Ward, k-means, and another method? I conducted both Ward and k-means clustering. The main results were the same, but some results were different, affecting the cluster's interpretation. In such cases, it would be better to report both results, but if I perform another method, and if its result is the same as the result of Ward or k-means, then either interpretation could be robust. Would you please let me know if there is any recommended third method, perhaps from recently developed methods? I would like to use methods other than traditional methods such as simple, average, complete, etc.
 A: As suggested by Tom M., my earlier comment posted as answer:
If you want to optimise the k-means objective function (which is what both k-means and Ward do), you should use the solution that gives you the better objective function value, which usually is k-means (depending on the algorithm you use; Hartigan-Wong trying out lots of different initialisations should pretty much always beat Ward). If you want to go for something different, there are lots of further methods (and I mean lots, as in hundreds, no joke). Generally the choice of method depends on what exactly your data are, aim of clustering etc., see
https://arxiv.org/abs/1503.02059
Regarding Ward vs. k-means, if you want to optimise the objective function, most likely k-means is better - better focus on improving that by trying out enough initialisations -; if you want a hierarchy for some reason, then Ward.  It is surely not wrong to present both solutions, however it really doesn't add much insight to showing just one of them, because  Ward and k-means supposedly optimise the same objective function, so the fact that they agree or about agree is to be expected anyway, and  doesn't prove the "robustness" of the clustering.
