At this point it is worth noting that covariance

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components. At this point, it is worth noting that covariance projection is similar to but not identical to the correlation. Supervised Pattern Recognition Assuming that the selected features defining the feature vector contain the information needed to distinguish the patterns, the next step is to design the classifier. The classifier design is based on comparison of sampled acoustic emission hits with previously known hits from each class. In this case, the classifier design learns from examples in a process called supervised pattern recognition. In this process, the designer has previous 161 Acoustic Emission Signal Processing F IGURE 13. Data in three-dimensional view. The addition of the third dimension reveals the true data structure. Amplitude (relative scale) Duration (relative scale) Energy (relative scale) Y O X Z T ABLE 1. Correlation matrix for the data of Figs. 12 and 13. Acoustic Energy Duration Amplitude (s) (dB) Acoustic energy 1.0 0.9626 0.7982 Duration (s) 0.9626 1.0 0.8006 Amplitude (dB) 0.7982 0.8006 1.0 F IGURE 14. Principal component projection (based on correlation matrix) for the data of Figs. 12 and 13: (a) scatter plot of the first and second principal component analyses; (b) scatter plot of the second and third principal component analyses. 1.5 1 0,5 0 –0.5 –1 Second principal component (arbitrary unit) First principal component (arbitrary unit) 50 60 70 80 90 100 (a) 0.75 0.5 0.25 0 –0.25 Third principal component (arbitrary unit) Second principal component (arbitrary unit) –1 –0.5 0 0.5 1 1.5 (b)
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knowledge about the number of classes as well as a set of known examples (called a training set ) to be used in the classifier design. Different supervised algorithms might be used, depending on the complexity of the problem, starting from the simplest minimum distance classifier up to complex neural networks. Classifier selection is primarily based on the ability to realize the desired decision surface, linear, piecewise linear and nonlinear, as imposed by the problem complexity. Two different classifiers, k nearest neighbors classifier and linear classifier, are presented here as representative of several widely accepted classification schemes. 1-6 The k nearest neighbors classifier is a simple and powerful algorithm basing its decision on direct distance measurements between the unknown pattern (hit under classification) and the patterns of the training set (previously known hits from each class). The k nearest neighbors classifier can realize piecewise linear decision boundaries and can be used for the classification of exclusive or (XOR) problems using two training patterns per class (see Fig. 15). Let the euclidean distance D ij of a test pattern X from the j th training pattern of the i th class serve as a measure of similarity between patterns where X ( i ) , i = 1, …, N denotes a set of N training samples distributed in C classes, C 1 , …, C C ). The k nearest neighbors classifier algorithm classifies the unknown pattern vector X by assigning it to the class label most frequently occurring among the k nearest samples.
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