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(1) Large interclass mean distance (discrimination): Features in different classes should have significantly different values.

(2) Small intraclass variance (reliability): Features should have similar values for objects of the same class.

(3) Low correlation with other features (independence): Features should not be strongly correlated to each other.

(4) Insensitivity to extraneous variables (little signal-to-noise ratio dependency): Features should not be affected significantly by changes in other features.

If the number of initially selected features is limited, direct measurement of feature characteristics can be a choice to search for effective features and eliminate redundant ones. In order to remove biases associated with different scaled feature values and to preserve good numerical behavior, all of the features should be first normalized using the entire database (samples in all classes) with where fk

(3) Cross-correlation coefficient. The cross-correlation coefficient between any pair of features is

where K is a normalization constant so that pkk = 1.

Besides computing these parameters, histograms and scatter diagrams also are useful tools that allow investigators to directly visualize the mean and standard deviation of each class, the separation between different classes, and the correlation between different features. Using these computation and diagram methods, investigators can sort the features based on the values of interclass distance, intraclass variance, and correlation coefficients with other features. Then, those features exhibiting the large interclass separation and small intraclass variance are chosen as input features to the classifier.

In medical image processing, many studies reported to date have used this direct measurement method to select optimal features in different machine learning classifiers. For example, Kupinski et al. reported one study using this method to enhance feature selection for an ANN to classify true-positive and false-positive mass regions in digitized mammograms [15]. In this study, 91 features were initially extracted from geometric, intensity-based, and gradient-based measurements around each suspicious mass region. The mean and standard deviation of each feature for the true-positive and false-positive regions were computed. Then, the features that showed the most separation, in a one-dimensional analysis, between true positives and false positives were selected for the ANN input. After this process of feature enhancement, the ANN could improve its performance by raising the Az value from 0.91 to 0.97 based on a round-robin validation approach using 102 true-positive mass regions and 302 false-positive mass regions.

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