Nonlinear classification problem using NN The Use of

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 S 1 and S 2 and two features x 1 and x 2: S 1 = {(4, 0), (0, 4)} S 2 ={(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 x 1 -2=0 Step 2: Specify Hyperplanes 4 -Veronoi cells 4 neurons at the hidden layer x 2 -2 = 0 Step 3: Form a cluster corresponding to each class: C 1 the cluster corresponding to class S 1: C 2 the cluster corresponding to class S 2: Fainan May 2006 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] Output layer ”OR function” 2 Bipolar discrete (outputs either 1 or +1) [0. 5] Layer Fainan May 2006 Ones 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