The Use of NN in Classification

1. The Use of NN in Classification Architecture Training • 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 • Backpropagation Algorithm • Disadvantages: • number of training epochs can not be determined • local minima Fainan May 2006 Pattern Classification and Machine Learning Course

2. Given two classes S1 and S2 and two features x1 and x2: S1 = {(4,0),(0,4)} S2 ={(0,0),(4,4)} Alternative: NN Design Using Voronoi Diagrams 2 features  two neurons at the first layer 2 classes  two neurons at the output layer Step 1: Draw convex hulls related to each class Solution: Fainan May 2006 Pattern Classification and Machine Learning Course

3. x1-2=0 Step 2: Specify Hyperplanes 4-Veronoi cells  4 neurons at the hidden layer Step 3: Form a cluster corresponding to each class: x2-2 = 0 C1 the cluster corresponding to class S1: C2 the cluster corresponding to class S2: Fainan May 2006 Pattern Classification and Machine Learning Course

4. Step 4: Now we are ready for the net synthesis Specification Layer Fainan May 2006 Pattern Classification and Machine Learning Course

5. 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