Representation learning is a hot area in machine learning. In natural language processing (for example), learning long vectors for words has proven quite effective on several tasks. Often, these representations have several hundred dimensions. To perform a qualitative analysis of the learned representations, it helps to visualize them. Thus, we need a principled approach to drop from this high dimensional space to a lower dimensional space (like $ \mathbb{R}^2 $ for instance).

In this blog post, I will discuss the Multidimensional scaling (MDS) algorithm - a manifold learning algorithm that recovers (or at least tries to recover) the underlying manifold that contains the data.

MDS aims to find a configuration in a lower-dimension space that preserves distances between points in the data. In this post, I will provide intuition for this algorithm and an implementation for clojure (incanter).