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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

Unsupervised data representation and visualization using tools from topology is an active and growing field of Topological Data Analysis (TDA) and data science. Its most prominent line of work is based on the so-called Mapper graph, which…

Machine Learning · Computer Science 2025-06-04 Ziyad Oulhaj , Mathieu Carrière , Bertrand Michel

Motivation: The Mapper algorithm is an essential tool to explore shape of data in topology data analysis. With a dataset as an input, the Mapper algorithm outputs a graph representing the topological features of the whole dataset. This…

Algebraic Topology · Mathematics 2025-01-31 Yuyang Tao , Shufei Ge

The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. However, the Mapper algorithm requires tuning several parameters in order to generate a…

Machine Learning · Computer Science 2025-02-19 Enrique Alvarado , Robin Belton , Emily Fischer , Kang-Ju Lee , Sourabh Palande , Sarah Percival , Emilie Purvine

Mapper, a topological algorithm, is frequently used as an exploratory tool to build a graphical representation of data. This representation can help to gain a better understanding of the intrinsic shape of high-dimensional genomic data and…

Genomics · Quantitative Biology 2023-07-19 Erik J. Amézquita , Farzana Nasrin , Kathleen M. Storey , Masato Yoshizawa

Mapper is an algorithm that summarizes the topological information contained in a dataset and provides an insightful visualization. It takes as input a point cloud which is possibly high-dimensional, a filter function on it and an open…

Algebraic Topology · Mathematics 2019-03-12 Bishal Deb , Ankita Sarkar , Nupur Kumari , Akash Rupela , Piyush Gupta , Balaji Krishnamurthy

Acquiring plausible pathways on high-dimensional structural distributions is beneficial in several domains. For example, in the drug discovery field, a protein conformational pathway, i.e. a highly probable sequence of protein structural…

Quantitative Methods · Quantitative Biology 2025-06-04 Ziyad Oulhaj , Yoshiyuki Ishii , Kento Ohga , Kimihiro Yamazaki , Mutsuyo Wada , Yuhei Umeda , Takashi Kato , Yuichiro Wada , Hiroaki Kurihara

Recent advancements in graph representation learning have led to the emergence of condensed encodings that capture the main properties of a graph. However, even though these abstract representations are powerful for downstream tasks, they…

Machine Learning · Computer Science 2020-02-21 Cristian Bodnar , Cătălina Cangea , Pietro Liò

Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of…

Algebraic Topology · Mathematics 2019-06-05 Francisco Belchí , Jacek Brodzki , Matthew Burfitt , Mahesan Niranjan

The Mapper algorithm is a fundamental tool in exploratory topological data analysis for identifying connectivity and topological clustering in data. Derived from the nerve construction, Mapper graphs can contain additional information about…

Computational Geometry · Computer Science 2025-09-30 Halley Fritze

The mapper algorithm is a popular tool from topological data analysis for extracting topological summaries of high-dimensional datasets. In this paper, we present Mapper Interactive, a web-based framework for the interactive analysis and…

Computational Geometry · Computer Science 2021-04-28 Youjia Zhou , Nithin Chalapathi , Archit Rathore , Yaodong Zhao , Bei Wang

Mapper and Ball Mapper are Topological Data Analysis tools used for exploring high dimensional point clouds and visualizing scalar-valued functions on those point clouds. Inspired by open questions in knot theory, new features are added to…

Algebraic Topology · Mathematics 2023-03-29 Paweł Dłotko , Davide Gurnari , Radmila Sazdanovic

Mapper algorithm can be used to build graph-based representations of high-dimensional data capturing structurally interesting features such as loops, flares or clusters. The graph can be further annotated with additional colouring of…

Numerical Analysis · Mathematics 2020-12-04 Ciara Frances Loughrey , Nick Orr , Anna Jurek-Loughrey , Paweł Dłotko

The limits of molecular dynamics (MD) simulations of macromolecules are steadily pushed forward by the relentless developments of computer architectures and algorithms. This explosion in the number and extent (in size and time) of MD…

Objective: The Mapper algorithm is a qualitative method in topological data analysis that constructs graphs from point clouds by combining dimensionality reduction and clustering techniques. The aim of this study is to apply Mapper,…

Quantitative Methods · Quantitative Biology 2026-04-22 Aina Ferrà Marcús , Carles Casacuberta , Josep Vives , Joan Guich , Gerard Amorós-Figueras , Jose M. Guerra

Effectively modeling non-stationary dynamics in probabilistic multivariate time series(MTS) forecasting requires balancing expressiveness with robustness. Existing parametric approaches benefit from strong inductive biases but lack…

Machine Learning · Computer Science 2026-05-25 Jinglin Li , Jun Tan , QI Fang , Ning Gui

This paper addresses the problem of modeling and estimating dynamic multi-valued mappings. While most mathematical models provide a unique solution for a given input, real-world applications often lack deterministic solutions. In such…

Computer Vision and Pattern Recognition · Computer Science 2024-07-02 Geng Li , Di Qiu , Lok Ming Lui

UMAP is a non-parametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) Compute a…

Machine Learning · Computer Science 2021-08-31 Tim Sainburg , Leland McInnes , Timothy Q Gentner

This paper is concerned with the problem of exact MAP inference in general higher-order graphical models by means of a traditional linear programming relaxation approach. In fact, the proof that we have developed in this paper is a rather…

Optimization and Control · Mathematics 2026-03-23 Ikhlef Bechar

The Mapper algorithm from topological data analysis constructs a graph summarizing the shape of a high-dimensional dataset, and groups of data points identified within this graph are widely interpreted as evidence of distinct subtypes.…

Methodology · Statistics 2026-04-21 Chad M. Topaz
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