Tensor is a natural representation for multi-dimensional data, and
tensor computation can avoid possible multi-linear data structure
loss in classical matrix computation-based data analysis. This book
is intended to provide non-specialists an overall understanding of
tensor computation and its applications in data analysis, and
benefits researchers, engineers, and students with theoretical,
computational, technical and experimental details. It presents a
systematic and up-to-date overview of tensor decompositions from
the engineer's point of view, and comprehensive coverage of tensor
computation based data analysis techniques. In addition, some
practical examples in machine learning, signal processing, data
mining, computer vision, remote sensing, and biomedical engineering
are also presented for easy understanding and implementation. These
data analysis techniques may be further applied in other
applications on neuroscience, communication, psychometrics,
chemometrics, biometrics, quantum physics, quantum chemistry, etc.
The discussion begins with basic coverage of notations, preliminary
operations in tensor computations, main tensor decompositions and
their properties. Based on them, a series of tensor-based data
analysis techniques are presented as the tensor extensions of their
classical matrix counterparts, including tensor dictionary
learning, low rank tensor recovery, tensor completion, coupled
tensor analysis, robust principal tensor component analysis, tensor
regression, logistical tensor regression, support tensor machine,
multilinear discriminate analysis, tensor subspace clustering,
tensor-based deep learning, tensor graphical model and tensor
sketch. The discussion also includes a number of typical
applications with experimental results, such as image
reconstruction, image enhancement, data fusion, signal recovery,
recommendation system, knowledge graph acquisition, traffic flow
prediction, link prediction, environmental prediction, weather
forecasting, background extraction, human pose estimation,
cognitive state classification from fMRI, infrared small target
detection, heterogeneous information networks clustering,
multi-view image clustering, and deep neural network compression.
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