How to compute minimum required VC dimension for a classifer to classify a specific data Suppose we're given an N dimensional data to classify. To cope with this task we may choose a classifier that suits our desires more. However obviously not every classifier is capable of classifying every data for many reasons including its VCD. Now I want to know is there a way to compute the minimum required VC-dimension for a classifier(Hypothesis) to classify a specific data?
As an example to make my question more clear, a classifier having VC-dimension of 2 is not capable of shattering this data set:
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 A: In general I don't think this is going to be possible (let alone useful). Recall that VC-dimension is an existence property, i.e., for some hypothesis class $H$,  $\text{VCdim}(H) = d$ if there exists some set $X \subseteq \mathcal{X}$ such that $|X| = d$ and $H$ shatters $X$ and there does not exist a set of size $> d$ which is shattered by $H$. Importantly, this does not mean every set of size $d$ is shattered, just at least one. 
To understand the difference let's take the canonical example where $H$ is the set of lines in 2d space. Then we know $\text{VCdim}(H) = 3$. To show this we first appeal to Radon's theorem to show $\text{VCdim}(h) < 4$. Next we observe that 3 points arranged in a triangle can be shatter by lines. Notice how this doesn't mean every set of three points in shattered. Indeed, no set of three collinear points can be shattered by lines.
I think to actually know if some hypothesis class shatters a specific set of points you would just need to try (unless you can make some special assumptions about the points).
Lastly, and most importantly, the process you are considering is seriously flawed. If you observe a set of points and then pick a hypothesis class that ensures this set of points is shattered, you throw away any VC style bounds you might get. For those type of bounds to hold you need to pick your hypothesis class before observing the data. What you propose actually results in a hypothesis class with infinite VC-dimension, since you just keep considering more and more complex hypothesis classes until you shatter the observed data. At this point you might as well be using a 1 nearest neighbor classifier.
