Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition

Abstract

In modern society huge amounts of data are collected and stored in computers with the purpose of later extracting useful information. Often it is not known at the occasion of collecting the data what information is going to be requested, and therefore the database is often not designed to distill any particular information, but rather it is to a large extent unstructured. The science of extracting useful information from large data sets is usually referred to as “data mining”, sometimes with the addition “knowledge discovery”. Pattern recognition is often considered as a technique separate from data mining, but its definition is related: “the act of taking in raw data and making an action based on the “category” of the pattern” [31]. In this book we will not emphasize the differences between the concepts. There are numerous application areas of data mining, ranging from e-business [10, 69] to bioinformatics [6], from scientific application such as the classification of volcanos on Venus [21] to information retrieval [3] and Internet search engines [11]. Data mining is a truly interdisciplinary science, where techniques from computer science, statistics and data analysis, linear algebra and optimization are used, often in a rather eclectic manner. Due to the practical importance of the applications, there are now numerous books and surveys in the area. We cite a few here: [24, 25, 31, 35, 45, 46, 47, 49, 108]. It is not an exaggeration to state that everyday life is filled with situations in which we depend, often unknowingly, on advanced mathematical methods for data mining. Linear algebra and data analysis are basic ingredients in many data mining techniques. This book will give an introduction to the mathematical and numerical methods, and their use in data mining and pattern recognition.