Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools underrepresent. 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 Topological 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.
https://arxiv.org/pdf/2511.13503
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