# MTC: Multiresolution Tensor Completion from Partial and Coarse Observations

arXiv: https://arxiv.org/abs/2106.07135 · HTML: https://mlsanity.com/paper/2106.07135/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 35 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 11 of 11)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [Canonical Tensor Decomposition for Knowledge Base Completion](https://mlsanity.com/paper/1806.07297/) (2018)
- [Tensor Completion Algorithms in Big Data Analytics](https://mlsanity.com/paper/1711.10105/) (2017)
- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [LSAR: Efficient Leverage Score Sampling Algorithm for the Analysis of Big Time Series Data](https://mlsanity.com/paper/1911.12321/) (2019)
- [STELAR: Spatio-temporal Tensor Factorization with Latent Epidemiological Regularization](https://mlsanity.com/paper/2012.04747/) (2020)
- [SWIFT: Scalable Wasserstein Factorization for Sparse Nonnegative Tensors](https://mlsanity.com/paper/2010.04081/) (2020)
- [Multiresolution Tensor Learning for Efficient and Interpretable Spatial Analysis](https://mlsanity.com/paper/2002.05578/) (2020)
- [PREMA: Principled Tensor Data Recovery from Multiple Aggregated Views](https://mlsanity.com/paper/1910.12001/) (2019)
- [Coupled Tensor Decomposition for Hyperspectral and Multispectral Image Fusion with Inter-Image Variability](https://mlsanity.com/paper/2006.16968/) (2020)

## Built on by (most cited first, 4 of 4)

- [ATD: Augmenting CP Tensor Decomposition by Self Supervision](https://mlsanity.com/paper/2106.07900/) (2021)
- [Influence-guided Data Augmentation for Neural Tensor Completion](https://mlsanity.com/paper/2108.10248/) (2021)
- [Variational Bayesian inference for CP tensor completion with side information](https://mlsanity.com/paper/2206.12486/) (2022)
- [GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completion](https://mlsanity.com/paper/2205.03749/) (2022)

## Abstract (arXiv)

Existing tensor completion formulation mostly relies on partial observations from a single tensor. However, tensors extracted from real-world data are often more complex due to: (i) Partial observation: Only a small subset (e.g., 5%) of tensor elements are available. (ii) Coarse observation: Some tensor modes only present coarse and aggregated patterns (e.g., monthly summary instead of daily reports). In this paper, we are given a subset of the tensor and some aggregated/coarse observations (along one or more modes) and seek to recover the original fine-granular tensor with low-rank factorization. We formulate a coupled tensor completion problem and propose an efficient Multi-resolution Tensor Completion model (MTC) to solve the problem. Our MTC model explores tensor mode properties and leverages the hierarchy of resolutions to recursively initialize an optimization setup, and optimizes on the coupled system using alternating least squares. MTC ensures low computational and space complexity. We evaluate our model on two COVID-19 related spatio-temporal tensors. The experiments show that MTC could provide 65.20% and 75.79% percentage of fitness (PoF) in tensor completion with only 5% fine granular observations, which is 27.96% relative improvement over the best baseline. To evaluate the learned low-rank factors, we also design a tensor prediction task for daily and cumulative disease case predictions, where MTC achieves 50% in PoF and 30% relative improvements over the best baseline.