ET07.pdf

# Classification algorithms the features computed in

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Classification Algorithms The features computed in the previous step are applied as input to a classification algorithm for data interpretation. Two of the most widely used pattern classification techniques are (1) clustering algorithms and (2) neural networks. These techniques are described next. K Means Clustering Clustering algorithms treat a feature vector as a point in the N -dimensional feature space. 16 Feature vectors from a similar class of signals then form a cluster in the feature space. The most popular of the clustering algorithms is the K means clustering algorithm, which uses an iterative procedure that classifies each input signal into one of K classes. K Means Algorithm The objective of the K means clustering algorithm is to partition the feature space into K mutually exclusive regions. The partitioning is performed in a way that S W S W b w = λ J W W S W W S W ( ) = T w T b S m m m m b T = ( ) ( ) ( ) = 1 1 M P C i i i i M S w = ( ) = 1 1 M P C i i i M Σ Σ i i i i E x C C = ( ) ( ) x m m T | = 198 Electromagnetic Testing

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minimizes a performance index or cost function F equal to the sum of the square of distance between the cluster center and all points within the cluster. Let the number of patterns be N c . 1. Assign any K (first K, randomly selected K or user assigned K ) patterns as the K cluster centers z i , where i = 1, 2, …, K. 2. Assign each of the remaining N c K patterns at the j th iteration to one of the K clusters whose center is closest (using the euclidian norm): (39) where w m j is the m th cluster in the j th iteration and: (40) for 1 m , n K . 3. Update the cluster centers z i j +1 , i = 1, 2, K , in a manner that minimizes the performance index: (41) where F i j is the cost function corresponding to the i th cluster in the j th iteration and N c j is the number of patterns in the c th cluster in the j th iteration. It can be shown that the centers z i j +1 , i = 1, 2, …, K ), which minimize the above performance index, are the sample mean of all points within the cluster: (42) 4. If z i j +1 = z i j for all i = 1, 2, …, K , the algorithm has converged and the process can be terminated. Otherwise go to step 2. The K means algorithm converges if the classes are linearly separable and the performance generally is better if the initial cluster centers are chosen from the K classes. Neural Networks Neural networks provide an alternate approach for classification. Interest in this approach arose from a desire to mimic biological nervous systems with respect to architecture as well as information processing strategies. 17 The network consists of simple processing elements interconnected by weights. The network is first trained using an appropriate learning algorithm for the estimation of interconnection weights. Once the network is trained, unknown test signals can be classified. The class of neural networks used most often for classification tasks is the multilayer perceptron network.
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