arXiv subjects

Stephan Günnemann

Publications and source records attributed to Stephan Günnemann.

203 records · Page 12Linked to original sources

arXiv2018

Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking

Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on large scale (attributed) graphs that show strong performance on tasks such as link prediction and node classification. Unlike most approaches that represent nodes as point vectors in a low-dimensional continuous space, we embed each node as a Gaussian distribution, allowing us to capture uncertainty about the representation. Furthermore, we propose an unsupervised method that handles inductive learning scenarios and is applicable to different types of graphs: plain/attributed, directed/undirected. By leveraging both the network structure and the associated node attributes, we are able to generalize to unseen nodes without additional training. To learn the embeddings we adopt a personalized ranking formulation w.r.t. the node distances that exploits the natural ordering of the nodes imposed by the network structure. Experiments on real world networks demonstrate the high performance of our approach, outperforming state-of-the-art network embedding methods on several different tasks. Additionally, we demonstrate the benefits of modeling uncertainty - by analyzing it we can estimate neighborhood diversity and detect the intrinsic latent dimensionality of a graph.

stat.ML↗

arXiv2017

Introduction to Tensor Decompositions and their Applications in Machine Learning

Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to numerous other disciplines, including machine learning. Tensors and their decompositions are especially beneficial in unsupervised learning settings, but are gaining popularity in other sub-disciplines like temporal and multi-relational data analysis, too. The scope of this paper is to give a broad overview of tensors, their decompositions, and how they are used in machine learning. As part of this, we are going to introduce basic tensor concepts, discuss why tensors can be considered more rigid than matrices with respect to the uniqueness of their decomposition, explain the most important factorization algorithms and their properties, provide concrete examples of tensor decomposition applications in machine learning, conduct a case study on tensor-based estimation of mixture models, talk about the current state of research, and provide references to available software libraries.

stat.ML↗

arXiv2016

Hyperbolae Are No Hyperbole: Modelling Communities That Are Not Cliques

Cliques are frequently used to model communities: a community is a set of nodes where each pair is equally likely to be connected. But studying real-world communities reveals that they have more structure than that. In particular, the nodes can be ordered in such a way that (almost) all edges in the community lie below a hyperbola. In this paper we present three new models for communities that capture this phenomenon. Our models explain the structure of the communities differently, but we also prove that they are identical in their expressive power. Our models fit to real-world data much better than traditional block models or previously-proposed hyperbolic models, both of which are a special case of our model. Our models also allow for intuitive interpretation of the parameters, enabling us to summarize the shapes of the communities in graphs effectively.

cs.SI↗

arXiv2014

Linearized and Single-Pass Belief Propagation

How can we tell when accounts are fake or real in a social network? And how can we tell which accounts belong to liberal, conservative or centrist users? Often, we can answer such questions and label nodes in a network based on the labels of their neighbors and appropriate assumptions of homophily ("birds of a feather flock together") or heterophily ("opposites attract"). One of the most widely used methods for this kind of inference is Belief Propagation (BP) which iteratively propagates the information from a few nodes with explicit labels throughout a network until convergence. One main problem with BP, however, is that there are no known exact guarantees of convergence in graphs with loops. This paper introduces Linearized Belief Propagation (LinBP), a linearization of BP that allows a closed-form solution via intuitive matrix equations and, thus, comes with convergence guarantees. It handles homophily, heterophily, and more general cases that arise in multi-class settings. Plus, it allows a compact implementation in SQL. The paper also introduces Single-pass Belief Propagation (SBP), a "localized" version of LinBP that propagates information across every edge at most once and for which the final class assignments depend only on the nearest labeled neighbors. In addition, SBP allows fast incremental updates in dynamic networks. Our runtime experiments show that LinBP and SBP are orders of magnitude faster than standard

cs.DB↗

arXiv2014

KDD-SC: Subspace Clustering Extensions for Knowledge Discovery Frameworks

Analyzing high dimensional data is a challenging task. For these data it is known that traditional clustering algorithms fail to detect meaningful patterns. As a solution, subspace clustering techniques have been introduced. They analyze arbitrary subspace projections of the data to detect clustering structures. In this paper, we present our subspace clustering extension for KDD frameworks, termed KDD-SC. In contrast to existing subspace clustering toolkits, our solution neither is a standalone product nor is it tightly coupled to a specific KDD framework. Our extension is realized by a common codebase and easy-to-use plugins for three of the most popular KDD frameworks, namely KNIME, RapidMiner, and WEKA. KDD-SC extends these frameworks such that they offer a wide range of different subspace clustering functionalities. It provides a multitude of algorithms, data generators, evaluation measures, and visualization techniques specifically designed for subspace clustering. These functionalities integrate seamlessly with the frameworks' existing features such that they can be flexibly combined. KDD-SC is publicly available on our website.

cs.DB↗