# Sparse Portfolio Selection via Topological Data Analysis based Clustering

arXiv: https://arxiv.org/abs/2401.16920 · HTML: https://mlsanity.com/paper/2401.16920/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 104 references that are in the map.
- First posted on arXiv 30 Jan 2024.

## Builds on (most cited first, 7 of 7)

- [Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances](https://mlsanity.com/paper/1802.04885/) (2018)
- [Kernel method for persistence diagrams via kernel embedding and weight factor](https://mlsanity.com/paper/1706.03472/) (2017)
- [The persistence landscape and some of its properties](https://mlsanity.com/paper/1810.04963/) (2018)
- [A novel approach for wafer defect pattern classification based on topological data analysis](https://mlsanity.com/paper/2209.08945/) (2022)
- [Topological Machine Learning for Multivariate Time Series](https://mlsanity.com/paper/1911.12082/) (2019)
- [Time Series Classification via Topological Data Analysis](https://mlsanity.com/paper/2102.01956/) (2021)
- [Sparse Index Tracking via Topological Learning](https://mlsanity.com/paper/2310.09578/) (2023)

## Abstract (arXiv)

This paper uses topological data analysis (TDA) tools and introduces a data-driven clustering-based stock selection strategy tailored for sparse portfolio construction. Our asset selection strategy exploits the topological features of stock price movements to select a subset of topologically similar (different) assets for a sparse index tracking (Markowitz) portfolio. We introduce new distance measures, which serve as an input to the clustering algorithm, on the space of persistence diagrams and landscapes that consider the time component of a time series. We conduct an empirical analysis on the S&P index from 2009 to 2022, including a study on the COVID-19 data to validate the robustness of our methodology. Our strategy to integrate TDA with the clustering algorithm significantly enhanced the performance of sparse portfolios across various performance measures in diverse market scenarios.