How to equalize the pairwise affinity perplexities when implementing t-SNE?
It simply means that you should set the bandwidths through binary search. The way it works is that you start with a preset target perplexity (Mark's link suggests values from 5 to 50 as reasonable values), and bounds for the bandwidth. If the target perplexity is inside the interval defined by the boundary perplexities, you iteratively halve the search space until you converge to the target:

$$2^{H(p; \sigma_L)} &lt; PP_\mathrm{target} &lt; 2^{H(p; \sigma_U)}$$

If the target was not in the initial interval, you expand the interval and try again.