%% Classification with a 2-input Perceptron
%  檔名：perceptron21.m   原檔案：C:\MATLAB7\toolbox\nnet\nndemos\demop1.m
% A 2-input hard limit neuron is trained to classify 5 input vectors into two
% categories.
%
% Copyright 1992-2002 The MathWorks, Inc.
% $Revision: 1.16 $  $Date: 2002/04/14 21:27:48 $
% 這是 Matlab 軟體中的一個展示(demo)程式，很適合 類神經網路 初學者，因為只有兩個輸入，一個神經元
% 讀者可在 Matlab 軟體 >>demo  => Neural Network  Perceptrons => Classification with a 2-input perceptron 中找到
%%
% 對於類神經網路 初學者，亦可在 Matlab 軟體中，執行 >>nntool  ，可以進入一 GUI 畫面，直接進行學習，這部分可參考：
%   Matlab 入門與進階，蒙以正 編著，儒林
% Each of the five column vectors in P defines a 2-element input vectors and a
% row vector T defines the vector's target categories.  We can plot these
% vectors with PLOTPV.
P = [ -0.5 -0.5 +0.3 -0.1;  ...
      -0.5 +0.5 -0.5 +1.0];
T = [1 1 0 0];
% 意即(-0.5,-0.5)、(-0.5,+0.5) 這兩點，希望輸出為 1 (分類在同一區)
% 而  (+0.3,-0.5)、(-0.1,+1.0) 這兩點，希望輸出為 0 (分類在同一區)
plotpv(P,T);    % PLOTPV  Plot perceptron input/target vectors.

%%
% The perceptron must properly classify the 5 input vectors in P into the two
% categories defined by T.  Perceptrons have HARDLIM neurons.  These neurons are
% capable of separating an input space with a straight line into two categories
% (0 and 1).
%
% NEWP creates a network object and configures it as a perceptron. The first
% argument specifies the expected ranges of two inputs.  The second determines
% that there is only one neuron in the layer.

net = newp([-1 1;-1 1],1);  % NEWP Create a perceptron. 注意這個 "p"
% input1,2 輸入範圍 皆為：([-1 1]，後面的1 表示 一個神經元
% 此時 觀察 IW(Input Layer) 初始值  >> net.IW{1,1}   得 ans = 0     0
% 此時 觀察 b(bias) 初始值 >> net.b{1}    得 ans = 0
% 此時也可以任意給定初始值，若給的好，可以加速學習
%%
% The input vectors are replotted with the neuron's initial attempt at
% classification.
%
% The initial weights are set to zero, so any input gives the same output and
% the classification line does not even appear on the plot.  Fear not... we are
% going to train it!

plotpv(P,T);
plotpc(net.IW{1},net.b{1});  
% PLOTPC Plot a classification line on a perceptron vector plot. 寫法：PLOTPC(W,B)

%%
% ADAPT returns a new network object that performs as a better classifier, the
% network output, and the error.

net.adaptParam.passes = 3;  % 這是學3次的意思
net = adapt(net,P,T);       % 這指令結束後，就表示學完三次了
% 以上也可改為 net = train(net,P,T); 結果比較好喔！ 
plotpc(net.IW{1},net.b{1}); % 觀察輸出圖，就會發現已經成功的 分類 了
% 以上 若令 net.adaptParam.passes = 1，個別學習3次，可紀錄三次學習後的係數如下：
% first  >> net.IW{1,1} ans = -0.2000   -0.5000    >> net.b{1}  ans = -2
% second >> net.IW{1,1} ans = -1.2000   -0.5000    >> net.b{1}  ans =  0
% third  => 學習結果同 第二次，可見已達到穩定。
%%
% Now SIM is used to classify any other input vector, like [0.7; 1.2]. A plot of
% this new point with the original training set shows how the network performs.
% To distinguish it from the training set, color it red.

p = [0.7; 1.2];    % 加入一個測試點，看看結果如何？
a = sim(net,p);
plotpv(p,a);
point = findobj(gca,'type','line');
set(point,'Color','red');

%%
% Turn on "hold" so the previous plot is not erased and plot the training set
% and the classification line.
%
% The perceptron correctly classified our new point (in red) as category "zero"
% (represented by a circle) and not a "one" (represented by a plus).

hold on;
plotpv(P,T);
plotpc(net.IW{1},net.b{1});
hold off;