Clustering functional data using projection

Thời gian: 14:00 đến 16:00 Ngày 14/11/2018

Địa điểm: B4-705, VIASM

Báo cáo viên: Tung Pham, University of Melbourne

Tóm tắt:
We show that, in the functional data context, by appropriately exploiting the functional nature of the data, it is possible to cluster the observations asymptotically perfectly. We demonstrate that this level of performance can sometimes be achieved by the k-means algorithm as long as the data are projected on 1 dimensional space. In general, the notion of ideal cluster is not clearly defined. We derive our results in the setting where the data come from two populations whose distributions differ at least in terms of means, and where an ideal cluster corresponds to one of these two populations. We propose an iterative algorithm to choose the projection functions in a way that optimises clustering performance.  We apply our iterative clustering procedure on simulated and real data, where we show that it works well.
Bio: I got my PhD in the University of Melbourne in 2010 under the supervision of Professor Peter Hall. After that, I worked as a postdoctoral in Wollongong with Professor Matt Wand for one year. Between 2011 and 2013, I worked with Professor Victor Panaretos in the EPFL in Lausanne, Switzerland on manifold data. Since 2013, I came back to Australia to work with my PhD supervisor again, until 2017. My works focus on problems  of functional data, high dimensional data, and manifold data.