### Ky Vu (Ă‰cole Polytechnique, France)

#### Using random projections for dimension reduction in optimization

*Wednesday 18 May 2016 at 15.00, JCMB 6206*

##### Abstract

Random projection is a very useful technique for reducing data dimension and
has been used widely in numerical linear algebra, text and image processing,
computer science, machine learning and so on. A random projection is often
defined as a random matrix constructed in certain ways such that it preserves
many important features, such as distances, inner products, volumes, of the
data set. One of the most famous examples is the Johnson-Lindenstrauss lemma,
in which a set of *m* points can be projected by a random projection,
to an Euclidean space of dimension *O(log n)* whilst still ensures that
the inner distances between them approximately unchanged.

In this talk, I will use random projections to study a number of important
optimization problems such as linear and integer programming, convex
membership problems and derivative-free optimization. We will try to convince
that random projection is a very promising tools for many other problems as
well.

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