# Nonparametric Extrema Analysis in Time Series for Envelope Extraction, Peak Detection and Clustering

arXiv: https://arxiv.org/abs/2109.02082 · HTML: https://mlsanity.com/paper/2109.02082/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 96 references that are in the map.
- First posted on arXiv 5 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics](https://mlsanity.com/paper/2108.12627/) (2021)
- [Sequential Outlier Detection based on Incremental Decision Trees](https://mlsanity.com/paper/1803.03674/) (2018)
- [Optimally Efficient Sequential Calibration of Binary Classifiers to Minimize Classification Error](https://mlsanity.com/paper/2108.08780/) (2021)
- [Recursive Experts: An Efficient Optimal Mixture of Learning Systems in Dynamic Environments](https://mlsanity.com/paper/2009.09249/) (2020)

## Built on by (most cited first, 12 of 12)

- [Smoothing with the Best Rectangle Window is Optimal for All Tapered Rectangle Windows](https://mlsanity.com/paper/2203.02997/) (2022)
- [Natural Hierarchical Cluster Analysis by Nearest Neighbors with Near-Linear Time Complexity](https://mlsanity.com/paper/2203.08027/) (2022)
- [Blind Source Separation for Mixture of Sinusoids with Near-Linear Computational Complexity](https://mlsanity.com/paper/2203.14324/) (2022)
- [Second Order Regret Bounds Against Generalized Expert Sequences under Partial Bandit Feedback](https://mlsanity.com/paper/2204.06660/) (2022)
- [Merging Knockout and Round-Robin Tournaments: A Flexible Linear Elimination Tournament Design](https://mlsanity.com/paper/2203.12011/) (2022)
- [Robust, Nonparametric, Efficient Decomposition of Spectral Peaks under Distortion and Interference](https://mlsanity.com/paper/2204.08411/) (2022)
- [An Auto-Regressive Formulation for Smoothing and Moving Mean with Exponentially Tapered Windows](https://mlsanity.com/paper/2206.14749/) (2022)
- [A 2-opt Algorithm for Locally Optimal Set Partition Optimization](https://mlsanity.com/paper/2303.08219/) (2023)
- [Formulation of Weighted Average Smoothing as a Projection of the Origin onto a Convex Polytope](https://mlsanity.com/paper/2303.11958/) (2023)
- [A Note On Nonlinear Regression Under L2 Loss](https://mlsanity.com/paper/2303.17745/) (2023)
- [Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses](https://mlsanity.com/paper/2304.02141/) (2023)
- [Kinematic-Based Assessment of Surgical Actions in Microanastomosis](https://mlsanity.com/paper/2512.23942/) (2025)

## Abstract (arXiv)

In this paper, we propose a nonparametric approach that can be used in envelope extraction, peak-burst detection and clustering in time series. Our problem formalization results in a naturally defined splitting/forking of the time series. With a possibly hierarchical implementation, it can be used for various applications in machine learning, signal processing and mathematical finance. From an incoming input signal, our iterative procedure sequentially creates two signals (one upper bounding and one lower bounding signal) by minimizing the cumulative L1 drift. We show that a solution can be efficiently calculated by use of a Viterbi-like path tracking algorithm together with an optimal elimination rule. We consider many interesting settings, where our algorithm has near-linear time complexities.