Foundations of Computational Intelligence Volume 5: Function Approximation and Classification Approximation theory is that area of analysis which is concerned with the ability to approximate functions by simpler and more easily calculated functions. It is an area which, like many other fields of analysis, has its primary roots in the mat- matics. The need for function approximation and classification arises in many branches of applied mathematics, computer science and data mining in particular. This edited volume comprises of 14 chapters, including several overview Ch- ters, which provides an up-to-date and state-of-the art research covering the theory and algorithms of function approximation and classification. Besides research ar- cles and expository papers on theory and algorithms of function approximation and classification, papers on numerical experiments and real world applications were also encouraged. The Volume is divided into 2 parts: Part-I: Function Approximation and Classification - Theoretical Foundations Part-II: Function Approximation and Classification - Success Stories and Real World Applications Part I on Function Approximation and Classification - Theoretical Foundations contains six chapters that describe several approaches Feature Selection, the use Decomposition of Correlation Integral, Some Issues on Extensions of Information and Dynamic Information System and a Probabilistic Approach to the Evaluation and Combination of Preferences Chapter 1 "Feature Selection for Partial Least Square Based Dimension Red- tion" by Li and Zeng investigate a systematic feature reduction framework by combing dimension reduction with feature selection. To evaluate the proposed framework authors used four typical data sets.