1. Non-linear classification problem using NN Fainan May 2006 Pattern Classification and Machine Learning Course 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 The Use of NN in Classification ArchitectureTraining Backpropagation Algorithm Disadvantages: number of training epochs can not be determined local minima

2. Non-linear classification problem using NN Fainan May 2006 Pattern Classification and Machine Learning Course Alternative: NN Design Using Voronoi Diagrams Given two classes S1 and S2 and two features x 1 and x 2 : S1 = {(4,0),(0,4)} S2 ={(0,0),(4,4)} Step 1: Draw convex hulls related to each class 2 features  two neurons at the first layer 2 classes  two neurons at the output layer Solution:

3. Non-linear classification problem using NN Fainan May 2006 Pattern Classification and Machine Learning Course Step 3: Form a cluster corresponding to each class: C2 the cluster corresponding to class S2: C1 the cluster corresponding to class S1: Step 2: Specify Hyperplanes x 2 -2 = 0 x 1 -2=0 4-Veronoi cells  4 neurons at the hidden layer

4. Non-linear classification problem using NN Fainan May 2006 Pattern Classification and Machine Learning Course Number of neurons Activation function Bias vectorWeight vector Input layer ”The hyperplanes” 2Bipolar discrete (outputs either -1 or +1) [-2 -2] Ones Hidden layer ”AND function” 4Bipolar discrete (outputs either -1 or +1) [-1.5 -1.5 -1.5] Output layer ”OR function” 2Bipolar discrete (outputs either -1 or +1) [0.5 0.5] Ones Step 4: Now we are ready for the net synthesis Layer Specification

5. Non-linear classification problem using NN Fainan May 2006 Pattern Classification and Machine Learning Course 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.