How to cluster some object in HAC but they have same value of Cosine Similarity
With Cosine similarity, you'll probably want to stop at 0...
But of course the problem of ties can arise with any distance function, too.
But there obviously is no mathematical answer. They are all equally good. Usually, one hopes that the order does not matter. For a it doesn't, but for all other it does. Don't forget that HAC cannot guarantee to find the best solution (except for single link).
So just choose any, or even all at once. It's fairly common to choose the first found. This allows getting different versions by shuffling the data.
I want to cluster Object A with Object B or Object C. But value of Cosine Similarity Object A with Object B is 0 and Cosine Similarity Object A with Object C is 0. Before it directly clustered, I need to cluster those object step by stem, which one should be combined first Object A with B or Object A with C?