i want to apply the perceptron algorithm for fisheriris data and i was tried this code
function [ ] = Per( )
%PERCEPTON_NN Summary of this function goes here
% Detailed explanation goes here
%%%%%%%%%%%STEP ONE INPUT DATA PREPERATION
%N=3000;
load fisheriris
tr=50; %traning
te=50; %test
epochs =150;
data=meas;
%N = size(meas,1);
%species=nonomil(species)
%figure,plot(data_shuffeled(1,:),data_shuffeled(2,:),'rx');
%%%%%%%%%%%%%%%%%%%STEP TWO INTIALIZE WEIGHT
baise=1;
w=[baise; 1 ; 1;1 ; 1];
eta=0.9; %%learning rate
%%%%%%%%%%%%%%%%%%%%%%%% Rosen Blatt learning Algo
for epoch=1 : epochs
for i=1 : tr
x=[1;data(i,1);data(i,2);data(i,3);data(i,4)]; % input vector
N = size(species,i); %desiard output
y=w'*x; % y=actual output ,w'= transpose w , mmoken y=w.*x
%%%%%%%%%%%%%%% Activation function (hardlimit)(step fn)
y=1*(y>=0)+(-1)*(y<0); % da badl el if
%%%%%%%%%%% Error calcualtion %%%%%%%
err(i)=N-y;
%%%%%%%%%%%%%% update weight %%%%%%%%%5
wnew=w+ eta*err(i)*x;
w=wnew;
end
mse(epoch)=mean(err.^2);
end
%%%%%%%%%%%%%%%%%%%%%% step four classification (testing) %%%%%%%%%%%%%%%%%%5
hold on
for i=1 : te
%x=[1;data(i,1);data(i,2),data(i,3);data(i,4)];
x=[1;data(i,1);data(i,2);data(i,3);data(i,4)];
% d=data_shuffeled(3,i+tr);
N = size(species,i);
y=w'*x;
y=1*(y>=0)+(-1)*(y<0);
if (y==1)
plot(x(2),x(3),x(4),x(5),'rx');
elseif y==-1
plot(x(2),x(3),x(4),x(5),'r&');
end
end
hold off
if abs(N-y)>1E-6
testerro=testerro+1;
end
i wrote this code to make the perceptron algorithm with fisheriris data "meas" as input and species as "output"
any help in the code or any modify on this code .
Thanks .
First, did you know that MATLAB has something for neural network training called the Neural network toolbox?
Second, think data_shuffeled is your own function. There is something called randperm in MATLAB that you should use to shuffle your data.
Third, you want to avoid using for-loops when you can use vectors/matrices in MATLAB.
Instead of doing (for testing)
for i = 1:te,
....
end
You might want to do
X = [ones(te,1), data]; %X is [50x5] so each row of X is x'
y = X*w; %y is [50x1], X is [50x5], w is [5x1]
idx_p1 = y==1; %all the indices of y where y is +1
idx_m1 = y==-1; %all the indicies of y where y is -1
plot(X(idx_p1,1),y(idx_p1),'rx');
plot(X(idx_m1,1),y(idx_m1),'r&');
I don't know how you were using plot with 4-dimensional X so the above just plots with the first feature (column) of X.
Additionally, the training looks strange to me. For one, I don't think you should use N for both the size of data matrix meas and for the desired output. 'yhat' or 'ybar' is a better name. Also, if N is the desired output, then why is it size(species,i) where i loops through 1:50? species is a [150x1] vector. size(species,1) = 150. And size(species,x) where x is 2 to 50 will be 1. Are you sure you want this? Shouldn't it be something like:
yhat = -ones(50,1); %Everything is -1
yhat(strmatch('virginica,species)) = 1; %except virginicas which are +1
Related
I have trained my Neural network model using MATLAB NN Toolbox. My network has multiple inputs and multiple outputs, 6 and 7 respectively, to be precise. I would like to clarify few questions based on it:-
The final regression plot showed at the end of the training shows a very good accuracy, R~0.99. However, since I have multiple outputs, I am confused as to which scatter plot does it represent? Shouldn't we have 7 target vs predicted plots for each of the output variable?
According to my knowledge, R^2 is a better method of commenting upon the accuracy of the model, whereas MATLAB reports R in its plot. Do I treat that R as R^2 or should I square the reported R value to obtain R^2.
I have generated the Matlab Script containing weight, bias and activation functions, as a final Result of the training. So shouldn't I be able to simply give my raw data as input and obtain the corresponding predicted output. I gave the exact same training set using the indices Matlab chose for training (to cross check), and plotted the predicted output vs actual output, but the result is not at all good. Definitely, not along the lines of R~0.99. Am I doing anything wrong?
code:
function [y1] = myNeuralNetworkFunction_2(x1)
%MYNEURALNETWORKFUNCTION neural network simulation function.
% X = [torque T_exh lambda t_Spark N EGR];
% Y = [O2R CO2R HC NOX CO lambda_out T_exh2];
% Generated by Neural Network Toolbox function genFunction, 17-Dec-2018 07:13:04.
%
% [y1] = myNeuralNetworkFunction(x1) takes these arguments:
% x = Qx6 matrix, input #1
% and returns:
% y = Qx7 matrix, output #1
% where Q is the number of samples.
%#ok<*RPMT0>
% ===== NEURAL NETWORK CONSTANTS =====
% Input 1
x1_step1_xoffset = [-24;235.248;0.75;-20.678;550;0.799];
x1_step1_gain = [0.00353982300884956;0.00284355877067267;6.26959247648903;0.0275865874012055;0.000366568914956012;0.0533831576137729];
x1_step1_ymin = -1;
% Layer 1
b1 = [1.3808996210168685;-2.0990163849711894;0.9651733083552595;0.27000953282929346;-1.6781835509820286;-1.5110463684800366;-3.6257438832309905;2.1569498669085361;1.9204156230460485;-0.17704342477904209];
IW1_1 = [-0.032892214008082517 -0.55848270745152429 -0.0063993424771670616 -0.56161004933654057 2.7161844536020197 0.46415317073346513;-0.21395624254052176 -3.1570133640176681 0.71972178875396853 -1.9132557838515238 1.3365248285282931 -3.022721627052706;-1.1026780445896862 0.2324603066452392 0.14552308208231421 0.79194435276493658 -0.66254679969168417 0.070353201192052434;-0.017994515838487352 -0.097682677816992206 0.68844109281256027 -0.001684535122025588 0.013605622123872989 0.05810686279306107;0.5853667840629273 -2.9560683084876329 0.56713425120259764 -2.1854386350040116 1.2930115031659106 -2.7133159265497957;0.64316656469750333 -0.63667017646313084 0.50060179040086761 -0.86827897068177973 2.695456517458648 0.16822164719859456;-0.44666821007466739 4.0993786464616679 -0.89370838440321498 3.0445073606237933 -3.3015566360833453 -4.492874075961689;1.8337574137485424 2.6946232855369989 1.1140472073136622 1.6167763205944321 1.8573696127039145 -0.81922672766933646;-0.12561950922781362 3.0711045035224349 -0.6535751823440773 2.0590707752473199 -1.3267693770634292 2.8782780742777794;-0.013438026967107483 -0.025741311825949621 0.45460734966889638 0.045052447491038108 -0.21794568374100454 0.10667240367191703];
% Layer 2
b2 = [-0.96846557414356171;-0.2454718918618051;-0.7331628718025488;-1.0225195290982099;0.50307202195645395;-0.49497234988401961;-0.21817117469133171];
LW2_1 = [-0.97716474643411022 -0.23883775971686808 0.99238069915206006 0.4147649511973347 0.48504023209224734 -0.071372217431684551 0.054177719330469304 -0.25963474838320832 0.27368380212104881 0.063159321947246799;-0.15570858147605909 -0.18816739764334323 -0.3793600124951475 2.3851961990944681 0.38355142531334563 -0.75308427071748985 -0.1280128732536128 -1.361052031781103 0.6021878865831336 -0.24725687748503239;0.076251356114485525 -0.10178293627600112 0.10151304376762409 -0.46453434441403058 0.12114876632815359 0.062856969143306296 -0.0019628163322658364 -0.067809039768745916 0.071731544062023825 0.65700427778446913;0.17887084584125315 0.29122649575978238 0.37255802759192702 1.3684190468992126 0.60936238465090853 0.21955911453674043 0.28477957899364675 -0.051456306721251184 0.6519451272106177 -0.64479205028051967;0.25743349663436799 2.0668075180209979 0.59610776847961111 -3.2609682919282603 1.8824214917530881 0.33542869933904396 0.03604272669356564 -0.013842766338427388 3.8534510207741826 2.2266745660915586;-0.16136175574939746 0.10407287099228898 -0.13902245286490234 0.87616472446622717 -0.027079111747601223 0.024812287505204988 -0.030101536834009103 0.043168268669541855 0.12172932035587079 -0.27074383434206573;0.18714562505165402 0.35267726325386606 -0.029241400610813449 0.53053853235049087 0.58880054832728757 0.047959541165126809 0.16152268183097709 0.23419456403348898 0.83166785128608967 -0.66765237856750781];
% Output 1
y1_step1_ymin = -1;
y1_step1_gain = [0.114200879346771;0.145581598485951;0.000139011547272197;0.000456244862967996;2.05816254143146e-05;5.27704485488127;0.00284355877067267];
y1_step1_xoffset = [-0.045;1.122;2.706;17.108;493.726;0.75;235.248];
% ===== SIMULATION ========
% Dimensions
Q = size(x1,1); % samples
% Input 1
x1 = x1';
xp1 = mapminmax_apply(x1,x1_step1_gain,x1_step1_xoffset,x1_step1_ymin);
% Layer 1
a1 = tansig_apply(repmat(b1,1,Q) + IW1_1*xp1);
% Layer 2
a2 = repmat(b2,1,Q) + LW2_1*a1;
% Output 1
y1 = mapminmax_reverse(a2,y1_step1_gain,y1_step1_xoffset,y1_step1_ymin);
y1 = y1';
end
% ===== MODULE FUNCTIONS ========
% Map Minimum and Maximum Input Processing Function
function y = mapminmax_apply(x,settings_gain,settings_xoffset,settings_ymin)
y = bsxfun(#minus,x,settings_xoffset);
y = bsxfun(#times,y,settings_gain);
y = bsxfun(#plus,y,settings_ymin);
end
% Sigmoid Symmetric Transfer Function
function a = tansig_apply(n)
a = 2 ./ (1 + exp(-2*n)) - 1;
end
% Map Minimum and Maximum Output Reverse-Processing Function
function x = mapminmax_reverse(y,settings_gain,settings_xoffset,settings_ymin)
x = bsxfun(#minus,y,settings_ymin);
x = bsxfun(#rdivide,x,settings_gain);
x = bsxfun(#plus,x,settings_xoffset);
end
The above one is the automatically generated code. The plot which I generated to cross-check the first variable is below:-
% X and Y are input and output - same as above
X_train = X(results.info1.train.indices,:);
y_train = Y(results.info1.train.indices,:);
out_train = myNeuralNetworkFunction_2(X_train);
scatter(y_train(:,1),out_train(:,1))
To answer your question about R: Yes, you should square R to get the R^2 value. In this case, they will be very close since R is very close to 1.
The graphs give the correlation between the estimated and real (target) values. So R is the strenght of the correlation. You can square it to find the R-square.
The graph you draw and matlab gave are not the graph of the same variables. The ranges or scales of the axes are very different.
First of all, is the problem you are trying to solve a regression problem? Or is it a classification problem with 7 classes converted to numeric? I assume this is a classification problem, as you are trying to get the success rate for each class.
As for your first question: According to the literature it is recommended to use the value "All: R". If you want to get the success rate of each of your classes, Precision, Recall, F-measure, FP rate, TP Rate, etc., which are valid in classification problems. values you need to reach. There are many matlab documents for this (help ROC) and you can look at the details. All the values I mentioned and which I think you actually want are obtained from the confusion matrix.
There is a good example of this.
[x,t] = simpleclass_dataset;
net = patternnet(10);
net = train(net,x,t);
y = net(x);
[c,cm,ind,per] = confusion(t,y)
I hope you will see what you want from the "nntraintool" window that appears when you run the code.
Your other questions have already been answered. Alternatively, you can consider using a machine learning algorithm with open source software such as Weka.
I am trying to implement SVM for classification. The goal is to output the correct grid of origin of a power signal (.wav file). The grids are titled A-I and there are 93 total signals for the training set and 49 practice signals. I have a 93x10x36 matrix of feature vectors. Does anyone know why I get the errors shown? TrainCorrectGrid and Training_Cepstrum1 both have 93 rows so I don't understand what the problem is. Any help is greatly appreciated.
My code is shown here:
clc; clear; close all;
load('avg_fft_feature (4).mat'); %training feature vectors
load('practice_fft_Mag_all (2).mat'); %practice feauture vectors
load('practice_GridOrigin.mat'); %correct grids of origin for practice data
load PracticeCorrectGrid.mat;
load Training_Cepstrum1;
load Practice_Cepstrum1a;
load fSet1.mat %load in correct practice grids
TrainCorrectGrid=['A';'A';'A';'A';'A';'A';'A';'A';'A';'B';'B';'B';'B';'B';'B';'B';'B';'B';'B';'C';'C';'C';'C';'C';'C';'C';'C';'C';'C';'C';'D';'D';'D';'D';'D';'D';'D';'D';'D';'D';'D';'E';'E';'E';'E';'E';'E';'E';'E';'E';'E';'E';'F';'F';'F';'F';'F';'F';'F';'F';'G';'G';'G';'G';'G';'G';'G';'G';'G';'G';'G';'H';'H';'H';'H';'H';'H';'H';'H';'H';'H';'H';'I';'I';'I';'I';'I';'I';'I';'I';'I';'I';'I'];
%[results,u] = multisvm(avg_fft_feature, TrainCorrectGrid, avg_fft_feature_practice);%avg_fft_feature);
[results,u] = multisvm(Training_Cepstrum1(93,:,1), TrainCorrectGrid, Practice_Cepstrum1a(49,:,1));
disp('Grids of Origin (SVM)');
%Display SVM Results
for i = 1:numel(u)
str = sprintf('%d: %s', i, u(i));
disp(str);
end
%Display Percent Correct
numCorrect = 0;
for i = 1:numel(u)
%if (strcmp(TrainCorrectGrid(i,1), u(i))==1); %compare training to
%training
if (strcmp(PracticeCorrectGrid(i,1), u(i))==1); %compare practice data to training
numCorrect = numCorrect + 1;
end
end
numberOfElements = numel(u);
percentCorrect = numCorrect / numberOfElements * 100;
% percentCorrect = round(percentCorrect, 2);
dispPercent = sprintf('Percent Correct = %0.3f%%', percentCorrect);
disp(dispPercent);
error shown here
The multisvm function is shown here:
function [result, u] = multisvm(TrainingSet,GroupTrain,TestSet)
%Models a given training set with a corresponding group vector and
%classifies a given test set using an SVM classifier according to a
%one vs. all relation.
%
%This code was written by Cody Neuburger cneuburg#fau.edu
%Florida Atlantic University, Florida USA and slightly modified by Renny Varghese
%This code was adapted and cleaned from Anand Mishra's multisvm function
%found at http://www.mathworks.com/matlabcentral/fileexchange/33170-multi-class-support-vector-machine/
u=unique(GroupTrain);
numClasses=length(u);
result = zeros(length(TestSet(:,1)),1);
%build models
for k=1:numClasses
%Vectorized statement that binarizes Group
%where 1 is the current class and 0 is all other classes
G1vAll=(GroupTrain==u(k));
models(k) = svmtrain(TrainingSet,G1vAll);
end
%classify test cases
for j=1:size(TestSet,1)
for k=1:numClasses
if(svmclassify(models(k),TestSet(j,:)))
break;
end
end
result(j) = k;
end
mapValues = 'ABCDEFGHI';
u = mapValues(result);
You state that Training_Cepstrum1 has size [93,10,36]. But when you call multisvm, you are only passing in Training_Cepstrum1(93,:,1) which has size [1,10]. Since TrainCorrectGrid has size [93,1], there is a mismatch in the number of rows.
It looks like you make the same error when passing in Practice_Cepstrum1a.
Try replacing your call to multisvm with
[results,u] = multisvm(Training_Cepstrum1(:,:,1), TrainCorrectGrid, Practice_Cepstrum1a(:,:,1));
This way Training_Cepstrum1(:,:,1) has size [93,10], the same number of rows as TrainCorrectGrid.
let us consider following equation
x(t)=sum(a(i)*sin(2*pi*f(i)*t+b(i)*cos(2*pi*f(i)*t))
where i=1,2,......m and frequencies f=[f1,f2,.....fm] and t=[t1,t2,....tn]
i want to create matrix by sin(2*pi*f(i)*t) and cos(2*pi*f(i)*t),clearly it would be matrix with dimension NX2*m,i have tried following code
function [amplitudes]=determine_amplitudes(y,f,t,n,m);
X=zeros(n,2*m);
for i=1:n
for k=1:m
if mod(k,2)==1
X(i,k)=sin(2*pi*f(k)*t(i));
else
X(i,k)=cos(2*pi*f(k)*t(i);
end
end
end
end
i used mod operator to determine that if k is odd index,then there should be written sin value,else cosine value,but problem is that i am not sure that given matrix would be with dimension NX2*m,so how to create such matrix so that not exceed index of bounds of frequency array ,recall that frequency array is following f=[f1,f2,..fm],so my problem simple is how to apply m frequency at 2*m position,thanks for help
UPDATE:
let say m=3, and frequencies f=[12.5 13.6 21.7]
then we have following matrix ,also assume
n=4 t=[0.01 0.02 0.03 0.04]
sin(2*pi*f(1)*t(1)) cos(2*pi*f(1)* t(1)) sin(2*pi*f(2)*t(1)) cos(2*pi*f(2)*t(1)) sin(2*pi*f(3)*t(1)) cos(2*pi*f(3)*t(1))
No loop version
[f1,t1] = meshgrid(f',t');
p1 = sin(bsxfun(#times,f1,2*pi*t')); %%// Create sin copy '
p2 = cos(bsxfun(#times,f1,2*pi*t')); %%// Create cos copy '
d1 = [p1;p2];
final_matrix = reshape(d1,size(p1,1),[]);
Naive loop version
final_matrx2 = zeros(n,2*m);
for k1=1:n
for k2=1:2*m
if rem(k2,2)==1
final_matrx2(k1,k2) = sin(2*pi*f(ceil(k2/2))*t(k1));
else
final_matrx2(k1,k2) = cos(2*pi*f(ceil(k2/2))*t(k1));
end
end
end
The problem says:
Three tensile tests were carried out on an aluminum bar. In each test the strain was measured at the same values of stress. The results were
where the units of strain are mm/m.Use linear regression to estimate the modulus of elasticity of the bar (modulus of elasticity = stress/strain).
I used this program for this problem:
function coeff = polynFit(xData,yData,m)
% Returns the coefficients of the polynomial
% a(1)*x^(m-1) + a(2)*x^(m-2) + ... + a(m)
% that fits the data points in the least squares sense.
% USAGE: coeff = polynFit(xData,yData,m)
% xData = x-coordinates of data points.
% yData = y-coordinates of data points.
A = zeros(m); b = zeros(m,1); s = zeros(2*m-1,1);
for i = 1:length(xData)
temp = yData(i);
for j = 1:m
b(j) = b(j) + temp;
temp = temp*xData(i);
end
temp = 1;
for j = 1:2*m-1
s(j) = s(j) + temp;
temp = temp*xData(i);
end
end
for i = 1:m
for j = 1:m
A(i,j) = s(i+j-1);
end
end
% Rearrange coefficients so that coefficient
% of x^(m-1) is first
coeff = flipdim(gaussPiv(A,b),1);
The problem is solved without a program as follows
MY ATTEMPT
T=[34.5,69,103.5,138];
D1=[.46,.95,1.48,1.93];
D2=[.34,1.02,1.51,2.09];
D3=[.73,1.1,1.62,2.12];
Mod1=T./D1;
Mod2=T./D2;
Mod3=T./D3;
xData=T;
yData1=Mod1;
yData2=Mod2;
yData3=Mod3;
coeff1 = polynFit(xData,yData1,2);
coeff2 = polynFit(xData,yData2,2);
coeff3 = polynFit(xData,yData3,2);
x1=(0:.5:190);
y1=coeff1(2)+coeff1(1)*x1;
subplot(1,3,1);
plot(x1,y1,xData,yData1,'o');
y2=coeff2(2)+coeff2(1)*x1;
subplot(1,3,2);
plot(x1,y2,xData,yData2,'o');
y3=coeff3(2)+coeff3(1)*x1;
subplot(1,3,3);
plot(x1,y3,xData,yData3,'o');
What do I have to do to get this result?
As a general advice:
avoid for loops wherever possible.
avoid using i and j as variable names, as they are Matlab built-in names for the imaginary unit (I really hope that disappears in a future release...)
Due to m being an interpreted language, for-loops can be very slow compared to their compiled alternatives. Matlab is named MATtrix LABoratory, meaning it is highly optimized for matrix/array operations. Usually, when there is an operation that cannot be done without a loop, Matlab has a built-in function for it that runs way way faster than a for-loop in Matlab ever will. For example: computing the mean of elements in an array: mean(x). The sum of all elements in an array: sum(x). The standard deviation of elements in an array: std(x). etc. Matlab's power comes from these built-in functions.
So, your problem. You have a linear regression problem. The easiest way in Matlab to solve this problem is this:
%# your data
stress = [ %# in Pa
34.5 69 103.5 138] * 1e6;
strain = [ %# in m/m
0.46 0.95 1.48 1.93
0.34 1.02 1.51 2.09
0.73 1.10 1.62 2.12]' * 1e-3;
%# make linear array for the data
yy = strain(:);
xx = repmat(stress(:), size(strain,2),1);
%# re-formulate the problem into linear system Ax = b
A = [xx ones(size(xx))];
b = yy;
%# solve the linear system
x = A\b;
%# modulus of elasticity is coefficient
%# NOTE: y-offset is relatively small and can be ignored)
E = 1/x(1)
What you did in the function polynFit is done by A\b, but the \-operator is capable of doing it way faster, way more robust and way more flexible than what you tried to do yourself. I'm not saying you shouldn't try to make these thing yourself (please keep on doing that, you learn a lot from it!), I'm saying that for the "real" results, always use the \-operator (and check your own results against it as well).
The backslash operator (type help \ on the command prompt) is extremely useful in many situations, and I advise you learn it and learn it well.
I leave you with this: here's how I would write your polynFit function:
function coeff = polynFit(X,Y,m)
if numel(X) ~= numel(X)
error('polynFit:size_mismathc',...
'number of elements in matrices X and Y must be equal.');
end
%# bad condition number, rank errors, etc. taken care of by \
coeff = bsxfun(#power, X(:), m:-1:0) \ Y(:);
end
I leave it up to you to figure out how this works.
I am coding a perceptron to learn to categorize gender in pictures of faces. I am very very new to MATLAB, so I need a lot of help. I have a few questions:
I am trying to code for a function:
function [y] = testset(x,w)
%y = sign(sigma(x*w-threshold))
where y is the predicted results, x is the training/testing set put in as a very large matrix, and w is weight on the equation. The part after the % is what I am trying to write, but I do not know how to write this in MATLAB code. Any ideas out there?
I am trying to code a second function:
function [err] = testerror(x,w,y)
%err = sigma(max(0,-w*x*y))
w, x, and y have the same values as stated above, and err is my function of error, which I am trying to minimize through the steps of the perceptron.
I am trying to create a step in my perceptron to lower the percent of error by using gradient descent on my original equation. Does anyone know how I can increment w using gradient descent in order to minimize the error function using an if then statement?
I can put up the code I have up till now if that would help you answer these questions.
Thank you!
edit--------------------------
OK, so I am still working on the code for this, and would like to put it up when I have something more complete. My biggest question right now is:
I have the following function:
function [y] = testset(x,w)
y = sign(sum(x*w-threshold))
Now I know that I am supposed to put a threshold in, but cannot figure out what I am supposed to put in as the threshold! any ideas out there?
edit----------------------------
this is what I have so far. Changes still need to be made to it, but I would appreciate input, especially regarding structure, and advice for making the changes that need to be made!
function [y] = Perceptron_Aviva(X,w)
y = sign(sum(X*w-1));
end
function [err] = testerror(X,w,y)
err = sum(max(0,-w*X*y));
end
%function [w] = perceptron(X,Y,w_init)
%w = w_init;
%end
%------------------------------
% input samples
X = X_train;
% output class [-1,+1];
Y = y_train;
% init weigth vector
w_init = zeros(size(X,1));
w = w_init;
%---------------------------------------------
loopcounter = 0
while abs(err) > 0.1 && loopcounter < 100
for j=1:size(X,1)
approx_y(j) = Perceptron_Aviva(X(j),w(j))
err = testerror(X(j),w(j),approx_y(j))
if err > 0 %wrong (structure is correct, test is wrong)
w(j) = w(j) - 0.1 %wrong
elseif err < 0 %wrong
w(j) = w(j) + 0.1 %wrong
end
% -----------
% if sign(w'*X(:,j)) ~= Y(j) %wrong decision?
% w = w + X(:,j) * Y(j); %then add (or subtract) this point to w
end
you can read this question I did some time ago.
I uses a matlab code and a function perceptron
function [w] = perceptron(X,Y,w_init)
w = w_init;
for iteration = 1 : 100 %<- in practice, use some stopping criterion!
for ii = 1 : size(X,2) %cycle through training set
if sign(w'*X(:,ii)) ~= Y(ii) %wrong decision?
w = w + X(:,ii) * Y(ii); %then add (or subtract) this point to w
end
end
sum(sign(w'*X)~=Y)/size(X,2) %show misclassification rate
end
and it is called from code (#Itamar Katz) like (random data):
% input samples
X1=[rand(1,100);rand(1,100);ones(1,100)]; % class '+1'
X2=[rand(1,100);1+rand(1,100);ones(1,100)]; % class '-1'
X=[X1,X2];
% output class [-1,+1];
Y=[-ones(1,100),ones(1,100)];
% init weigth vector
w=[.5 .5 .5]';
% call perceptron
wtag=perceptron(X,Y,w);
% predict
ytag=wtag'*X;
% plot prediction over origianl data
figure;hold on
plot(X1(1,:),X1(2,:),'b.')
plot(X2(1,:),X2(2,:),'r.')
plot(X(1,ytag<0),X(2,ytag<0),'bo')
plot(X(1,ytag>0),X(2,ytag>0),'ro')
legend('class -1','class +1','pred -1','pred +1')
I guess this can give you an idea to make the functions you described.
To the error compare the expected result with the real result (class)
Assume your dataset is X, the datapoins, and Y, the labels of the classes.
f=newp(X,Y)
creates a perceptron.
If you want to create an MLP then:
f=newff(X,Y,NN)
where NN is the network architecture, i.e. an array that designates the number of neurons at each hidden layer. For example
NN=[5 3 2]
will correspond to an network with 5 neurons at the first layers, 3 at the second and 2 a the third hidden layer.
Well what you call threshold is the Bias in machine learning nomenclature. This should be left as an input for the user because it is used during training.
Also, I wonder why you are not using the builtin matlab functions. i.e newp or newff. e.g.
ff=newp(X,Y)
Then you can set the properties of the object ff to do your job for selecting gradient descent and so on.