I'm struggling to find a way to solve this problem.
I have derived a $m \times n$ matrix containing in each row the Mahalanobis distance from a certain centroid. So at the end I have $m$ rows each expressing the distance of that variable from $n$ features.
Now I want to obtain another matrix such that each row of the new matrix is the measure of similarity ($\in [0,1]$) between the $i$-th variable and the $j$-th feature. Also, I want the rows of this matrix to be normalized to 1, since I want to plot each of this variable as a convex combination of a the vertices of a regular polytope. For a very naive example (the numbers are completely off my head):
$d_i = [13 \,\, 60 \,\, 4]$ $\rightarrow$ $s_i = [0.15 \,\, 0.05 \,\, 0.8]$
In such a way that I can express $x_i$ and $y_i$ as $\sum_{j=1}^ns_{ij}\,p_{x,y}$ (where $p$ is the $x$ or $y$ coordinate of a vertex).
Initially I tried $s_i = \dfrac{\dfrac{1}{d_i}}{\sum_{i=1}^n\dfrac{1}{d_i}} \, \forall i$, but then I discovered that using the reciprocal I'm loosing some propriety of the distribution. With some research I also found the RBF kernel, but after normalization I just obtain a list of values which are basically identical.
Do you have any clue on how I can achieve this?
Thanks
