Stefan Huber

Bio: Stefan Huber is an academic researcher from Institute of Science and Technology Austria. The author has contributed to research in topics: Straight skeleton & Polygon. The author has an hindex of 13, co-authored 39 publications receiving 793 citations. Previous affiliations of Stefan Huber include University of Salzburg.

A stable multi-scale kernel for topological machine learning

Abstract: Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes.

Statistical topological data analysis - a kernel perspective

Abstract: We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel enabling a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in two-sample hypothesis testing on synthetic as well as real-world data.

Topology-oriented incremental computation of Voronoi diagrams of circular arcs and straight-line segments

Abstract: We introduce an algorithm for computing Voronoi diagrams of points, straight-line segments and circular arcs in the two-dimensional Euclidean plane. Based on a randomized incremental insertion, we achieve a Voronoi algorithm that runs in expected time O(nlogn) for a total of n points, segments and arcs, if at most a constant number of segments and arcs is incident upon every point. Our theoretical contribution is a careful extension of the topology-oriented approach by Sugihara and Iri in order to make the incremental insertion applicable to circular arcs. Our main practical contribution is the extension of Held's Voronoi code Vroni to circular arcs. We discuss implementational issues such as the computation of the Voronoi nodes. As demonstrated by test runs on several thousands of synthetic and real-world data sets, this circular-arc extension of Vroni is reliable and exhibits the average-case time complexity predicted by theory. As a service to the community, all circular-arc data sets (except for proprietary data) have been made public. To our knowledge, this enhanced version of Vroni constitutes the first implementation that computes Voronoi diagrams of genuine circular arcs on a standard floating-point arithmetic reliably and efficiently, without resorting to some form of approximation or sampling of the circular arcs.

A Stable Multi-Scale Kernel for Topological Machine Learning

Abstract: Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes.

"Open": the changing relation between citizens, public administration, and political authority Towards researching the Public Value of Open Government

Abstract: Open" is not just a fancy synonym for transparent and accountable. The "Open" in Open Government, Open Data, Open Information, and Open Innovation stands for the changing relation between citizens and authorities. Many citizens no longer accept the passive stance representative democracy held for them. They take an active approach in setting up better means of collaboration by ICTs. They demand and gain access to their historically grown collective knowledge stored in government data. Not just on a local level, they actively shape the political agenda. Open Government is to be seen in the context of citizens' rights: the right to actively participate in the process of agenda-setting and decision-making. Research into open government needs to address the value of the changing relation between citizens, public administration, and political authority. The paper argues finally for the application of the Public Value concept to research into open government.

Bowling alone: The collapse and revival of American community

Abstract: The present historical moment may seem a particularly inopportune time to review Bowling Alone, Robert Putnam's latest exploration of civic decline in America. After all, the outpouring of volunteerism, solidarity, patriotism, and self-sacrifice displayed by Americans in the wake of the September 11 terrorist attacks appears to fly in the face of Putnam's central argument: that \"social capital\" -defined as \"social networks and the norms of reciprocity and trustworthiness that arise from them\" (p. 19)'has declined to dangerously low levels in America over the last three decades. However, Putnam is not fazed in the least by the recent effusion of solidarity. Quite the contrary, he sees in it the potential to \"reverse what has been a 30to 40-year steady decline in most measures of connectedness or community.\"' As an example of how the current \"war on terrorism\" could generate a durable civic renewal, Putnam points to the burst in civic practices that occurred during and after World War II, which he says \"permanently marked\" the generation that lived through it and had a \"terrific effect on American public life over the last half-century.\" 3 If Americans can follow this example and channel their current civic

Triangulating a simple polygon in linear time

Abstract: We give a deterministic algorithm for triangulating a simple polygon in linear time. The basic strategy is to build a coarse approximation of a triangulation in a bottom-up phase and then use the information computed along the way to refine the triangulation in a top-down phase. The main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals. Only elementary data structures are required by the algorithm. In particular, no dynamic search trees, of our algorithm.

A roadmap for the computation of persistent homology

Abstract: Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates, and provides a compact representation of the qualitative features of the input. The computation of PH is an open area with numerous important and fascinating challenges. The field of PH computation is evolving rapidly, and new algorithms and software implementations are being updated and released at a rapid pace. The purposes of our article are to (1) introduce theory and computational methods for PH to a broad range of computational scientists and (2) provide benchmarks of state-of-the-art implementations for the computation of PH. We give a friendly introduction to PH, navigate the pipeline for the computation of PH with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of PH. Based on our benchmarking, we indicate which algorithms and implementations are best suited to different types of data sets. In an accompanying tutorial, we provide guidelines for the computation of PH. We make publicly available all scripts that we wrote for the tutorial, and we make available the processed version of the data sets used in the benchmarking.

Discrete Applied Mathematics

Abstract: : Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization. There has also been research on the application of techniques from combinational optimization to nonlinear problems.

An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists

Abstract: Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to basic fundamental and practical aspects of \tda\ for non experts.