Overview of the Multivariate Embedding Platform

The Multivariate Embedding platform performs dimension reduction, which maps points from a high-dimensional space, {x1, x2,..., xn}, to points in a low-dimensional space, {y1, y2,..., yn}. The goal of dimension reduction is to map points to the lower dimension while still retaining the important information present in the high-dimensional data. The specific technique used in the Multivariate Embedding platform is the t-Distributed Stochastic Neighbor Embedding (t-SNE) method. This is a variation of Stochastic Neighbor Embedding (Hinton and Roweis, 2002).

The t-SNE method is based on the pairwise similarities between points. Each pairwise similarity is represented by the conditional probability that two points are neighbors. In the high-dimensional space, the distances are converted into conditional probabilities using the Gaussian distribution. In the low-dimensional map, the distances are converted into probabilities using the Student’s t distribution with one degree of freedom. This is where the t-SNE method gets its name (van der Maaten and Hinton, 2008).

For a good low-dimensional mapping, the pairwise similarity between {xi, xj} in the high-dimensional space is the same as the pairwise similarity between {yi, yj} in the low-dimensional space. Under this assumption, the t-SNE method finds a low-dimensional mapping that minimizes the difference between the high-dimensional similarity and the low-dimensional similarity. The difference is measured using a version of the Kullback-Leibler divergence, which is then minimized using gradient descent. For more information about the t-SNE method, see Statistical Details for the Multivariate Embedding Platform.