Sparse Inductive Embedding: An Explorative Data Visualization Technique

Metric Multi-Dimensional Scaling is one of the most popular visualization techniques aiming to determine a point configuration of the data in a low-dimensional space, while preserving the original pairwise dissimilarities amongst the data points. In this paper we propose Sparse Inductive Multi- Dimensional Scaling approach, an exploratory data analysis and visualization tool. Its kernel-based nature provides an inductive method, and hence allows for embedding of previously unseen data even with non-numerical features. Furthermore, via the use of a sparsity-promoting regularizer, the technique is capable of identifying key training samples, whose contribution in defining the embedded manifold's specific structure is most influential. As we will show, the influence of these samples leads us to interesting interpretations in the context of the data at hand. We adequately train the consequent non-convex framework via an Iterative Majorization approach, for which a stable closed-form solution is obtained. Experimental results showcase the potential benefits of the proposed embedding method on both artificial and real-world data.