Open access peer-reviewed Edited Volume

Projective Geometry - the Application of Projective Geometry in Principal Component Analysis, Independent Component Analysis and Pattern Classification and Recognition

Min Lei

Shanghai Jiao Tong University


principal component analysis SVD symplectic geometry KPCA independent component analysis linear discriminant analysis blind source separation deep learning pattern classification recognition support vector machine feature extraction

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About the book

Projective geometry has a long history of development, which can be traced back to the 4th century BC when the ancient Greeks discovered the conic curve. Until the 17th century, the French mathematician R. Descartes (1596-1650) algebraized geometry, i.e. solved geometric problems by using algebraic equations, which led to the emergence of analytic geometry, followed by analytic projective geometry. Projective geometry mainly studies the invariant geometric properties of graphics under projective transformation. It has beautiful mathematical principles and contents such as duality principle, continuity principle, and butterfly theorem. "all geometry is projective geometry!" said by British mathematician A. Cayley (1821-1895). With the development of algebraic theory and the application of the determinant theory of equations and coordinate transformation methods, projective geometry has been applied and developed in various fields, especially in large data analysis, such as principal component analysis, independent component analysis, pattern classification, and recognition, etc. This book focuses on the application of projective geometry in principal component analysis, independent component analysis, and pattern classification and recognition.

Publishing process

Book initiated and editor appointed

Date completed: October 28th 2019

Applications to edit the book are assessed and a suitable editor is selected, at which point the process begins.

Chapter proposals submitted and reviewed

Deadline Extended: Open for Submissions

Potential authors submit chapter proposals ready for review by the academic editor and our publishing review team.

Approved chapters written in full and submitted

Deadline for full chapters: January 17th 2020

Once approved by the academic editor and publishing review team, chapters are written and submitted according to pre-agreed parameters

Full chapters peer reviewed

Review results due: April 6th 2020

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Book compiled, published and promoted

Expected publication date: June 5th 2020

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About the editor

Min Lei

Shanghai Jiao Tong University

She has worked in Shanghai Jiaotong University as an associate professor since 2004. From February 2003 to February 2004, she worked as Research Fellow in the Department of Mechanical Engineering, Nanyang University of Technology, Singapore. From 2000 to 2002, she worked as a postdoctoral fellow in the Institute of Mechanical and Electrical Control, School of Mechanical and Power Engineering, Shanghai Jiaotong University. She received a doctoral degree from the Department of Biomedical Engineering, Shanghai Jiaotong University, in 2000. She has been engaged in biomedical signal processing, modern signal processing, pattern recognition and classification, and nonlinear dynamics for a long time.

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Book chapters authored 2

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