Why does k-fold cross validations help obtain stable clustering results? Why applying k-fold cross validation helps obtaining stable clustering results in unsupervised learning? How is this done? Thanks
 A: I'm not completely sure what information you are asking for exactly, so I'll  just give the explanation I think might help you most. 
$K$ fold cross validation trains a model $K$ times, using different evaluation data each time (that has not been seen by the model during training). Therefore your $K$ results from your $K$ models will be different. This does not cause the model(s) to be more stable than without doing CV (actually, after doing CV you usually train the model again using all training data) - but it will give you information about how stable your model(s) are. For example, obtaining the same clusters $N$ times would ensure you in your models being more stable than if you would obtain very different clusters each time.
This is similar to models in supervised ML problems, where your $K$ results give you an idea of the variance of your error when training such a model multiple times (e.g. by choosing an easy test partition by chance will give you better results, while being unlucky and choosing a difficult test partition by chance will have worse results). Therefore, the more such resamples you have, the more information you have about the stability of the model, which helps in estimating how likely you just get a good or bad model. This is also one of the reasons why repeated $K$ fold cross validation is frequently preferred over simple cross validation. 
