# HIIT Kumpula Seminar: Computational Intelligence in Image Analysis and Optimal Hyperplanes for Data Bi-partitioning

**Spiros Georgakopoulos (at 10:15): Computational Intelligence in Image Analysis **

Pattern recognition in digital images is a very common task in most computer vision applications. In particular in the field of medical images, abnormalities detection and ambient intelligence are of crucial importance. The first part of this talk is focused on the presentation of an automatic software tool for detection and quantification of fibrosis on various tissues types in microscopy images. Then I will present a recent work focused on the detection of human poses via an omni-directional camera with fisheye lense.

**Bio:** Spiros Georgakopoulos is a close to completion PhD candidate at the department of Computer Science and Biomedical Informatics of University of Thessaly. He has previously graduated from the Department of Mathematics, University of Patras, and holds a Master at Mathematics and Modern Application with specialize at Computational Mathematics and Computational Intelligent.His research interests revolve around computational intelligence, pattern recognition in image and video applications and machine learning in visual data.

**David Hofmeyr (roughly at 11:00): Optimal Hyperplanes for Data Bi-partitioning **

We study the problem of finding the optimal hyperplane for inducing a binary partition of a set of multivariate data. In this talk we will look at two approaches to this problem. The first is motivated by `high density clustering`, in which different classes are assumed to arise uniquely from the modes of a probability density function. The optimal hyperplane is that which has the minimum density along it. The second is motivated by normalised graph partitioning. This is a combinatorial problem for which no known efficient algorithms exist. The continuous relaxation of the problem can, however, be solved by spectral clustering. The optimal hyperplane in this case minimises the 'algebraic' or 'spectral' connectedness of the data projected onto the unit vector normal to the hyperplane. While different in motivation, these two approaches are connected in that asymptotically, as their smoothing parameters tend to zero, they both converge to the largest margin hyperplane through the data. In order to solve these problems, we formulate them in the context of 'projection pursuit', in which a projection index is optimised over the space of projection vectors. In our case the projection indices for a projection, v, are the minimum density admitted by a hyperplane orthogonal to v, and the second eigenvalue of the graph Laplacian of the data projected onto v. Both projection indices are Lipschitz continuous, and continuously differentiable almost everywhere v for any continuous sampling distribution. This allows us to use modern techniques for the optimisation of non-smooth functions in order to find locally optimal solutions.

**Bio:** I received my Bachelor's degree in maths and mathematical statistics from the university of the Witwatersrand, and my honours in pure maths from the university of Cape Town. I have a masters in operations research from the university of Edinburgh, and a second masters in operations research and statistics from the university of Lancaster. I'm currently in my final year of PhD at the university of Lancaster, supervised by Dr. Nicos Pavlidis and Prof. Idris Eckley.