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Procrustes Metrics and Optimal Transport for Covariance Operators

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Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes

Victor Panaretos, Yoav Zemel, Valentina Masarotto

Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loeve expansion. These operators may themselves be subject to variation, for instance in contexts wh ...

2019

Fréchet means and Procrustes analysis in Wasserstein space

Victor Panaretos, Yoav Zemel

We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fréchet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed random measures and ...

2019

Two-Tier Mapper, an unbiased topology-based clustering method for enhanced global gene expression analysis

Cathrin Brisken, Kathryn Hess Bellwald, Jacques Rougemont

Motivation: Unbiased clustering methods are needed to analyze growing numbers of complex data sets. Currently available clustering methods often depend on parameters that are set by the user, they lack stability, and are not applicable to small data sets. ...

2019

There is a growing need for unbiased clustering algorithms, ideally automated to analyze complex data sets. Topological data analysis (TDA) has been used to approach this problem. This recent field of mathematics discerns characteristic features of a space ...

EPFL2018

Validation of probabilistic classifiers

Michel Bierlaire, Timothy Michael Hillel

Non-parametric probabilistic classification models are increasingly being investigated as an alternative to Discrete Choice Models (DCMs), e.g. for predicting mode choice. There exist many strategies within the literature for model selection between DCMs, ...

2018

We showthat any k-th closed sphere-of-influence graph in a d-dimensional normed space has a vertex of degree less than 5dk, thus obtaining a common generalization of results of Furedi and Loeb (Proc AmMath Soc 121(4): 1063-1073, 1994 [1]) and Guibas et al. ...

SPRINGER2018

Geometric spects A of Similarity Problems

Peter Clemens Schlicht

This article presents a geometric approach to some similarity problems involving metric arguments in the non-positively curved space of positive invertible operators of an operator algebra and the canonical isometric action by invertible elements on the co ...

OXFORD UNIV PRESS2018

Traditional approaches to analysing functional data typically follow a two-step procedure, consisting in first smoothing and then carrying out a functional principal component analysis. The idea underlying this procedure is that functional data are well ap ...

EPFL2017

Dynamic Graffiti Stylisation with Stochastic Optimal Control

Sylvain Calinon

We present a method for the interactive generation of stylised letters, curves and motion paths that are similar to the ones that can be observed in art forms such as graffiti and calligraphy. We define various stylisations of a letter form over a common g ...

ACM2017

Attributing Aliasing Artifacts in Dirty Intensity Fields to their Parent Source

Matthieu Martin Jean-André Simeoni

Estimating intensity fields of stochastic phenomenons is of crucial interest in many scientific applications. Typical experimental setups involve an acquisition system, that subsequently filters and samples the probed intensity field. This equivalently def ...

2016