Data mining was one of the buzz-words at the verge of the third millennium. It was already a multi-million dollar industry in the late 1990s and experts expected a continuing growth for the first decade of the 21st century. Although this expectation has not quite materialized in recent years, data mining still is an important field of scientific research with great potential for commercial usage. The ubiquitous computer makes it possible to collect huge data bases that contain potentially valuable information. Sophisticated analysis techniques are needed to explore these large, often heterogeneous, data sets and to extract the small pieces of information that are valuable to the data owner.
The importance of exploring and analyzing real data sets is not new to statistics. It has been reinforced in the late 1960s by John W. Tukey who realized that putting too much emphasis on the mathematical theories of statistics did not help in solving the real world problems. It was his mantra that statistical work is detective work ([31]) and that one should let the data speak for itself. The branch of exploratory data analysis emerged, but was dismissed by mathematical statisticians for a long period of time. Many of them proclaimed that proper statistical analysis must be based on hypothesis and distributional assumptions. Their argument was that looking at data before formulating a scientific hypothesis will bias the hypothesis towards what the data might show. The term data mining typically was used in a derogatory connotation. The argument culminated in the reproach of improper scientific use, the reproach of torturing the data until it confesses everything.
The advent of information technology that allowed to easily collect and store data of previously unimaginable quantities brought a rapid change to the scene and superseded academic disputes. Once the computer power and technology was there, that made it easy to collect information of all customers in a super market, or for all customers of a telephone company, the need arose to make use of these large information sources.
Now, Data Mining is a thriving field of research and application, to which both statisticians and computer scientists have contributed new ideas and new techniques. In this contribution, we will introduce the main components, tasks, and computational methods for data mining. After an attempt to define data mining, we relate it to the larger field of knowledge discovery in databases in Sect. 13.2. Section 13.3 deals with the two flavors of learning from data: supervised and unsupervised learning. We will then discuss the different data mining tasks in Sect. 13.4, before we present the computational methods to tackle them in Sect. 13.5. In the final Sect. 13.5.2, we present some recent trends in visual methods for data mining.