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4.2.1.4 Scrap Selection construction ranking using attribute pattern (Scrap) [285] is an instance-based lter that determines feature relevance by performing a sequential search within the instance space. Scrap considers objects (instances) one at a time, instead of typical forward or backward search. The central idea is to identify those features that change at decision boundaries in the data table the features assumed to be the most informative. An algorithmic overview may be seen in Figure 4.10. A sequential search is conducted, starting from a random object, which becomes the rst point of class change (PoC). Its nearest object with a different class label becomes the next PoC. These two PoCs de ne a neighborhood; features that change between them de ne the dimensionality of decision boundary between the two classes. If there is only one such feature that changes, this is determined to be absolutely relevant and is included in the feature subset. If more than one feature changes, their associated relevance weights, initially zero, are incremented. If objects of the same class label are closer than this new PoC and differ in only one feature, then that feature s weight is decremented. Objects determined to belong to neighborhoods are then removed from processing. The process stops when all objects have been assigned to a neighborhood. Features that have a positive relevance weight and those that have been determined to be absolutely relevant are chosen as the nal feature subset.
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SCRAP(O) Input: O, the set of all objects Output: R, the feature subset (1) A {}; Wi , Wi = 0; (2) T randomObject(); PoC T (3) while O = {} (4) O O PoC; PoCnew NewPoC(PoC) (5) n = dist(PoC,PoCnew ) (6) if n = = 1 (7) i = diffFeature(PoC,X); A A {i} (8) N getClosestNeighbours(PoC,n) (9) foreach X N (10) if classLabel(X) = = classLabel(N) (11) O O X (12) if dist(PoC,X) = = 1 (13) i = diffFeature(PoC,X); Wi = Wi 1 (14) else if dist(PoC,X) > 1 (15) incrementDifferingFeatures(X,W) (16) R A (17) foreach Wi (18) if Wi > 0 R R { i} (19) return R
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From the example dataset, Scrap rst chooses a random object, say object 1, and proceeds to nd its nearest neighbor with a different class label. In this case object 12 is the PoC with two features that differ, d and e. These features are said to be weakly relevant, and their weights (initially zero) are incremented. The objects of a lesser distance away than object 12 with the same label as object 1 are assigned to this neighborhood. Only object 5 is closer as it differs in one feature, b. This results in b s weight being decremented. If more than one feature differed here, the weights would not have been affected only those cases where one feature differs result in weights being reduced. Object 12 now becomes the new PoC, and the algorithm continues. Object 4 is the nearest neighbor with a different class label, with only one feature differing in value, feature a. This feature is determined to be absolutely relevant and is added to the nal subset regardless of its nal relevance weight. When the algorithm eventually terminates, the subset {a, b, c, d, e, f } is returned: a is absolutely relevant, the rest have a positive nal weight. No reduction of this dataset is achieved. The example above serves to illustrate one of the main weaknesses of this instance-based approach it regularly chooses too many features. This is due, in part, to the situation where weights are decremented. If more than one feature changes between a PoC and an object of the same class label, then the corresponding feature weights remain unaffected. This drawback could be tackled by reducing the weights of the affected features when the change occurs. With the modi cation in place and the algorithm run on the dataset, a smaller subset, {a, b, e, f }, is obtained. Another alteration may be to decrement each weight proportionally, such as for three irrelevant features whose weights will be reduced by one-third each. This modi cation combined with a similar one for incrementing weights may produce a more accurate re ection of a feature s importance within a dataset. Currently Scrap will only handle nominal values, although it is relatively straightforward to extend this algorithm to continuously valued features.
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4.2.1.5 EBR Another technique for lter-based feature selection is entropy-based reduction (EBR), which developed from work carried out in [164]. This approach is based on the entropy heuristic employed by machine learning techniques such as C4.5 [281]. A similar approach was adopted in [67] where an entropy measure is used for ranking features. EBR is concerned with examining a dataset and determining those attributes that provide the most gain in information. The entropy of attribute A (which can take values a1 . . . am ) with respect to the conclusion C (of possible values c1 . . . cn ) is de ned as
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This expression can be extended to deal with subsets of attributes instead of individual attributes only. By this entropy measure the algorithm used in rough
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