Research on Tensor Computation and Its Application on Data Science

Research on Tensor Computation and Its Application on Data Science
Author: Zequn Zheng
Publisher:
Total Pages: 0
Release: 2023
Genre:
ISBN:

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Tensors or multidimensional arrays are higher order generalizations of matrices. They are natural structures for expressing data that have inherent higher order structures. Tensor decompositions and Tensor approximations play an important role in learning those hidden structures. They have many applications in machine learning, statistical learning, data science, signal processing, neuroscience, and more. Canonical Polyadic Decomposition (CPD) is a tensor decomposition that decomposes a tensor to minimal number of summation of rank 1 tensors. While for a given tensor, Low-Rank Tensor Approximation (LRTA) aims at finding a new one whose rank is small and that is close to the given one. We study the generating polynomials for computing tensor decompositions and low-rank approximations for given tensors and propose methods that can compute tensor decompositions for generic tensors under certain rank conditions. For low-rank tensor approximation, the proposed method guarantees that the constructed tensor is a good enough low-rank approximation if the tensor is to be approximated is close enough to a low-rank one. The proof built on perturbation analysis is presented. When the rank is higher than the second dimension, we are not able to find the common zeros of generating polynomials directly. In this case, we need to use the quadratic equations that we get from those generating polynomials. We show that under certain conditions, we are able to find the tensor decompositions using standard linear algebra operations (i.e., solving linear systems, singular value decompositions, QR decompositions). Numerical examples and some comparisons are presented to show the performance of our algorithm. Multi-view learning is frequently used in data science. The pairwise correlation maximization is a classical approach for exploring the consensus of multiple views. Since the pairwise correlation is inherent for two views, the extensions to more views can be diversified and the intrinsic interconnections among views are generally lost. To address this issue, we propose to maximize the high-order tensor correlation. This can be formulated as a low-rank approximation problem with the high-order correlation tensor of multi-view data. We propose to use the generating polynomial method to efficiently solve the high-order correlation maximization problem of tensor canonical correlation analysis for multi-view learning. Numerical results on simulated data and two real multi-view data sets demonstrate that our proposed method not only consistently outperforms existing methods but also is efficient for large scale tensors.

Tensor Computation for Data Analysis

Tensor Computation for Data Analysis
Author: Yipeng Liu
Publisher: Springer Nature
Total Pages: 347
Release: 2021-08-31
Genre: Technology & Engineering
ISBN: 3030743861

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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.

User-Defined Tensor Data Analysis

User-Defined Tensor Data Analysis
Author: Bin Dong
Publisher: Springer Nature
Total Pages: 111
Release: 2021-09-29
Genre: Computers
ISBN: 3030707504

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The SpringerBrief introduces FasTensor, a powerful parallel data programming model developed for big data applications. This book also provides a user's guide for installing and using FasTensor. FasTensor enables users to easily express many data analysis operations, which may come from neural networks, scientific computing, or queries from traditional database management systems (DBMS). FasTensor frees users from all underlying and tedious data management tasks, such as data partitioning, communication, and parallel execution. This SpringerBrief gives a high-level overview of the state-of-the-art in parallel data programming model and a motivation for the design of FasTensor. It illustrates the FasTensor application programming interface (API) with an abundance of examples and two real use cases from cutting edge scientific applications. FasTensor can achieve multiple orders of magnitude speedup over Spark and other peer systems in executing big data analysis operations. FasTensor makes programming for data analysis operations at large scale on supercomputers as productively and efficiently as possible. A complete reference of FasTensor includes its theoretical foundations, C++ implementation, and usage in applications. Scientists in domains such as physical and geosciences, who analyze large amounts of data will want to purchase this SpringerBrief. Data engineers who design and develop data analysis software and data scientists, and who use Spark or TensorFlow to perform data analyses, such as training a deep neural network will also find this SpringerBrief useful as a reference tool.

Tensors for Data Processing

Tensors for Data Processing
Author: Yipeng Liu
Publisher: Academic Press
Total Pages: 598
Release: 2021-10-21
Genre: Technology & Engineering
ISBN: 0323859658

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Tensors for Data Processing: Theory, Methods and Applications presents both classical and state-of-the-art methods on tensor computation for data processing, covering computation theories, processing methods, computing and engineering applications, with an emphasis on techniques for data processing. This reference is ideal for students, researchers and industry developers who want to understand and use tensor-based data processing theories and methods. As a higher-order generalization of a matrix, tensor-based processing can avoid multi-linear data structure loss that occurs in classical matrix-based data processing methods. This move from matrix to tensors is beneficial for many diverse application areas, including signal processing, computer science, acoustics, neuroscience, communication, medical engineering, seismology, psychometric, chemometrics, biometric, quantum physics and quantum chemistry. Provides a complete reference on classical and state-of-the-art tensor-based methods for data processing Includes a wide range of applications from different disciplines Gives guidance for their application

Programming with TensorFlow

Programming with TensorFlow
Author: Kolla Bhanu Prakash
Publisher: Springer Nature
Total Pages: 190
Release: 2021-01-22
Genre: Technology & Engineering
ISBN: 3030570770

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This practical book provides an end-to-end guide to TensorFlow, the leading open source software library that helps you build and train neural networks for deep learning, Natural Language Processing (NLP), speech recognition, and general predictive analytics. The book provides a hands-on approach to TensorFlow fundamentals for a broad technical audience—from data scientists and engineers to students and researchers. The authors begin by working through some basic examples in TensorFlow before diving deeper into topics such as CNN, RNN, LSTM, and GNN. The book is written for those who want to build powerful, robust, and accurate predictive models with the power of TensorFlow, combined with other open source Python libraries. The authors demonstrate TensorFlow projects on Single Board Computers (SBCs).

Tensor Regression

Tensor Regression
Author: Jiani Liu
Publisher:
Total Pages:
Release: 2021-09-27
Genre:
ISBN: 9781680838862

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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.

Theory and Computation of Complex Tensors and its Applications

Theory and Computation of Complex Tensors and its Applications
Author: Maolin Che
Publisher: Springer Nature
Total Pages: 250
Release: 2020-04-01
Genre: Mathematics
ISBN: 9811520593

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The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective. A systematic description about how to extend the numerical linear algebra to the numerical multi-linear algebra is also delivered in this book. The authors design the neural network model for the computation of the rank-one approximation of real tensors, a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors and a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors, adaptive randomized algorithms for computing the approximate tensor decompositions, and the QR type method for computing U-eigenpairs of complex tensors. This book could be used for the Graduate course, such as Introduction to Tensor. Researchers may also find it helpful as a reference in tensor research.

A Greater Foundation for Machine Learning Engineering

A Greater Foundation for Machine Learning Engineering
Author: Dr. Ganapathi Pulipaka
Publisher: Xlibris Corporation
Total Pages: 382
Release: 2021-10-01
Genre: Computers
ISBN: 1664151273

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This research scholarly illustrated book has more than 250 illustrations. The simple models of supervised machine learning with Gaussian Naïve Bayes, Naïve Bayes, decision trees, classification rule learners, linear regression, logistic regression, local polynomial regression, regression trees, model trees, K-nearest neighbors, and support vector machines lay a more excellent foundation for statistics. The author of the book Dr. Ganapathi Pulipaka, a top influencer of machine learning in the US, has created this as a reference book for universities. This book contains an incredible foundation for machine learning and engineering beyond a compact manual. The author goes to extraordinary lengths to make academic machine learning and deep learning literature comprehensible to create a new body of knowledge. The book aims at readership from university students, enterprises, data science beginners, machine learning and deep learning engineers at scale for high-performance computing environments. A Greater Foundation of Machine Learning Engineering covers a broad range of classical linear algebra and calculus with program implementations in PyTorch, TensorFlow, R, and Python with in-depth coverage. The author does not hesitate to go into math equations for each algorithm at length that usually many foundational machine learning books lack leveraging the JupyterLab environment. Newcomers can leverage the book from University or people from all walks of data science or software lives to the advanced practitioners of machine learning and deep learning. Though the book title suggests machine learning, there are several implementations of deep learning algorithms, including deep reinforcement learning. The book's mission is to help build a strong foundation for machine learning and deep learning engineers with all the algorithms, processors to train and deploy into production for enterprise-wide machine learning implementations. This book also introduces all the concepts of natural language processing required for machine learning algorithms in Python. The book covers Bayesian statistics without assuming high-level mathematics or statistics experience from the readers. It delivers the core concepts and implementations required with R code with open datasets. The book also covers unsupervised machine learning algorithms with association rules and k-means clustering, metal-learning algorithms, bagging, boosting, random forests, and ensemble methods. The book delves into the origins of deep learning in a scholarly way covering neural networks, restricted Boltzmann machines, deep belief networks, autoencoders, deep Boltzmann machines, LSTM, and natural language processing techniques with deep learning algorithms and math equations. It leverages the NLTK library of Python with PyTorch, Python, and TensorFlow's installation steps, then demonstrates how to build neural networks with TensorFlow. Deploying machine learning algorithms require a blend of cloud computing platforms, SQL databases, and NoSQL databases. Any data scientist with a statistics background that looks to transition into a machine learning engineer role requires an in-depth understanding of machine learning project implementations on Amazon, Google, or Microsoft Azure cloud computing platforms. The book provides real-world client projects for understanding the complete implementation of machine learning algorithms. This book is a marvel that does not leave any application of machine learning and deep learning algorithms. It sets a more excellent foundation for newcomers and expands the horizons for experienced deep learning practitioners. It is almost inevitable that there will be a series of more advanced algorithms follow-up books from the author in some shape or form after setting such a perfect foundation for machine learning engineering.