What is the difference between t-SNE and plain SNE? T-Distributed Stochastic Neighbor Embedding (t-SNE) is a (prize-winning) technique for dimensionality reduction that is particularly well suited for the visualization of high-dimensional datasets.
What is the difference between t-SNE and Stochastic Neighbor Embedding (SNE)?
 A: Actually, I find that because the t-Distribution is a long tail distribution, it prevents the crowding problem (which is one of the disadvantages of SNE).
A: You can also watch this lecture from 17:48 to 20:12 to hear the reason with a great example from the author of t-SNE.
A: The cluster structure produced by tSNE tend to be more separated, to have more stable shape; and be more repeatable.
A: We are learning a topological structure here. So mapping the neighbors in the lower dimension is the necessary and fundamental objective of SNE. Note that, in lower dimension we don't have much space to accommodate all the neighbors.
for motivation note that, we can accommodate maximum $n+1$ equidistant points in a $n$ dimensional space. So, what will a basic SNE algorithm do is collapse all the equidistant point to one point in lower dimension. This phenomenon is called Crowding probelm.
To mitigate this problem t-distribution was suggested. As it has a heavy tail it allows those points suffering from the crowding problem to be placed in a somewhat distant place (but not too much).
