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The use of rough set theory (RST) [261] to achieve data reduction is one approach that has proved successful. Over the past 20 years RST has become a topic of great interest to researchers and has been applied to many domains (e.g.,
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classi cation [54,84,164], systems monitoring [322], clustering [131], and expert systems [354]; see LNCS Transactions on Rough Sets for more examples). This success is due in part to the following aspects of the theory:
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Only the facts hidden in data are analyzed. No additional information about the data is required such as thresholds or expert knowledge on a particular domain. It nds a minimal knowledge representation.
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The work on RST offers an alternative, and formal, methodology that can be employed to reduce the dimensionality of datasets, as a preprocessing step to assist any chosen modeling method for learning from data. It helps select the most information-rich features in a dataset, without transforming the data, all the while attempting to minimize information loss during the selection process. Computationally, the approach is highly ef cient, relying on simple set operations, which makes it suitable as a preprocessor for techniques that are much more complex. Unlike statistical correlation-reducing approaches [77], it requires no human input or intervention. Most importantly, it also retains the semantics of the data, which makes the resulting models more transparent to human scrutiny. Combined with an automated intelligent modeler, say a fuzzy system or a neural network, the feature selection approach based on RST not only can retain the descriptive power of the learned models but also allow simpler system structures to reach the knowledge engineer and eld operator. This helps enhance the interoperability and understandability of the resultant models and their reasoning. As RST handles only one type of imperfection found in data, it is complementary to other concepts for the purpose, such as fuzzy set theory. The two elds may be considered analogous in the sense that both can tolerate inconsistency and uncertainty the difference being the type of uncertainty and their approach to it. Fuzzy sets are concerned with vagueness; rough sets are concerned with indiscernibility. Many deep relationships have been established, and more so, most recent studies have concluded at this complementary nature of the two methodologies, especially in the context of granular computing. Therefore it is desirable to extend and hybridize the underlying concepts to deal with additional aspects of data imperfection. Such developments offer a high degree of exibility and provide robust solutions and advanced tools for data analysis.
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As many systems in a variety of elds deal with datasets of large dimensionality, feature selection has found wide applicability. Some of the main areas of application are shown in Figure 1.2. Feature selection algorithms are often applied to optimize the classi cation performance of image recognition systems [158,332]. This is motivated by a peaking phenomenon commonly observed when classi ers are trained with a limited
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Typical feature selection application areas
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set of training samples. If the number of features is increased, the classi cation rate of the classi er decreases after a peak. In melanoma diagnosis, for instance, the clinical accuracy of dermatologists in identifying malignant melanomas is only between 65% and 85% [124]. With the application of FS algorithms, automated skin tumor recognition systems can produce classi cation accuracies above 95%. Structural and functional data from analysis of the human genome have increased many fold in recent years, presenting enormous opportunities and challenges for AI tasks. In particular, gene expression microarrays are a rapidly maturing technology that provide the opportunity to analyze the expression levels of thousands or tens of thousands of genes in a single experiment. A typical classi cation task is to distinguish between healthy and cancer patients based on their gene expression pro le. Feature selectors are used to drastically reduce the size of these datasets, which would otherwise have been unsuitable for further processing [318,390,391]. Other applications within bioinformatics include QSAR [46], where the goal is to form hypotheses relating chemical features of molecules to their molecular activity, and splice site prediction [299], where junctions between coding and noncoding regions of DNA are detected. The most common approach to developing expressive and human readable representations of knowledge is the use of if-then production rules. Yet real-life problem domains usually lack generic and systematic expert rules for mapping feature patterns onto their underlying classes. In order to speed up the rule
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