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

翻译：电离分解是维度减少和对诸如信号等多维数据进行特征解释的有力工具。现有的分解目标(如Frobenius规范)旨在根据统计假设(可能不符合下游分类任务)来安装原始数据,这些假设可能与下游分类任务不相符。在实践上,原始输入压强可能包含不相关的信息,而数据增强技术可能用来在样本中平息与阶级无关的噪音。本文件通过提出增强的反光分解(ATD)来应对上述挑战,这有效地结合了数据增强和自我监督的学习(SSL)来推动下游分类。为解决新扩大的目标的不均匀性,我们开发了一种迭接方法,使优化能够遵循交替最小平方(ALS)的方式。我们在多个数据集上评估了我们提议的ATD。它能够实现0.8%-2.5%的精度超过基于温度的基线。此外,我们的ATD模型显示在自我监督和自动分解基线基线上可比较或更好的性(例如高达15%),同时使用低于5%的可学习参数。