artificial neural networks 0909 560 01 0909 454 01 fall 2004 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Artificial Neural Networks 0909.560.01/0909.454.01 Fall 2004 PowerPoint Presentation
Download Presentation
Artificial Neural Networks 0909.560.01/0909.454.01 Fall 2004

Loading in 2 Seconds...

play fullscreen
1 / 13

Artificial Neural Networks 0909.560.01/0909.454.01 Fall 2004 - PowerPoint PPT Presentation


  • 129 Views
  • Uploaded on

Artificial Neural Networks 0909.560.01/0909.454.01 Fall 2004. Lecture 6 October 18, 2004. Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/spring04/ann/. Plan. Radial Basis Function Networks RBF Formulation Network Implementation

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Artificial Neural Networks 0909.560.01/0909.454.01 Fall 2004' - ciaran-lang


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
artificial neural networks 0909 560 01 0909 454 01 fall 2004

Artificial Neural Networks0909.560.01/0909.454.01Fall 2004

Lecture 6October 18, 2004

Shreekanth Mandayam

ECE Department

Rowan University

http://engineering.rowan.edu/~shreek/spring04/ann/

slide2
Plan
  • Radial Basis Function Networks
        • RBF Formulation
        • Network Implementation
        • Matlab Implementation
  • Design Issues
      • Center Selection: K-means Clustering Algorithm
      • Input data processing
        • Selection of training and test data - cross-validation
        • Pre-processing: Feature Extraction
  • Lab Project 3
rbf principle
RBF Principle

Transform to

“higher”-dimensional

vector space

Non-linearly

separable classes

Linearly

separable classes

example x or problem

j2(x)

x2

j1(x)

x1

Example: X-OR Problem

Decision

Boundary

rbf formulation
RBF Formulation

Problem Statement

  • Given a set of N distinct real data vectors (xj; j=1,2,…,N) and a set of N real numbers (dj; j=1,2,…,N), find a function that satisfies the interpolating condition

F(xj) = dj; j=1,2,…,N

rbf network

j

1

j

1

1

1

j

1

j

1

0.5

0

-5

5

RBF Network

Hidden

Layer

Input

Layer

Output

Layer

x1

y1

Outputs

x2

Inputs

y2

x3

wij

1

j(t)

t

matlab implementation
Matlab Implementation

%Radial Basis Function Network

%S. Mandayam/ECE Dept./Rowan University

%Neural Nets/Fall 04

clear;close all;

%generate training data (input and target)

p = [0:0.25:4];

t = sin(p*pi);

%Define and train RBF Network

net = newrb(p,t);

plot(p,t,'*r');hold;

%generate test data

p1 = [0:0.1:4];

%test network

y = sim(net,p1);

plot(p1,y,'ob');

legend('Training','Test');

xlabel('input, p');

ylabel('target, t')

Matlab Demos

» demorb1

» demorb3

» demorb4

rbf center selection

x2

x1

Centers

Data points

RBF - Center Selection
k means clustering algorithm
K-means Clustering Algorithm
  • N data points, xi; i = 1, 2, …, N
  • At time-index, n, define K clusters with cluster centers cj(n); j = 1, 2, …, K
  • Initialization: At n=0, let cj(n)= xj; j = 1, 2, …, K(i.e. choose the first K data points as cluster centers)
  • Compute the Euclidean distance of each data point from the cluster center, d(xj , cj(n)) = dij
  • Assign xj to cluster cj(n)if dij = mini,j {dij}; i = 1, 2, …, N, j = 1, 2, …, K
  • For each cluster j = 1, 2, …, K, update the cluster center cj(n+1)= mean {xjcj(n)}
  • Repeat until ||cj(n+1)- cj(n)||< e
selection of training and test data method of cross validation

Train

Train

Train

Test

Train

Train

Test

Train

Train

Test

Train

Train

Test

Train

Train

Train

Selection of Training and Test Data: Method of Cross-Validation
  • Vary network parameters until total mean squared error is minimum for all trials
  • Find network with the least mean squared output error

Trial 1

Trial 2

Trial 3

Trial 4

feature extraction
Feature Extraction

Objective:

  • Increase information content
  • Decrease vector length
  • Parametric invariance
    • Invariance by structure
    • Invariance by training
    • Invariance by transformation
lab project 3 radial basis function neural networks
Lab Project 3: Radial Basis Function Neural Networks

http://engineering.rowan.edu/~shreek/fall04/ann/lab3.html