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# Ellipsoidally Symmetric

The design of an ellipsoidally symmetric classifier is similar to the Gaussian classifier. We form a discriminant function v acting on feature vector x

The Gaussian classifier assigns a feature vector x to class 1 when y < t , where t is a threshold value depending on the log of the determinants of the covariance matrices for class 1 and class 2. The Ellipsoidally symmetric classifier uses v as a scalar feature and computes the class conditional probability P(v | class 1) and P(v | class 2) by simply partitioning the range of the discriminant into K equal size bins and determining the fraction of measurements falling into each bin for class 1 features and for class 2 features. We take the number of bins K to be 100 and the class prior probabilities P(class1) and P(class 2) to be the fractions observed in the sample.

Discriminant feature v is assigned to class 1 when

P(v | class 1)P(class1) > P(v | class 2)P(class 2).

Results
As in the case for the Gaussian classifier, there is some difference between the feature distribution coming from the maximal ELS phrases of the Torah text and those of the monkey text for a skip range of 2 through 100. But instead of finding a more significant p-value, it is slightly less significant. Probably when K=100 bins the sample size of some 40,000 is too small or the bin size is too large.
The results in the larger skip range show no difference between the Torah text and monkey text maximal ELS phrases. We conclude, therefore, that the difficulty class and conditional entropy per letter features do not carry information that can be used to distinguish between maximal ELS phrases coming from the Torah text and coming from the monkey text.

 Skip Range Number of Maximal ELS Phrases Torah Text Number of Maximal ELS Phrases Monkey Text P-value 2-100 40,977 41,694 21.5/1000 2-1000 406,206 410,668 798.5/1000 1002-2000 391,500 395,582 796/1000