# Roughness regularization for functional data analysis with free knots spline estimation

arXiv: https://arxiv.org/abs/2407.05159 · HTML: https://mlsanity.com/paper/2407.05159/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2024.

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

- [Closed-Form Beta Distribution Estimation from Sparse Statistics with Random Forest Implicit Regularization](https://mlsanity.com/paper/2507.23767/) (2025)

## Abstract (arXiv)

In the era of big data, an ever-growing volume of information is recorded, either continuously over time or sporadically, at distinct time intervals. Functional Data Analysis (FDA) stands at the cutting edge of this data revolution, offering a powerful framework for handling and extracting meaningful insights from such complex datasets. The currently proposed FDA me-thods can often encounter challenges, especially when dealing with curves of varying shapes. This can largely be attributed to the method's strong dependence on data approximation as a key aspect of the analysis process. In this work, we propose a free knots spline estimation method for functional data with two penalty terms and demonstrate its performance by comparing the results of several clustering methods on simulated and real data.