ROUGH SET BASED APPROACHES TO FEATURE SELECTION in .NET framework

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3000 2400 Time (s) 1800 1200 600 AntRSAR SimRSAR GenRSAR
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Figure 5.13 Average runtimes for AntRSAR, SimRSAR and GenRSAR
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chosen rst. When a clause is selected, the features appearing within the clause are added to every set in Subsets. For example, if Subsets contains {a, b} and {c, d}, and the next considered clause is {d e}, then each appearing attribute is added. The Subsets list will now contain {a, b, d}, {a, b, e}, {c, d}, and {c, d, e}. This guarantees that each set in Subsets satis es all the clauses that have been encountered so far. If one of these subsets satis es all clauses, the algorithm terminates as a reduct has been found. If not, then the process continues by selecting the next clause and adding these features. This process will result in a minimal subset, but it has an exponential time and space complexity. The results of the application of these three methods to the 13 datasets can be found in Table 5.3. HC and NS perform similarly throughout, differing only in their results for the Letters and WQ datasets. CS will always nd the smallest valid feature subset, although it is too costly to apply to larger datasets in its present form. On the whole, all three methods perform as well as or better
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TABLE 5.3 Subset sizes found for discernibility matrix-based techniques Dataset Features HC NS M-of-N 13 6 6 13 6 6 Exactly Exactly2 13 10 10 Heart 13 6 6 16 8 8 Vote Credit 20 10 10 Mushroom 22 4 4 24 5 5 LED Letters 25 9 10 Derm 34 6 6 34 9 9 Derm2 WQ 38 14 13 56 4 4 Lung
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than the dependency-based methods. However, HC, NS, and CS all require the calculation of the discernibility matrix beforehand.
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Feature selection seeks to reduce data while retaining semantics by selecting attributes as opposed to transforming them. This aspect is particularly useful when feature selection precedes other processes that require the original feature meanings to be intact, for example, rule induction where rules may need to be human-comprehensible. This chapter focused on some of the recent developments in rough set theory for the purpose of feature selection. Several approaches to discovering rough set reducts were experimentally evaluated and compared. The results highlighted the shortcomings of conventional hill-climbing approaches to feature selection. These techniques often fail to nd minimal data reductions. Some guiding heuristics are better than others, but as no perfect heuristic exists, there can be no guarantee of optimality. From the experimentation it appears that the entropy-based measure is a more useful hill-climbing heuristic than the rough set based measure. However, the entropy measure is a more costly operation than that of dependency evaluation, and this may be an important factor when processing large datasets. Because of the failure of hill-climbing methods and the fact that exhaustive searches are not feasible for even medium-sized datasets, stochastic approaches provide a promising feature selection mechanism. User-supplied information is essential to many existing algorithms for feature selection in the literature. This is a signi cant drawback. Some feature selectors require noise levels to be speci ed by the user beforehand; some simply rank features, leaving the users to choose their own subsets. There are those feature selectors that require the user to state how many features are to be chosen, or they must supply a threshold that determines when the algorithm should terminate. All of these require users to make decisions based on their own (possibly faulty) judgments. It is most often the case that the values of attributes are both crisp and real valued , and this is where many feature selectors, particularly those based on traditional rough set theory, encounter a problem. It is not possible to say whether two attribute values are similar and to what extent they are the same; for example, two close values may only differ as a result of noise, but in RST they are considered to be as different as two values of a different order of magnitude. According to RST, the values 0.1 and 0.11 are as different as 0.1 and 300. One answer to this problem has been to discretize the dataset beforehand, producing a new dataset with crisp values. This is often still inadequate, however, as the degrees of membership of values to discretized values are not considered at all. For example, two values may both be mapped to the same label Negative, but one may be much more negative than the other. The values 0.1 and 2000 could both be mapped to this class, although they are signi cantly different.
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