I had at hand back then, but that will be of less interest for you, I assume.
I'm not sure if it will be considered and answer as in fact is a pointer to a possible answer, but at the same time, I don't have enough reputation to add it as a comment. So it will go here, maybe someone with more rights can move it as comment.
I'm struggling with this theme too and today I found this PhD thesis
"CROSS-VALIDATION FOR UNSUPERVISED LEARNING" by Patrick O. Perry September 2009 - Stanford University in the abstract the author states
This thesis discusses some extensions of cross-validation to unsupervised learning, specifically focusing on the problem of choosing how many principal components to keep. We introduce the latent factor model, define an objective criterion, and show how CV can be used to estimate the intrinsic dimensionality of a data set. Through both simulation and theory, we demonstrate that cross-validation is a valuable tool for unsupervised learning.
