Classification errors

A subsequent study by the same research group focused on pits in olives. This time the olives travelled at various speeds through a 2 T horizontal bore magnet. Segregating 300 pitted and non-pitted olives gave classification errors of 4.3, 4.7, 2.3 and 4% at belt speeds of 0, 5,15 and 25 cm/s, respectively. 

Wenker et al. used dispersion polygons to show the differences in the dispersion of some classes of French brandies. The number of classification errors on the basis of these dispersion polygons appears to be very small in comparison with that based on the discriminating scores (i.e., when the canonical discriminating fimctions are used, and the classification made on the basis of the distance from category centroids). 

The terms classification ability and classification error used above refer to a procedure in which we have N objects of G categories, and all objects are used to compute class means and a pooled intraclass covariance matrix. The objects are then classified according to their highest discriminant score. This procedure is that commonly used. However, the classification ability (percentage of correctly classifiai objects) is an overestimate of the real utility of information, which must be considered as the ability to classify correctly unknown samples predictive ability. 

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. 

Simon et al. (14) also showed that cross-validating the prediction rule after selection of differentially expressed genes from the full data set does little to correct the bias of the re-substitution estimator 90.2% of simulated data sets with no true relationship between expression data and class still result in zero misclassifications. When feature selection was also re-done in each cross-validated training set, however, appropriate estimates of mis-classification error were obtained the median estimated misclassification rate was approximately 50%. 

To achieve that, an object reconstruction algorithm detects connected components (blobs) in the binary images of each material class. In a first step, blobs that do not meet pre-defined size restrictions are considered as classification errors and filtered out (e.g. the black line due to a faulty camera pixel in object D). The binary image of each material class (material and overlay) is then morphologically dilated... 

Table 15-3. Pathways ranked by RF-based classification error rate46...

We compared the classification for three libraries (1) the original normahzed spectra, (2) the full set of axis and (3) the selection of meaningful axis. We observed that the classification works best on the set of mearungful axes where the cross validation resulted in no classification error for all applicable WEKA classifiers. Wrong classifications occurred for the normalized spectra and the full set of axes. 

Another classification reference parameter is the random classification error, which is the error rate obtained if the objects are randomly assigned to the classes. It is defined as ... 

Classification is probably the most common supervised machine learning formalism where an example is assigned a grouping based on some hypothesis learned over a set of training examples x,y). A classification algorithm (or classifier) searches for hypothesis h that minimizes the classification error e =... 

Through SDA all compounds of the training set were classified as presented in Table 5. The classification error rate was 0% resulting in a satisfactory separation between more and less active compounds. 

Figure 5.36a demonstrates the fractions of misclassifica-tions in dependence on the maximum number of splits for both resubstitution and cross-validation in a bagged CART model. Although the resubstitution error might be close to zero, a more realistic model is based on the maximum number of splits for which a minimal classification error for cross-validation is observed. The smallest error for the bagged trees is found at 16 splits where the cross-validated fraction of misclassification is 12.0% (cf. Figure 5.36b for the decision boundaries). 

In intrusion detection, there are two types of mis-classification errors. The type I of error occurs when non-intrusion are classified into intrusion group. The type II of error occurs when intrusion are classified into normal group. So the fitness function can be set as follows ... 

Analogously, the total classification error and the mean classification error for the test set eire defined for discrete cases as ... 

In the discrete case total and mean classification error for LOOCV are given by... 

In the recent past SVM have been increasingly used to solve problems in computational chemistry. In a comparison of SVM and ANN for classification of pharmaceutically inactive or active compounds, SVM consistently yielded smaller classification errors [41]. For the classification of mass spectra (see Subsection 8.5.2), SVM with a radial kernel proved to be the best predicting functions. 

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