Nonnegative Matrix Factorization Method Proposed for Time Series Forecasting with Missing Data
Researchers have introduced the Sliding Mask Method (SMM), a nonnegative matrix factorization-based approach for forecasting multiple time series that contain missing or noisy values. The method represents time series data as convex combinations of a small number of nonnegative archetype vectors, with two estimators—mAMF and mNMF—proven to recover true archetypes with error proportional to noise. In benchmark comparisons against state-of-the-art methods including Transformers, LSTMs, and SARIMAX, SMM outperformed competitors in most experiments.
The paper, posted to arXiv and updated in June 2026, presents the Sliding Mask Method (SMM) as a principled solution to the common real-world problem of forecasting multiple time series when observations are incomplete or corrupted by noise. The core idea is to arrange observed and forecast values into a matrix and decompose it using nonnegative matrix completion, expressing each row as a convex combination of a small set of nonnegative archetype vectors. Two estimators are proposed: the mask Archetypal Matrix Factorization (mAMF) and the mask normalized Nonnegative Matrix Factorization (mNMF), both of which come with theoretical guarantees showing archetype recovery error scales proportionally with noise level. Optimization is carried out via a Proximal Alternating Linearized Minimization (PALM) algorithm. Empirical evaluations on real datasets show the method outperforms deep learning approaches such as Transformers and LSTMs, as well as classical statistical models like SARIMAX, in the majority of tested scenarios. The work bridges matrix completion theory and practical time series forecasting, offering both interpretability through archetypes and competitive predictive performance.
What's missing
It is also unclear whether the computational cost of PALM optimization scales favorably compared to deep learning baselines at large data volumes. The conditions under which SMM underperforms competitors are not detailed.
What different sources said
- arXiv cs.LGCenter
Time series forecasting from partial observations via Non-negative Matrix Factorization
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