Machine learning is a research field involving the study of theories and technologies to adapt a system model using a training dataset, so that the learned model will be able to generalize and provide a correct classification or useful guidance even when the inputs to the system are previously unknown. Machine learning builds its foundation on linear algebra, statistical learning theory, pattern recognition, and artificial intelligence. The development of practical machine learning tools requires multi-disciplinary knowledge including matrix theory, signal processing, regression analysis, discrete mathematics, and optimization theory. It covers a broad spectrum of application domains in multimedia processing, network optimization, biomedical analysis, etc.

Since the publication of Vapnik's book entitled The Nature of Statistical Learning Theory (Springer-Verlag, 1995) and the introduction of the celebrated support vector machine (SVM), research on kernel-based machine learning has flourished steadily for nearly two decades. The enormous amount of research findings on unsupervised and supervised learning models, both theory and applications, should already warrant a new textbook, even without considering the fact that this fundamental field will undoubtedly continue to grow for a good while.

The book first establishes algebraic and statistical foundations for kernel-based learning methods. It then systematically develops kernel-based learning models both for unsupervised and for supervised scenarios.

• The secret of success of a machine learning system lies in finding an effective representation for the objects of interest. In a basic representation, an object is represented as a feature vector in a finite-dimensional vector space.