# Learning Representations from Imperfect Time Series Data via Tensor Rank Regularization

arXiv: https://arxiv.org/abs/1907.01011 · HTML: https://mlsanity.com/paper/1907.01011/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2019.

## Built on by (most cited first, 30 of 30)

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- [Efficient Multimodal Transformer with Dual-Level Feature Restoration for Robust Multimodal Sentiment Analysis](https://mlsanity.com/paper/2208.07589/) (2022)
- [MAESTRO : Adaptive Sparse Attention and Robust Learning for Multimodal Dynamic Time Series](https://mlsanity.com/paper/2509.25278/) (2025)
- [Multimodal Fusion Interactions: A Study of Human and Automatic Quantification](https://mlsanity.com/paper/2306.04125/) (2023)
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- [Partial Information Decomposition via Normalizing Flows in Latent Gaussian Distributions](https://mlsanity.com/paper/2510.04417/) (2025)
- [Brainish: Formalizing A Multimodal Language for Intelligence and Consciousness](https://mlsanity.com/paper/2205.00001/) (2022)
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- [CT2C-QA: Multimodal Question Answering over Chinese Text, Table and Chart](https://mlsanity.com/paper/2410.21414/) (2024)
- [Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inference](https://mlsanity.com/paper/2311.10671/) (2023)
- [Meta-Learn Unimodal Signals with Weak Supervision for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2408.16029/) (2024)
- [Curriculum Learning Meets Weakly Supervised Modality Correlation Learning](https://mlsanity.com/paper/2212.07619/) (2022)
- [Modality-Collaborative Transformer with Hybrid Feature Reconstruction for Robust Emotion Recognition](https://mlsanity.com/paper/2312.15848/) (2023)
- [Uncertainty-Aware Collaborative System of Large and Small Models for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2509.04459/) (2025)
- [REMIND: Rethinking Medical High-Modality Learning under Missingness--A Long-Tailed Distribution Perspective](https://mlsanity.com/paper/2603.00046/) (2026)
- [Addressing Missing and Noisy Modalities in One Solution: Unified Modality-Quality Framework for Low-quality Multimodal Data](https://mlsanity.com/paper/2603.02695/) (2026)
- [Head-wise Modality Specialization within MLLMs for Robust Fake News Detection under Missing Modality](https://mlsanity.com/paper/2604.09711/) (2026)
- [Collaborative Position Reasoning Network for Referring Image Segmentation](https://mlsanity.com/paper/2401.11775/) (2024)
- [ADMC: Attention-based Diffusion Model for Missing Modalities Feature Completion](https://mlsanity.com/paper/2507.05624/) (2025)
- [GRCF: Two-Stage Groupwise Ranking and Calibration Framework for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2601.09606/) (2026)
- [Reliability-aware Cross-sample Enhancement for Robust Multimodal Sentiment Analysis](https://mlsanity.com/paper/2609.30470/) (2026)

## Abstract (arXiv)

There has been an increased interest in multimodal language processing including multimodal dialog, question answering, sentiment analysis, and speech recognition. However, naturally occurring multimodal data is often imperfect as a result of imperfect modalities, missing entries or noise corruption. To address these concerns, we present a regularization method based on tensor rank minimization. Our method is based on the observation that high-dimensional multimodal time series data often exhibit correlations across time and modalities which leads to low-rank tensor representations. However, the presence of noise or incomplete values breaks these correlations and results in tensor representations of higher rank. We design a model to learn such tensor representations and effectively regularize their rank. Experiments on multimodal language data show that our model achieves good results across various levels of imperfection.