# Neural Ordinary Differential Equation Model for Evolutionary Subspace Clustering and Its Applications

arXiv: https://arxiv.org/abs/2107.10484 · HTML: https://mlsanity.com/paper/2107.10484/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 62 references that are in the map.
- First posted on arXiv 22 Jul 2021.

## Builds on (most cited first, 12 of 12)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit](https://mlsanity.com/paper/1507.01238/) (2015)
- [Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework](https://mlsanity.com/paper/1610.05211/) (2016)
- [Robust Subspace Clustering via Thresholding](https://mlsanity.com/paper/1307.4891/) (2013)
- [Greedy Feature Selection for Subspace Clustering](https://mlsanity.com/paper/1303.4778/) (2013)
- [Correlation Adaptive Subspace Segmentation by Trace Lasso](https://mlsanity.com/paper/1501.04276/) (2015)
- [Theoretical Analysis of Sparse Subspace Clustering with Missing Entries](https://mlsanity.com/paper/1801.00393/) (2018)
- [Subspace Clustering with Missing and Corrupted Data](https://mlsanity.com/paper/1707.02461/) (2017)
- [Sparse Linear Regression via Generalized Orthogonal Least-Squares](https://mlsanity.com/paper/1602.06916/) (2016)
- [Accelerated Sparse Subspace Clustering](https://mlsanity.com/paper/1711.00126/) (2017)
- [Evolutionary Self-Expressive Models for Subspace Clustering](https://mlsanity.com/paper/1810.11957/) (2018)
- [LSTM-Assisted Evolutionary Self-Expressive Subspace Clustering](https://mlsanity.com/paper/1910.08862/) (2019)

## Abstract (arXiv)

The neural ordinary differential equation (neural ODE) model has attracted increasing attention in time series analysis for its capability to process irregular time steps, i.e., data are not observed over equally-spaced time intervals. In multi-dimensional time series analysis, a task is to conduct evolutionary subspace clustering, aiming at clustering temporal data according to their evolving low-dimensional subspace structures. Many existing methods can only process time series with regular time steps while time series are unevenly sampled in many situations such as missing data. In this paper, we propose a neural ODE model for evolutionary subspace clustering to overcome this limitation and a new objective function with subspace self-expressiveness constraint is introduced. We demonstrate that this method can not only interpolate data at any time step for the evolutionary subspace clustering task, but also achieve higher accuracy than other state-of-the-art evolutionary subspace clustering methods. Both synthetic and real-world data are used to illustrate the efficacy of our proposed method.