Class meaning

Many investigations of relationships between composition and properties take into account only the concentration of the asphaltenes, independendy of any quality criterion. However, a distinction should be made between the asphaltenes which occur in straight mn asphalts and those which occur in blown asphalts. Remembering that asphaltenes are a solubiUty class rather than a distinct chemical class means that vast differences occur in the make-up of this fraction when it is produced by different processes. 

Class Mean half-life (hours) Range (hours) ... 

The Mahalanobis distance is simply a weighted Euclidean distance, where each of the dimensions is inversely weighted by its overall variance in the calibration data. As a result, deviations in a dimension that has high variance in the calibration data will not be weighted as much as deviations in a dimension that has low variance in the calibration data. With this in mind, it becomes clear that the Mahalanobis distances of the two unknowns shown in Figure 12.15 from the origin are not equal. Furthermore, it becomes qualitatively apparent that unknown 2 becomes closer to the class mean than unknown 1, if Mahalanobis distance is used instead of Euclidean distance. 

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. 

Some common classification parameters are the mean values of the classes in the classification space, the variance of the class s calibration samples around the class mean, and the unmodeled variance in the calibration samples. Classification logic varies widely between classification methods. The following section provides details on some commonly encountered classification methods. 

In principle, with this F-test we test deviations of class mean values from a total mean value. 

In the case of two groups one describes the groups by the discriminant scores of one discriminant function. The coordinates of the two class means with their variances are known and the new object may easily be discriminated, in other words classified to one of the groups. This is achieved simply by attributing the unknown object to that class into which confidence region it falls. This may be tested using ... 

Tab. 8-3. Class means of the features of the optimum separation set for differentiation of the sampling times...

The QDC calculates a mean and the covariance for each class, allowing the classifier to find more accurate discriminative functions. Each sample is assigned to the class with the highest log-likelihood calculated following Equation (7.2), with the class mean /x and the class covariance . 

The second term on the right side of (26-22) is S, the sum of squares of deviations between classes, obtained by summing the squares of deviations of the class mean from the overall mean ... 

Hazard class means the nature of the physical, health or environmental hazard, e.g. flammable solid, carcinogen, oral acute toxicity ... 

Half-life class definitions Class Mean half-Ufe Range (h) ... 

Missing class means no chance to ask questions, participate in discussions... 

CLASS CUTPOINT CONCENTRATION NUMBER OF OBSERVATIONS CLASS MEAN CONCENTRATION (ppb)... 

THRESHOLD CONCENTRATION CONDITIONAL WITHIN CLASS MEAN PROBABILITY... 

X = true value, or the class mean s = standard deviation of the. true value... 

---