Data Mining for the category management in the retail market

Worldwide the retail market is under a severe competitive pressure. The retail trade in Germany in particular is internationally recognized as the most competitive market. To survive in this market most retailers use undirected mass marketing extensively. All prospective customers receive the same huge catalogues, countless advertising pamphlets, intrusive speaker announcements and flashy banner ads. In the end the customers are not only annoyed but the response rates of advertising campaigns are dropping for years. To avoid this, an individualization of mass marketing is recommended where customers receive individual offers specific to their needs. The objective is to offer the right customer at the right time for the right price the right product or content. This turns out to be primarily a mathematical problem concerning the areas of statistics, optimization, analysis and numerics. The arising problems of regression, clustering, and optimal control are typically of high dimensions and have huge amounts of data and therefore need new mathematical concepts and algorithms. The underlying concept is the (semi)-automatic knowledge discovery via the analysis of huge databases, also known as data mining. The algorithmic core of the data mining process is called machine learning. This subject area originally belonged to computer science; the connection to statistics played a significant role from the beginnings. In recent years, further mathematical aspects were being considered especially in research, an example is the field of statistical learning theory. Algorithms with such a background are used successfully in many applications, not least due to their mathematical foundation. The underlying assumption is that similar customer data signifies similar customer behaviour, this allows to assess new customers on the basis of the behaviour of former customers. Of fundamental importance is that many modern machine learning approaches use the representation of functions over high dimensional attribute spaces. This allows the coupled non-linear treatment of different attributes like income, debt, number of children, or type of car which results in an improved estimation of the likely customer behaviour. Approximation theory and numerics already play a substantial role for the development