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In this chapter a method for feature selection based on fuzzy-rough sets was presented. An algorithm for nding feature subsets, based on the new fuzzy-rough dependency measure, was introduced and illustrated by means of two simple examples. The examples were chosen to demonstrate the fact that FRFS can be
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applied to datasets containing crisp or real-valued features, or a mixture of both. Implemented optimizations were brie y discussed that can signi cantly improve the runtime of FRFS. This was demonstrated by comparing the execution times of the different implementations on real-world data. One real-world and several arti cial datasets were also used to evaluate the utility of the fuzzy-rough measure and provide comparisons with other leading feature importance measures. The results show that the new metric presented here is slightly better than the leading measures at locating the relevant features. FRFS can be applied to any of the domains highlighted previously where feature selection has been employed. For the purposes of this book, three challenging domains of interest were chosen to illustrate its potential utility: Web content categorization, complex systems monitoring, and algae population estimation. The problem of Web content categorization is a signi cant one due to the explosive increase of information available on the Web and its increasing popularity. Techniques for automated categorization of Web documents help in the building of catalogues and facilitate the retrieval of material. In order to deal with the large number of features involved in such classi cation, feature selectors are typically used [309]. The dimensionality of the problem datasets can be suf ciently reduced to enable more sophisticated learning algorithms to perform their tasks. The work presented here looks speci cally at addressing the issues of bookmark/favorite classi cation and Web page classi cation. FRFS reduces the size of the datasets involved by several orders of magnitude, retaining most of the information present in the datasets and making the classi cation task manageable. In systems monitoring it is important to reduce the number of features involved for several reasons. First, there is an associated cost with the measurement of a feature. It is desirable simply from an expense-saving point of view to reduce the number of monitored variables. Second, the resultant transparency of the monitoring process can be improved if fewer variables are involved. Third, it is often observed that the accuracy of the monitoring system can be signi cantly improved using fewer variables [322]. FRFS is here applied to the water treatment plant dataset [38] as an example of how this fuzzy-rough method can be used within the systems monitoring domain. Additionally the new feature grouping and ant colony optimization-based methods are applied to this domain to show their potential utility. Algae population estimation is another important area that bene ts greatly from the use of feature selection. FRFS can be used to signi cantly reduce computer time and space requirements. Also it decreases the cost of obtaining measurements and increases runtime ef ciency, making the system more viable economically. Through the use of fuzzy-rough sets the FRFS-based method can handle real-valued decision features (algae populations), unlike many existing approaches. The system does not alter the domain semantics, making any distilled knowledge human-readable.
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Fuzzy-rough set-based feature selection has been shown to be highly useful at reducing data dimensionality, but it possesses several problems that render it ineffective for large datasets. This chapter presents three new approaches to fuzzy-rough feature selection based on fuzzy similarity relations. In particular, a fuzzy extension to crisp discernibility matrices is proposed and utilized. Initial experimentation shows that the methods greatly reduce dimensionality while preserving classi cation accuracy.
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