# Topological Data Analysis in smart manufacturing: State of the art and futuredirections

arXiv: https://arxiv.org/abs/2310.09319 · HTML: https://mlsanity.com/paper/2310.09319/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 101 references that are in the map.
- First posted on arXiv 13 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Connectivity-Optimized Representation Learning via Persistent Homology](https://mlsanity.com/paper/1906.09003/) (2019)
- [Anomaly Detection in Medical Imaging -- A Mini Review](https://mlsanity.com/paper/2108.11986/) (2021)
- [Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes](https://mlsanity.com/paper/2203.03060/) (2022)
- [Topological Time Series Analysis](https://mlsanity.com/paper/1812.05143/) (2018)
- [Chatter Classification in Turning Using Machine Learning and Topological Data Analysis](https://mlsanity.com/paper/1804.02261/) (2018)
- [A novel approach for wafer defect pattern classification based on topological data analysis](https://mlsanity.com/paper/2209.08945/) (2022)
- [Efficient Planning of Multi-Robot Collective Transport using Graph Reinforcement Learning with Higher Order Topological Abstraction](https://mlsanity.com/paper/2303.08933/) (2023)
- [Topological Feature Vectors for Chatter Detection in Turning Processes](https://mlsanity.com/paper/1905.08671/) (2019)
- [Data-driven and Automatic Surface Texture Analysis Using Persistent Homology](https://mlsanity.com/paper/2110.10005/) (2021)
- [Chatter Diagnosis in Milling Using Supervised Learning and Topological Features Vector](https://mlsanity.com/paper/1910.12359/) (2019)
- [A Classification of Topological Discrepancies in Additive Manufacturing](https://mlsanity.com/paper/1904.13210/) (2019)
- [Transfer Learning for Autonomous Chatter Detection in Machining](https://mlsanity.com/paper/2204.05400/) (2022)
- [Imaging-based representation and stratification of intra-tumor Heterogeneity via tree-edit distance](https://mlsanity.com/paper/2208.04829/) (2022)
- [Pattern Characterization Using Topological Data Analysis: Application to Piezo Vibration Striking Treatment](https://mlsanity.com/paper/2210.06333/) (2022)
- [Parameters, Properties, and Process: Conditional Neural Generation of Realistic SEM Imagery Towards ML-assisted Advanced Manufacturing](https://mlsanity.com/paper/2302.08495/) (2023)

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

- [Advanced Clustering Framework for Semiconductor Image Analytics Integrating Deep TDA with Self-Supervised and Transfer Learning Techniques](https://mlsanity.com/paper/2505.03848/) (2025)

## Abstract (arXiv)

Topological Data Analysis (TDA) is a discipline that applies algebraic topology techniques to analyze complex, multi-dimensional data. Although it is a relatively new field, TDA has been widely and successfully applied across various domains, such as medicine, materials science, and biology. This survey provides an overview of the state of the art of TDA within a dynamic and promising application area: industrial manufacturing and production, particularly within the Industry 4.0 context. We have conducted a rigorous and reproducible literature search focusing on TDA applications in industrial production and manufacturing settings. The identified works are categorized based on their application areas within the manufacturing process and the types of input data. We highlight the principal advantages of TDA tools in this context, address the challenges encountered and the future potential of the field. Furthermore, we identify TDA methods that are currently underexploited in specific industrial areas and discuss how their application could be beneficial, with the aim of stimulating further research in this field. This work seeks to bridge the theoretical advancements in TDA with the practical needs of industrial production. Our goal is to serve as a guide for practitioners and researchers applying TDA in industrial production and manufacturing systems. We advocate for the untapped potential of TDA in this domain and encourage continued exploration and research.