# Topological data analysis of human vowels: Persistent homologies across representation spaces

arXiv: https://arxiv.org/abs/2310.06508 · HTML: https://mlsanity.com/paper/2310.06508/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 59 references that are in the map.
- First posted on arXiv 10 Oct 2023.

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

- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [End-to-End Speech Recognition: A Survey](https://mlsanity.com/paper/2303.03329/) (2023)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [Robust Topological Inference: Distance To a Measure and Kernel Distance](https://mlsanity.com/paper/1412.7197/) (2014)
- [Persistent homology detects curvature](https://mlsanity.com/paper/1905.13196/) (2019)
- [The persistence landscape and some of its properties](https://mlsanity.com/paper/1810.04963/) (2018)
- [Confidence sets for persistence diagrams](https://mlsanity.com/paper/1303.7117/) (2013)
- [Understanding the Topology and the Geometry of the Space of Persistence Diagrams via Optimal Partial Transport](https://mlsanity.com/paper/1901.03048/) (2019)
- [Topological Data Analysis](https://mlsanity.com/paper/1609.08227/) (2016)
- [Topological Data Analysis for Speech Processing](https://mlsanity.com/paper/2211.17223/) (2022)
- [Applying Topological Persistence in Convolutional Neural Network for Music Audio Signals](https://mlsanity.com/paper/1608.07373/) (2016)
- [Bayesian Topological Learning for Brain State Classification](https://mlsanity.com/paper/1912.08348/) (2019)
- [Classification of ALS patients based on acoustic analysis of sustained vowel phonations](https://mlsanity.com/paper/2012.07347/) (2020)
- [Topological Data Analysis for Object Data](https://mlsanity.com/paper/1804.10255/) (2018)
- [Unsupervised classification of the spectrogram zeros](https://mlsanity.com/paper/2210.05459/) (2022)

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

- [Topological Data Analysis Applications in Natural Language Processing: A Survey](https://mlsanity.com/paper/2411.10298/) (2024)

## Abstract (arXiv)

Topological Data Analysis (TDA) has been successfully used for various tasks in signal/image processing, from visualization to supervised/unsupervised classification. Often, topological characteristics are obtained from persistent homology theory. The standard TDA pipeline starts from the raw signal data or a representation of it. Then, it consists in building a multiscale topological structure on the top of the data using a pre-specified filtration, and finally to compute the topological signature to be further exploited. The commonly used topological signature is a persistent diagram (or transformations of it). Current research discusses the consequences of the many ways to exploit topological signatures, much less often the choice of the filtration, but to the best of our knowledge, the choice of the representation of a signal has not been the subject of any study yet. This paper attempts to provide some answers on the latter problem. To this end, we collected real audio data and built a comparative study to assess the quality of the discriminant information of the topological signatures extracted from three different representation spaces. Each audio signal is represented as i) an embedding of observed data in a higher dimensional space using Taken's representation, ii) a spectrogram viewed as a surface in a 3D ambient space, iii) the set of spectrogram's zeroes. From vowel audio recordings, we use topological signature for three prediction problems: speaker gender, vowel type, and individual. We show that topologically-augmented random forest improves the Out-of-Bag Error (OOB) over solely based Mel-Frequency Cepstral Coefficients (MFCC) for the last two problems. Our results also suggest that the topological information extracted from different signal representations is complementary, and that spectrogram's zeros offers the best improvement for gender prediction.