How to make similarity matrix from two distributions? I have two different distributions, first has studentIDs as columns and features in row. 
First Distribution
feat.   std1    std2    std3    std4
nose    3.0cm   3.5cm   2.9cm   3.1cm
height  170cm   173cm   167cm   165cm
hair    5.0cm   20cm    7.0cm   2.0cm

Second distribution has more details about features, lets say about hair.
Second Distribution
hair    std1    std2    std3    std4
thick   .01mm   0.2mm   0.12mm  0.22mm
density (per sq cm) 500 650 200 900
root    3mm 2.9mm   3.1mm   3mm

Is it possible to make similarity matrix for the feature hair among different students? Meaning, how distant std1 is from std3 based on feature hair ?
 A: There's no way to do this without making an arbitrary assumption about the relative importance of your variables (thick, density, root, etc.) in determining the degree of difference between students.  If you are willing to make such assumptions however, then yes, it's possible.
One simple thing to do is treat all the variables equally. In that case, start by normalizing the range of values for each variable independently so that they each lie between [0, 1].  For example, if you have a variable $v$ (which could represent thick, density, root, or whatever), then calculate the normalized value as follows: v = (v - min(v)) / (max(v)-min(v)).
After you have normalized the variables, each student ID then has an $N$ component vector associated with it.  Each component corresponds to exactly one of the original variables (thick, density, root, etc.) and each component lies on the interval [0,1].
Once you have these vectors, simply calculate the "distance" between any two students as the $N$-dimensional Euclidian distance between them, in this new $N$-dimensional space.  For example, the distance $D_{ij}$ between student $i$ and student $j$, for a vector of $k$ normalized variables, would be $$D_{ij} = \sqrt{\sum_{k=1}^{N} (v_{ik} - v_{jk})^{2}}$$
This procedure will definitely give you an "answer", in some sense; just be sure to bear in mind of course that you are making a hidden assumption (i.e., that all the variables do indeed deserve equal weight) in order to get there.
