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Non-linear classification problem using NN The Use of NN in Classification Architecture Three layers Feedforward Neural Network (FFNN) is sufficient for realizing a broad class of input/output non-linear maps (Kolmogorov’s theorem) Disadvantages: • number of neurons in the hidden layer cannot be determined • number of neurons can be large implying expensive calculation Fainan May 2006 Training Backpropagation Algorithm Disadvantages: • number of training epochs can not be determined • local minima Pattern Classification and Machine Learning Course Non-linear classification problem using NN Alternative: NN Design Using Voronoi Diagrams Given two classes S1 and S2 and two features x1 and x2: S1 = {(4,0),(0,4)} S2 ={(0,0),(4,4)} 2 features two neurons at the first layer 2 classes two neurons at the output layer Solution: Fainan May 2006 Step 1: Draw convex hulls related to each class Pattern Classification and Machine Learning Course Non-linear classification problem using NN x1-2=0 Step 2: Specify Hyperplanes 4-Veronoi cells 4 neurons at the hidden layer x2-2 = 0 Step 3: Form a cluster corresponding to each class: C1 the cluster corresponding to class S1: C2 the cluster corresponding to class S2: Fainan May 2006 H 1 H 1 H 2 H1 H 2 H 2 H1 H 2 Pattern Classification and Machine Learning Course Non-linear classification problem using NN Step 4: Now we are ready for the net synthesis Specification Number of neurons Activation function Bias vector Weight vector Input layer ”The hyperplanes” 2 Bipolar discrete (outputs either -1 or +1) [-2 -2] Ones Hidden layer ”AND function” 4 Bipolar discrete (outputs either -1 or +1) [-1.5 -1.5 -1.5 -1.5] 1 1 1 1 1 1 1 1 Output layer ”OR function” 2 Bipolar discrete (outputs either -1 or +1) [0.5 0.5] Ones Layer Fainan May 2006 Pattern Classification and Machine Learning Course Non-linear classification problem using NN FFNN to solve non-linear classification problem [Ref.] N. K. Bose, and A. K. Garga, ”Neural Network Design Using Voronoi Diagrams,” IEEE trans. On Neural Networks, vol. 4, no. 5, Sept. 1993. Fainan May 2006 Pattern Classification and Machine Learning Course