Distribution classification interval

From the probability density distributions of the discriminant scores u for class A and B an optimal decision threshold Mo can be determined, If an unknown has to be classified it is assigned to class A if its discriminant variable is lower than Mo, Otherwise to class B, In the case of a substantial overlap of the probability density distributions an interval may be defined for a rejection of classifications. The decision vector (a linear combination of the features) together with the rule how to assign the classes is called a classifier. 

In processes where classification or separation of particles is required, the efficiency of separation will be a function of one or more distributed properties of the particles. The function which describes the efficiency with which particles are separated by size (d) is usually termed the grade efficiency, G(d). For particles in a narrow size interval between d and d + Ad, G(d) is defined as the mass ratio of such particles in the underflow to that in the feed. The overall separation efficiency E corresponds to the particle size d for which G(d) equals E. 

The split-sample method is often used with so few samples in the test set, however, that the validation is almost meaningless. One can evaluate the adequacy of the size of the test set by computing the statistical significance of the classification error rate on the test set or by computing a confidence interval for the test set error rate. Because the test set is separate from the training set, the number of errors on the test set has a binomial distribution. 

If p(x 1) and p(x. 2) are approximated by Gaussian distributions, only two parameters have to be stored for each feature. If an approximation by a mathematical function is not possible then all functions q(x. ) must be tabulated for several intervals of x (e.g. 3 to 20 intervals). The boundaries of the intervals should be selected such that approximately equal numbers of patterns fall into each interval. Usually, the boundaries are different for each feature and classification of unknowns requires the storage of a large amount of data C2483. 

The application of discriminant analysis can be extended to include probabilities of class membership and, assuming a multivariate normal distribution of data, confidence intervals for class boundaries can be calculated. The Bayes rule for classification simply states that an object should be assigned to that... 

The rate of feed and the particle size distribution of the material supplied to the classifier affect the classification result. Therefore these two parameters should be kept constant during the period of the trials, and the grinding plant should be operating under steady conditions (equilibrium). In order to compensate for any variations in the feed, the samples of the material flow rates A, F and G are taken over periods of 5 —10 minutes at close intervals of 1 —2 minutes. Gross samples of the three flows — classifier feed, fines, tailings — are respectively prepared and the specific surface values and particle size distributions are determined. 

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