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Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…

Working with big data using data mining tools is rapidly becoming a trend in education industry. The combination of the current capacity to collect, store, manage and process data in a timely manner, and data from online educational…

Computation and Language · Computer Science 2022-07-22 Vahid Ashrafimoghari

Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we introduce a statistical protocol that reduces TDA's memory…

Quantitative Methods · Quantitative Biology 2025-09-05 Andrew J. Stier , Naichen Shi , Raed Al Kontar , Chad Giusti , Marc G. Berman

The Big Data is the most popular paradigm nowadays and it has almost no untouched area. For instance, science, engineering, economics, business, social science, and government. The Big Data are used to boost up the organization performance…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-11-26 Ripon Patgiri

In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…

Machine Learning · Computer Science 2021-04-06 Lior Aloni , Omer Bobrowski , Ronen Talmon

The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…

General Topology · Mathematics 2025-04-15 Vine Nwabuisi Madukpe , Bright Chukwuma Ugoala , Nur Fariha Syaqina Zulkepli

The amount of data generated in the modern society is increasing rapidly. New problems and novel approaches of data capture, storage, analysis and visualization are responsible for the emergence of the Big Data research field. Machine…

Software Engineering · Computer Science 2016-03-09 Ivens Portugal , Paulo Alencar , Donald Cowan

This paper reviews recent advances in big data optimization, providing the state-of-art of this emerging field. The main focus in this review are optimization techniques being applied in big data analysis environments. Integer linear…

Neural and Evolutionary Computing · Computer Science 2021-02-04 Ricardo Di Pasquale , Javier Marenco

Data mining environment produces a large amount of data, that need to be analyzed, patterns have to be extracted from that to gain knowledge. In this new era with boom of data both structured and unstructured, in the field of genomics,…

Databases · Computer Science 2013-07-23 Chanchal Yadav , Shuliang Wang , Manoj Kumar

Big data research has attracted great attention in science, technology, industry and society. It is developing with the evolving scientific paradigm, the fourth industrial revolution, and the transformational innovation of technologies.…

Artificial Intelligence · Computer Science 2015-07-24 Hai Zhuge

The term of big data was used since 1990s, but it became very popular around 2012. A recent definition of this term says that big data are information assets characterized by high volume, velocity, variety and veracity that need special…

General Economics · Economics 2024-06-19 Bogdan Oancea

Topological data analysis (TDA) offers novel mathematical tools for deep learning. Inspired by Carlsson et al., this study designs topology-aware convolutional kernels that significantly improve speech recognition networks. Theoretically,…

Machine Learning · Computer Science 2025-05-28 Zhiwang Yu

The increasing application of social and human-enabled systems in people's daily life from one side and from the other side the fast growth of mobile and smart phones technologies have resulted in generating tremendous amount of data, also…

Human-Computer Interaction · Computer Science 2016-04-19 Mohammad Allahbakhsh , Saeed Arbabi , Hamid-Reza Motahari-Nezhad , Boualem Benatallah

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

Applications · Statistics 2016-11-30 Matthew Pietrosanu

Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…

Applications · Statistics 2017-11-07 Sarit Agami , Robert J. Adler

'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…

Machine Learning · Statistics 2019-02-20 Tom Lorimer , Karlis Kanders , Ruedi Stoop

Data originating from the Web, sensor readings and social media result in increasingly huge datasets. The so called Big Data comes with new scientific and technological challenges while creating new opportunities, hence the increasing…

Artificial Intelligence · Computer Science 2020-02-19 Ilias Tachmazidis , Grigoris Antoniou , Wolfgang Faber

Evaluating the quality of reasoning traces from large language models remains understudied, labor-intensive, and unreliable: current practice relies on expert rubrics, manual annotation, and slow pairwise judgments. Automated efforts are…

Artificial Intelligence · Computer Science 2026-05-28 Xue Wen Tan , Nathaniel Tan , Galen Lee , Stanley Kok

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…

Statistics Theory · Mathematics 2021-02-26 Frédéric Chazal , Bertrand Michel

Informatics and technological advancements have triggered generation of huge volume of data with varied complexity in its management and analysis. Big Data analytics is the practice of revealing hidden aspects of such data and making…

Databases · Computer Science 2018-03-30 Bikram Karmakar , Indranil Mukhopadhyay