Related papers: Untangling Gaussian Mixtures
In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
Data sets are growing in complexity thanks to the increasing facilities we have nowadays to both generate and store data. This poses many challenges to machine learning that are leading to the proposal of new methods and paradigms, in order…
In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…
Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently complex network theory has been applied to quantum systems, where complex…
Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…
Tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks. This paper begins with an expository account of tangle machines motivated by the problem of describing `covariance intersection'…
Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this…
The aggregated journal-journal citation matrix derived from the Journal Citation Reports 2001 can be decomposed into a unique subject classification by using the graph-analytical algorithm of bi-connected components. This technique was…
Today's data-heavy research environment requires the integration of different sources of information into structured data sets that can not be analyzed as simple matrices. We introduce an old technique, known in the European data analyses…
In the last decade it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks: separable elements, with connections (or interactions) between certain pairs of them.…
How can we find a good graph clustering of a real-world network, that allows insight into its underlying structure and also potential functions? In this paper, we introduce a new graph clustering algorithm Dcut from a density point of view.…
The goal of data clustering is to partition data points into groups to minimize a given objective function. While most existing clustering algorithms treat each data point as vector, in many applications each datum is not a vector but a…
This article proposes a graphical model that handles mixed-type, multi-group data. The motivation for such a model originates from real-world observational data, which often contain groups of samples obtained under heterogeneous conditions…
Clustering a graph, i.e., assigning its nodes to groups, is an important operation whose best known application is the discovery of communities in social networks. Graph clustering and community detection have traditionally focused on…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…
Gaussian mixture model is very useful in many practical problems. Nevertheless, it cannot be directly generalized to non Euclidean spaces. To overcome this problem we present a spherical Gaussian-based clustering approach for partitioning…
Widespread use of the Internet and social networks invokes the generation of big data, which is proving to be useful in a number of applications. To deal with explosively growing amounts of data, data analytics has emerged as a critical…