# ATD: Augmenting CP Tensor Decomposition by Self Supervision

arXiv: https://arxiv.org/abs/2106.07900 · HTML: https://mlsanity.com/paper/2106.07900/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 15 Jun 2021.

## Builds on (most cited first, 18 of 18)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Debiased Contrastive Learning](https://mlsanity.com/paper/2007.00224/) (2020)
- [Time Series Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2002.12478/) (2020)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [A Kernel Theory of Modern Data Augmentation](https://mlsanity.com/paper/1803.06084/) (2018)
- [Subject-Aware Contrastive Learning for Biosignals](https://mlsanity.com/paper/2007.04871/) (2020)
- [Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition](https://mlsanity.com/paper/1707.02477/) (2017)
- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [Stochastic Gradients for Large-Scale Tensor Decomposition](https://mlsanity.com/paper/1906.01687/) (2019)
- [Fast and Accurate Randomized Algorithms for Low-rank Tensor Decompositions](https://mlsanity.com/paper/2104.01101/) (2021)
- [LSAR: Efficient Leverage Score Sampling Algorithm for the Analysis of Big Time Series Data](https://mlsanity.com/paper/1911.12321/) (2019)
- [MTC: Multiresolution Tensor Completion from Partial and Coarse Observations](https://mlsanity.com/paper/2106.07135/) (2021)
- [Distributed-Memory Tensor Completion for Generalized Loss Functions in Python using New Sparse Tensor Kernels](https://mlsanity.com/paper/1910.02371/) (2019)
- [Analysis of the Stochastic Alternating Least Squares Method for the Decomposition of Random Tensors](https://mlsanity.com/paper/2004.12530/) (2020)

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

- [Self-supervised EEG Representation Learning for Automatic Sleep Staging](https://mlsanity.com/paper/2110.15278/) (2021)
- [ManyDG: Many-domain Generalization for Healthcare Applications](https://mlsanity.com/paper/2301.08834/) (2023)
- [BIOT: Cross-data Biosignal Learning in the Wild](https://mlsanity.com/paper/2305.10351/) (2023)
- [NeuroBOLT: Resting-state EEG-to-fMRI Synthesis with Multi-dimensional Feature Mapping](https://mlsanity.com/paper/2410.05341/) (2024)
- [Enabling Tensor Decomposition for Time-Series Classification via A Simple Pseudo-Laplacian Contrast](https://mlsanity.com/paper/2409.15200/) (2024)
- [Intelligently Augmented Contrastive Tensor Factorization: Empowering Multi-dimensional Time Series Classification in Low-Data Environments](https://mlsanity.com/paper/2505.03825/) (2025)
- [Disentangled Mode-Specific Representations for Tensor Time Series via Contrastive Learning](https://mlsanity.com/paper/2602.23663/) (2026)

## Abstract (arXiv)

Tensor decompositions are powerful tools for dimensionality reduction and feature interpretation of multidimensional data such as signals. Existing tensor decomposition objectives (e.g., Frobenius norm) are designed for fitting raw data under statistical assumptions, which may not align with downstream classification tasks. In practice, raw input tensors can contain irrelevant information while data augmentation techniques may be used to smooth out class-irrelevant noise in samples. This paper addresses the above challenges by proposing augmented tensor decomposition (ATD), which effectively incorporates data augmentations and self-supervised learning (SSL) to boost downstream classification. To address the non-convexity of the new augmented objective, we develop an iterative method that enables the optimization to follow an alternating least squares (ALS) fashion. We evaluate our proposed ATD on multiple datasets. It can achieve 0.8% - 2.5% accuracy gain over tensor-based baselines. Also, our ATD model shows comparable or better performance (e.g., up to 15% in accuracy) over self-supervised and autoencoder baselines while using less than 5% of learnable parameters of these baseline models