Related papers: Topology-based Clusterwise Regression for User Seg…
This work is devoted to a comprehensive analysis of topological data analysis fortime series classification. Previous works have significant shortcomings, such aslack of large-scale benchmarking or missing state-of-the-art methods. In this…
Data clustering is an instrumental tool in the area of energy resource management. One problem with conventional clustering is that it does not take the final use of the clustered data into account, which may lead to a very suboptimal use…
Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this…
Through Ecological Momentary Assessment (EMA) studies, a number of time-series data is collected across multiple individuals, continuously monitoring various items of emotional behavior. Such complex data is commonly analyzed in an…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…
Improvements in experimental and computational technologies have led to significant increases in data available for analysis. Topological data analysis (TDA) is an emerging area of mathematical research that can identify structures in these…
With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…
In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review the recently proposed level-set construction of filtered simplicial complexes, and we then examine persistent homology in two…
Improving the future of healthcare starts by better understanding the current actual practices in hospital settings. This motivates the objective of discovering typical care pathways from patient data. Revealing typical care pathways can be…
Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural…
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…
Clustering is one of the most common tasks of Machine Learning. In this paper we examine how ideas from topology can be used to improve clustering techniques.
Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…
Deep learning has shown its efficacy in extracting useful features to solve various computer vision tasks. However, when the structure of the data is complex and noisy, capturing effective information to improve performance is very…
Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…
Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological…
Accurate prediction of typhoon trajectories is essential for mitigating the impact of these extreme weather events. This study proposes a functional data analysis (FDA) framework for modeling and forecasting typhoon paths using historical…
Multivariate time series data come as a collection of time series describing different aspects of a certain temporal phenomenon. Anomaly detection in this type of data constitutes a challenging problem yet with numerous applications in…
Entrepreneurial regimes are topic, receiving ever more research attention. Existing studies on entrepreneurial regimes mainly use common methods from multivariate analysis and some type of institutional related analysis. In our analysis,…