To solve this problem, Eshuis et al. (ref. 45) suggested the use of a feature scaling factor based on the ratio between outer and mean inner deviation, in order to bring out those features which are both highly different between different classes of patterns (high outer deviation) and highly stable within each given class (low mean inner deviation). This "characteristicity" factor is closely related to the well known Fisher ratio. Eshuis et al. have shown that the use of this factor dramatically improves the separation of two classes of Listeria without making previous assumptions about the existence of these two classes (ref. 45). If used in this manner, the feature scaling acts as a contrast-enhancing procedure not entirely dissimilar to the computer procedures used for contrast enhancement in digital image processing operations.
A distinct disadvantage of feature scaling techniques incorporating outer deviation values in the scaling factor, however, is the strong dependence of this factor on the particular set of samples used. Addition of a different sample to the set may appreciably change the scaling factors, sometimes making direct comparison between results obtained with different sets of samples difficult, if not impossible. This problem does not necessarily exist when mean inner deviation is used in the scaling factors only, since the sources of biological and instrumental "noise" variations may often be assumed to be similar for different sets of samples. In fact, this condition is almost a prerequisite for further statistical processing of combined data from different sets of samples. Referring again to Table 5, the column labelled "characteristicity" value lists the ratio of the outer to inner sample deviations for the fifteen masses with the largest "characteristicity" values.
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