6.5 Computer Science - Pattern Recognition THIS is the books DL content - http:/
ID: 3841967 • Letter: 6
Question
6.5 Computer Science - Pattern Recognition
THIS is the books DL content - http://extras.springer.com/2013/978-1-4614-5322-2
Follow the signals through the network, and find the required values of the three thresholds.
(What are the thresholds? How did you solve it? Prove that it works).
Question 6.5
Follow the signals through the network, and find the required values of the three thresholds.
(a. What are the thresholds? b. How did you solve it? c. Prove that it works).
5. Example 6.2 in the text considers a two-layer network (Fig. 6.17b) to implement the XOR function, with w11 W 12 -1; w21 W22 1: b 0.5 and b2 0.5. We could also make w 1, Wo 1 and b 0. Follow the signals through the network, and find the required values of the three thresholds. (See spreadsheet, Q6.5.xls, downloadable from http://extras.springer.com)Explanation / Answer
% Logistics Map % Classic chaos example. Plots semi-stable values of % x(n+1) = r*x(n)*(1-x(n)) as r increases to 4. % % Michael Hanchak, Dayton OH, USA, 2011 clear scale = 10000; % determines the level of rounding maxpoints = 200; % determines maximum values to plot N = 3000; % number of "r" values to simulate a = 2.0; % starting value of "r" b = 4; % final value of "r"... anything higher diverges. rs = linspace(a,b,N); % vector of "r" values M = 500; % number of iterations of logistics equation % Loop through the "r" values for j = 1:length(rs) r=rs(j); % get current "r" x=zeros(M,1); % allocate memory x(1) = 0.5; % initial condition (can be anything from 0 to 1) for i = 2:M, % iterate x(i) = r*x(i-1)*(1-x(i-1)); end % only save those unique, semi-stable values out{j} = unique(round(scale*x(end-maxpoints:end))); end % Rearrange cell array into a large n-by-2 vector for plotting data = []; for k = 1:length(rs) n = length(out{k}); data = [data; rs(k)*ones(n,1),out{k}]; end % Plot the data figure(97);clf h=plot(data(:,1),data(:,2)/scale,'k.'); set(h,'markersize',1) axis tight set(gca,'units','normalized','position',[0 0 1 1]) set(gcf,'color','white') axis off
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