Opportunities in tensorial data analytics for chemical and biological manufacturing processes

•New types of higher order tensorial information streams are becoming available.•The types of higher order data in chemical and biological systems are described.•Examples include real-time video, chemical imaging, and hyphenated methods.•Multilinear subspace learning methods and software are available for tensorial data.•Future directions and research needs for tensorial data analytics are discussed. With the development of technology in data collection and storage, new types of higher order tensorial information streams are available in chemical and biological manufacturing processes, which contain valuable information about the process condition and product quality. However, tensorial data have not been fully utilized yet and the application of tensorial data analytics to manufacturing processes has not been thoroughly investigated. In this article, different types of higher order data in manufacturing processes are described, and their potential usage is addressed. Then some perspectives are provided on the application of tensorial data analytics to manufacturing processes, with an emphasis on multilinear subspace learning problems. In particular, the most representative multilinear subspace learning methods are reviewed. Looking into the future, the potential and research needs for tensorial data analytics are briefly discussed. [Display omitted]