Seminar Details
2017-12-12 (14:00) : Positive semi-definite embedding for dimensionality reduction and out-of-sample extensions
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Michaël Fanuel (UCL)
Abstract :
Dimensionality reduction of data is often an important preprocessing step in statistics or machine learning. Several non-linear techniques exist, for instance, Diffusion Maps or, more generally, manifold learning. In this context, we will discuss a recent proposal to reduce the dimension of Euclidean data by relying on methods developed for graph embedding. More specifically, we discuss a numerical method phrased as a Semi-Definite Program for estimating a distance (semi-metric) on the data cloud. As an interesting feature, this positive semi-definite "matrix" can be extended to a "kernel" function thanks to an out-of-sample formula. Indeed, if any new data point arises, it may also be embedded at a low computational cost thanks to the extension formula. Inspired by this property, we will also briefly discuss an infinite dimensional analogue of this discrete problem in the context of machine learning.