The original Japanese edition of this book, published by Saiensu-sha, Japan, in March 2005, has fortunately acquired a favorable reputation. I am grateful to the readers for their kind feedbacks, many of which are included in this edition. I hope this English publication attracts readers in wider areas, and evokes valuable feedbacks furthermore. In the months after the Japanese publication, researches on the compl- valued neural networks have kept evolution in respective directions. There are some plans of special sessions in international conferences and special issues in journals. The bibliography has been slightly modi?ed to include the special sessions and latest journal publications. On the other hand, references written in Japanese on domestic circumstances have been omitted. Besides, Fig.1.1 has been added, and Fig.2.1 has been modi?ed, which are related to theSpecial Issue on Complex-Valued Neural Networks, The Journal of the IEICE, 87 (6), June 2004 (in Japanese), so that even readers not having glancedtheissuecanobtainclearconcepts.Withthesemodi?cations,Iexpect a higher appeal in this English edition. I am very much obliged to Dr. Thomas Ditzinger, Engineering Editor, Springer-Verlag, for his continuous help in publication. Tokyo, Japan Akira Hirose April 2006 Preface The studies on complex-valued neural networks have recently been evolving in various directions. The pioneering areas include electromagnetic-wave and lightwave sensing and imaging, independent component analysis in blind s- aration, blur restoration in image processing, and so on. Developing appli- tionsinvolveadaptivequantumdevices,quantumcomputation,socialsystems related to periodicity and oscillation, and so forth. This book is the first monograph ever on complex-valued neural networks, which lends itself to graduate and undergraduate courses in electrical engineering, informatics, control engineering, mechanics, robotics, bioengineering, and other relevant fields. It is useful for those beginning their studies, for instance, adaptive signal processing for highly functional sensing and imaging, control in unknown and changing environment, brainlike information processing, robotics inspired by human neural systems, and interdisciplinary studies to realize comfortable society. It is also helpful to those who carry out research and development regarding new products and services at companies. The author wrote this book hoping in particular that it provides the readers with meaningful hints to make good use of neural networks in fully practical applications. The book emphasizes basic ideas and ways of thinking. Why do we need to consider neural networks that deal with complex numbers? What advantages do the complex-valued neural networks have? What is the origin of the advantages? In what areas do they develop principal applications? This book answers these questions by describing details and examples, which will inspire the readers with new ideas This monograph instructs graduate- and undergraduate-level students in electrical engineering, informatics, control engineering, mechanics, robotics, bioengineering on the concepts of complex-valued neural networks. Emphasizing basic concepts and ways of thinking about neural networks, the author focuses on neural networks that deal with complex numbers; the practical advantages of complex-valued neural networks, and their origins; the development of principal applications? The book uses detailed examples to answer these questions and more. The art of the artificial neural networks is a technological framework in which we introduce and/or imitate the functions, constructions, and dynamics of the brain to realize an adaptive and useful information processing.
