# Dynamic Multivariate Functional Data Modeling via Sparse Subspace Learning

arXiv: https://arxiv.org/abs/1804.03797 · HTML: https://mlsanity.com/paper/1804.03797/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2018.

## Built on by (most cited first, 7 of 7)

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- [A Novel Sparse Bayesian Learning and Its Application to Fault Diagnosis for Multistation Assembly Systems](https://mlsanity.com/paper/2210.16176/) (2022)
- [Non-stationary and Sparsely-correlated Multi-output Gaussian Process with Spike-and-Slab Prior](https://mlsanity.com/paper/2409.03149/) (2024)
- [Adaptive Resources Allocation CUSUM for Binomial Count Data Monitoring with Application to COVID-19 Hotspot Detection](https://mlsanity.com/paper/2208.05045/) (2022)
- [A Novel Black Box Process Quality Optimization Approach based on Hit Rate](https://mlsanity.com/paper/2305.20003/) (2023)

## Abstract (arXiv)

Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar features, while some others may have almost no cross-correlations with quite diverse features; and (2) the cross-correlation structure may also change over time due to the system evolution. With this regard, this paper presents a dynamic subspace learning method for multivariate functional data modeling. In particular, we consider different functions come from different subspaces, and only functions of the same subspace have cross-correlations with each other. The subspaces can be automatically formulated and learned by reformatting the problem as a sparse regression. By allowing but regularizing the regression change over time, we can describe the cross-correlation dynamics. The model can be efficiently estimated by the fast iterative shrinkage-thresholding algorithm (FISTA), and the features of every subspace can be extracted using the smooth multi-channel functional PCA. Numerical studies together with case studies demonstrate the efficiency and applicability of the proposed methodology.