# Kernel Clustering with Sigmoid-based Regularization for Efficient Segmentation of Sequential Data

arXiv: https://arxiv.org/abs/2106.11541 · HTML: https://mlsanity.com/paper/2106.11541/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 68 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 9 of 9)

- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [Minimizing Finite Sums with the Stochastic Average Gradient](https://mlsanity.com/paper/1309.2388/) (2013)
- [Katyusha: The First Direct Acceleration of Stochastic Gradient Methods](https://mlsanity.com/paper/1603.05953/) (2016)
- [D3TW: Discriminative Differentiable Dynamic Time Warping for Weakly Supervised Action Alignment and Segmentation](https://mlsanity.com/paper/1901.02598/) (2019)
- [Set-Constrained Viterbi for Set-Supervised Action Segmentation](https://mlsanity.com/paper/2002.11925/) (2020)
- [Scan B-Statistic for Kernel Change-Point Detection](https://mlsanity.com/paper/1507.01279/) (2015)
- [On Optimal Multiple Changepoint Algorithms for Large Data](https://mlsanity.com/paper/1409.1842/) (2014)
- [Listening to the World Improves Speech Command Recognition](https://mlsanity.com/paper/1710.08377/) (2017)
- [Greedy Gaussian Segmentation of Multivariate Time Series](https://mlsanity.com/paper/1610.07435/) (2016)

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

- [A PyTorch-Enabled Tool for Synthetic Event Camera Data Generation and Algorithm Development](https://mlsanity.com/paper/2503.09754/) (2025)

## Abstract (arXiv)

Kernel segmentation aims at partitioning a data sequence into several non-overlapping segments that may have nonlinear and complex structures. In general, it is formulated as a discrete optimization problem with combinatorial constraints. A popular algorithm for optimally solving this problem is dynamic programming (DP), which has quadratic computation and memory requirements. Given that sequences in practice are too long, this algorithm is not a practical approach. Although many heuristic algorithms have been proposed to approximate the optimal segmentation, they have no guarantee on the quality of their solutions. In this paper, we take a differentiable approach to alleviate the aforementioned issues. First, we introduce a novel sigmoid-based regularization to smoothly approximate the combinatorial constraints. Combining it with objective of the balanced kernel clustering, we formulate a differentiable model termed Kernel clustering with sigmoid-based regularization (KCSR), where the gradient-based algorithm can be exploited to obtain the optimal segmentation. Second, we develop a stochastic variant of the proposed model. By using the stochastic gradient descent algorithm, which has much lower time and space complexities, for optimization, the second model can perform segmentation on overlong data sequences. Finally, for simultaneously segmenting multiple data sequences, we slightly modify the sigmoid-based regularization to further introduce an extended variant of the proposed model. Through extensive experiments on various types of data sequences performances of our models are evaluated and compared with those of the existing methods. The experimental results validate advantages of the proposed models. Our Matlab source code is available on github.