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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.
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.
Regression analysis is a key area of interest in the field of data
analysis and machine learning which is devoted to exploring the
dependencies between variables, often using vectors. The emergence
of high dimensional data in technologies such as neuroimaging,
computer vision, climatology and social networks, has brought
challenges to traditional data representation methods. Tensors, as
high dimensional extensions of vectors, are considered as natural
representations of high dimensional data. In this book, the authors
provide a systematic study and analysis of tensor-based regression
models and their applications in recent years. It groups and
illustrates the existing tensor-based regression methods and covers
the basics, core ideas, and theoretical characteristics of most
tensor-based regression methods. In addition, readers can learn how
to use existing tensor-based regression methods to solve specific
regression tasks with multiway data, what datasets can be selected,
and what software packages are available to start related work as
soon as possible. Tensor Regression is the first thorough overview
of the fundamentals, motivations, popular algorithms, strategies
for efficient implementation, related applications, available
datasets, and software resources for tensor-based regression
analysis. It is essential reading for all students, researchers and
practitioners of working on high dimensional data.
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