Visualizing Data Velocity using DSNE

We present a new technique called "DSNE" which learns the velocity embeddings of low dimensional map points when given the high-dimensional data points with its velocities. The technique is a variation of Stochastic Neighbor Embedding, which uses the Euclidean distance on the unit sphere between the unit-length velocity of the point and the unit-length direction from the point to its near neighbors to define similarities, and try to match the two kinds of similarities in the high dimension space and low dimension space to find the velocity embeddings on the low dimension space. DSNE can help to visualize how the data points move in the high dimension space by presenting the movements in two or three dimensions space. It is helpful for understanding the mechanism of cell differentiation and embryo development.