Related papers: Automatic topography of high-dimensional data sets…

Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…

One aim of data mining is the identification of interesting structures in data. For better analytical results, the basic properties of an empirical distribution, such as skewness and eventual clipping, i.e. hard limits in value ranges, need…

We propose a method for the unsupervised clustering of hyperspectral images based on spatially regularized spectral clustering with ultrametric path distances. The proposed method efficiently combines data density and geometry to…

Spatial scientometrics has attracted a lot of attention in the very recent past. The visualization methods (density maps) presented in this paper allow for an analysis revealing regions of excellence around the world using computer programs…

Deep neural networks are a family of computational models that have led to a dramatical improvement of the state of the art in several domains such as image, voice or text analysis. These methods provide a framework to model complex,…

In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…

We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…

Detecting the dimension of a hidden manifold from a point sample has become an important problem in the current data-driven era. Indeed, estimating the shape dimension is often the first step in studying the processes or phenomena…

This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of…

Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have…

Random forests are a machine learning method used to automatically classify datasets and consist of a multitude of decision trees. While these random forests often have higher performance and generalize better than a single decision tree,…

Unsupervised classification called clustering is a process of organizing objects into groups whose members are similar in some way. Clustering of uncertain data objects is a challenge in spatial data bases. In this paper we use Probability…

This work seeks to tackle the inherent complexity of dataspaces by introducing a novel data structure that can represent datasets across multiple levels of abstraction, ranging from local to global. We propose the concept of a multilevel…

Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

Line-based density plots are used to reduce visual clutter in line charts with a multitude of individual lines. However, these traditional density plots are often perceived ambiguously, which obstructs the user's identification of…

We present a nonparametric method for selecting informative features in high-dimensional clustering problems. We start with a screening step that uses a test for multimodality. Then we apply kernel density estimation and mode clustering to…

Clustering is a common technique for statistical data analysis, Clustering is the process of grouping the data into classes or clusters so that objects within a cluster have high similarity in comparison to one another, but are very…

A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be…

An important task in visualization is the extraction and highlighting of dominant features in data to support users in their analysis process. Topological methods are a well-known means of identifying such features in deterministic fields.…