# The Shape of Data: Topology Meets Analytics. A Practical Introduction to Topological Analytics and the Stability Index (TSI) in Business

arXiv: https://arxiv.org/abs/2511.13503 · HTML: https://mlsanity.com/paper/2511.13503/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 6 of 6)

- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Persistence Homology of Networks: Methods and Applications](https://mlsanity.com/paper/1907.08708/) (2019)
- [The Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series](https://mlsanity.com/paper/2506.19759/) (2025)
- [Topology of Currencies: Persistent Homology for FX Co-movements: A Comparative Clustering Study](https://mlsanity.com/paper/2510.19306/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Topological Stability Index: A Variance-Based Measure for Persistence Barcodes](https://mlsanity.com/paper/2605.29839/) (2026)

## Abstract (arXiv)

Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected components, loops and voids, across scales. This paper provides an intuitive, figure-driven introduction to persistent homology and a practical, reproducible TDA pipeline for applied analysts. Through comparative case studies in consumer behavior, equity markets (SAX/eSAX vs. TDA) and foreign exchange dynamics, we demonstrate how topological features can reveal segmentation patterns and structural relationships beyond classical statistical methods. We discuss methodological choices regarding distance metrics, complex construction and interpretation, and we introduce the textitTopological Stability Index (TSI), a simple yet interpretable indicator of structural variability derived from persistence lifetimes. We conclude with practical guidelines for TDA implementation, visualization and communication in business and economic analytics.