Pattern classification is a very general concept with numerous applications ranging from science, engineering, target marketing, medical diagnosis and electronic commerce to weather forecast based on satellite imagery. A typical application of pattern classification is mass mailing for marketing. For example, credit card companies often mail solicitations to consumers. Naturally, they would like to target those consumers who are most likely to respond. Often, demographic information is available for those who have responded previously to such solicitations, and this information may be used in order to target the most likely respondents. Another application is electronic commerce of the new economy. E-commerce provides a rich environment to advance the state-of-the-art in classification because it demands effective means for text classification in order to make rapid product and market recommendations. Recent developments in data mining have posed new challenges to pattern classification. Data mining is a knowledge discovery process whose aim is to discover unknown relationships and/or patterns from a large set of data, from which it is possible to predict future outcomes. As such, pattern classification becomes one of the key steps in an attempt to uncover the hidden knowledge within the data. The primary goal is usually predictive accuracy, with secondary goals being speed, ease of use, and interpretability of the resulting predictive model. While pattern classification has shown promise in many areas of practical significance, it faces difficult challenges posed by real world problems, of which the most pronounced is Bellman’s curse of dimensionality: it states the fact that the sample size required to perform accurate prediction on problems with high dimensionality is beyond feasibility. This is because in high dimensional spaces data become extremely sparse and are apart from each other. As a result, severe bias that affects any estimation process can be introduced in a high dimensional feature space with finite samples. Learning tasks with data represented as a collection of a very large number of features abound. For example, microarrays contain an overwhelming number of genes relative to the number of samples. The Internet is a vast repository of disparate information growing at an exponential rate. Efficient and effective document retrieval and classification systems are required to turn the ocean of bits around us into useful information, and eventually into knowledge. This is a challenging task, since a word level representation of documents easily leads 30000 or more dimensions. This chapter discusses classification techniques to mitigate the curse of dimensionality and reduce bias, by estimating feature relevance and selecting features accordingly. This issue has both theoretical and practical relevance, since many applications can benefit from improvement in prediction performance.
In a classification problem an observation is characterized by q feature measurements and is presumed to be a member of one of J classes, Lj, . The particular group is unknown, and the goal is to assign the given object to the correct group using its measured features x.
Feature relevance has a local nature. Therefore, any chosen fixed metric violates the assumption of locally constant class posterior probabilities, and fails to make correct predictions in different regions of the input space. In order to achieve accurate predictions, it becomes crucial to be able to estimate the different degrees of relevance that input features may have in various locations of the feature space.