Related papers: Topological data analysis of C. elegans locomotion…

With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural…

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

Recent whole-brain calcium imaging recordings of the nematode C. elegans have demonstrated that neural activity is dominated by dynamics on a low-dimensional manifold that can be clustered according to behavioral states. Despite progress in…

Reticulate evolutionary processes result in phylogenetic histories that cannot be modeled using a tree topology. Here, we apply methods from topological data analysis to molecular sequence data with reticulations. Using a simple example, we…

Rapid advances in high-throughput technologies have led to considerable interest in analyzing genome-scale data in the context of biological pathways, with the goal of identifying functional systems that are involved in a given phenotype.…

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…

E-commerce companies deal with a high volume of customer service requests daily. While a simple annotation system is often used to summarize the topics of customer contacts, thoroughly exploring each specific issue can be challenging. This…

Topological data analyses are rapidly turning into key tools for quantifying large volumes of neurobiological data, e.g., for organizing the spiking outputs of large neuronal ensembles and thus gaining insights into the information produced…

Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a…

In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such signature consists of a vector obtained by persistent homology which captures the topological and geometric changes of…

Topological data analysis is becoming increasingly relevant to support the analysis of unstructured data sets. A common assumption in data analysis is that the data set is a sample---not necessarily a uniform one---of some high-dimensional…

We use topological data analysis to study "functional networks" that we construct from time-series data from both experimental and synthetic sources. We use persistent homology with a weight rank clique filtration to gain insights into…

Increasingly, malwares are becoming complex and they are spreading on networks targeting different infrastructures and personal-end devices to collect, modify, and destroy victim information. Malware behaviors are polymorphic, metamorphic,…

Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…

We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and…

Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…

This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…

Video-based person re-identification aims to match pedestrians from video sequences across non-overlapping camera views. The key factor for video person re-identification is to effectively exploit both spatial and temporal clues from video…

Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional…