We collected hygiene data from six cluster of Northern Bangladesh. We want see the variations among the clusters? Can we go for K-Means cluster analysis?
Yes, definitely. Also you may use statistical methods, e.g., variational methods of von Misses clustering/classification, clustering on Bingham distributions or Kent or Fisher distribution etc.
K means can be used to explore the variations or to be more specific, data cluster variances... in other words.. to analyze which parts of data cluster due to their variances similarity and distance to the means of those clusters. It should be kept in mind that K means is a parametric Unsupervised machine learning approach...so there are parametric assumptions that come with it....
If the clusters are obtained by different algorithms, the criteria will indicate different ways of forming clusters. In the case of a good cluster structure, different algorithms will give approximately the same result. And vice versa - getting different results by different algorithms indicates classification problems.
When you are using a dataset, for example any dataset from UCI repository, the clusters of the dataset are known. When you use this for any new algorithm developed then first you have to train the model by taking 70% or 80% of the data. Then you have to test the trained model using the rest 30% or 20% data left.
So, basically you are clustering it. The accuracy or any such measure will determine the efficiency of your algorithm.