A Survey on Tensor Techniques and Applications in Machine Learning

This survey gives a comprehensive overview of tensor techniques and applications in machine learning. Tensor represents higher order statistics. Nowadays, many applications based on machine learning algorithms require a large amount of structured high-dimensional input data. As the set of data increases, the complexity of these algorithms increases exponentially with the increase of vector size. Some scientists found that using tensors instead of the original input vectors can effectively solve these high-dimensional problems. This survey introduces the basic knowledge of tensor, including tensor operations, tensor decomposition, some tensor-based algorithms, and some applications of tensor in machine learning and deep learning for those who are interested in learning tensors. The tensor decomposition is highlighted because it can effectively extract structural features of data and many algorithms and applications are based on tensor decomposition. The organizational framework of this paper is as follows. In part one, we introduce some tensor basic operations, including tensor decomposition. In part two, applications of tensor in machine learning and deep learning, including regression, supervised classification, data preprocessing, and unsupervised classification based on low rank tensor approximation algorithms are introduced detailly. Finally, we briefly discuss urgent challenges, opportunities and prospects for tensor.