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Lie group machine learning
Fanzhang L., Li Z., Zhao Z., Walter de Gruyter & Co., Berlin, Germany, 2018. 533 pp. Type: Book (978-3-110500-68-4)
Date Reviewed: Dec 4 2019

Machine learning, one of the evergreen fields of electrical engineering, has recently gained momentum and has a number of new and innovative applications. Related fields, such as artificial intelligence, deep learning, brain learning, tensor flow, and so on, help to develop machine learning applications in a better way.

Lie groups, which are a complement to topological groups, are a kind of differentiable manifold that is a combination of algebra and geometry structure. Lie groups can be used to describe natural models using real parameters. A lie group, due to its inherent characteristics, is well suited to describe machine learning clearly at an advanced level.

This book provides a framework to study machine learning applications using lie groups. It has 16 chapters and an appendix. It covers various advanced machine learning algorithms, including quantum group learning, fiber bundle learning, deep learning, kernel learning, tensor learning, and so on.

All 16 chapters are comprehensive and well written. They neatly present the latest state-of-the-art algorithms, and the mathematical treatment is superb. In addition to the theoretical foundations, the authors have conducted experiments and present the results along with detailed discussions. Each chapter has a nice summary and highly useful bibliography.

When possible, the authors provide examples, case studies, and numerical illustrations. Had the authors written a strong introductory chapter and used the same experimental setups and parameters to analyze the results (wherever possible), this book would have been the best material. In absence of these, it appears to me as an edited volume rather than an authored book.

Overall, I must congratulate the authors for taking up this nice and challenging task of writing a book on lie group machine learning. The book will be a great asset to postgraduate students, researchers, and industry experts who work in machine learning and pattern recognition.

Reviewer:  S. Ramakrishnan Review #: CR146804 (2004-0070)
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