Training Neural network to predict sin(x) matlab - matlab

It's been 3 days since i'm trying to train many neural networks to predict sin(x) function, i'm using matlab 2016b (i have to work with it in my assignement)
what i did :
change layers
duplicate dataset (big , small)
add/sub periods
shuffle the data
change neural's number per layer
change learning function
change the transfer function and mapped the target
all that with no good prediction, can anyone explain me what i'm doing wrong ,
and it would be very helpful to paste any good book for ("preparing dataset befor traing", "knowing the best NN's structure for your project",...
and any book seems helpful)
my actual code : (i'm using nntool for the training )
%% input and target
input = 0:pi/100:8*pi;
target = sin(input) ;
plot(input,sin(input)),
hold on,
inputA = input;
targetA = target;
plot(inputA,targetA),
hold on,
%simulate input
output=sim(network2,inputA);
plot(inputA,output,'or')
hold off

Related

Data augmentation techniques for general datasets?

I am working in a machine learning problem and want to build neural network based classifiers on it in matlab. One problem is that the data is given in the form of features and number of samples is considerably lower. I know about data augmentation techniques for images, by rotating, translating, affine translation, etc.
I would like to know whether there are data augmentation techniques available for general datasets ? Like is it possible to use randomness to generate more data ? I read the answer here but I did not understand it.
Kindly please provide answers with the working details if possible.
Any help will be appreciated.
You need to look into autoencoders. Effectively you pass your data into a low level neural network, it applies a PCA-like analysis, and you can subsequently use it to generate more data.
Matlab has an autoencoder class as well as a function, that will do all of this for you. From the matlab help files
Generate the training data.
rng(0,'twister'); % For reproducibility
n = 1000;
r = linspace(-10,10,n)';
x = 1 + r*5e-2 + sin(r)./r + 0.2*randn(n,1);
Train autoencoder using the training data.
hiddenSize = 25;
autoenc = trainAutoencoder(x',hiddenSize,...
'EncoderTransferFunction','satlin',...
'DecoderTransferFunction','purelin',...
'L2WeightRegularization',0.01,...
'SparsityRegularization',4,...
'SparsityProportion',0.10);
Generate the test data.
n = 1000;
r = sort(-10 + 20*rand(n,1));
xtest = 1 + r*5e-2 + sin(r)./r + 0.4*randn(n,1);
Predict the test data using the trained autoencoder, autoenc .
xReconstructed = predict(autoenc,xtest');
Plot the actual test data and the predictions.
figure;
plot(xtest,'r.');
hold on
plot(xReconstructed,'go');
You can see the green cicrles which represent additional data generated with the auto-encoder.

Classification using GMM with MATLAB

I'm trying to classify a testset using GMM. I have a trainset (n*4 matrix) with labels {1,2,3}, n means the number of training examples, which have 4 properties. And I also have a testset (m*4) to be classified.
My goal is to have a probability matrix (m*3) for each testing example giving each label P(x_test|labels). Just like soft clustering.
first, I create a GMM with k=9 components over the whole trainset. I know in some papers, the author create a GMM for each label in trainset. But I want to deal with the data from all of the classes.
GMModel = fitgmdist(trainset,k_component,'RegularizationValue',0.1,'Start','plus');
My problem is, I want to confirm the relationship P(component|labels)between components and labels. So I write a code as below, but not sure if it's right,
idx_ex_of_c1 = find(trainset_label==1);
idx_ex_of_c2 = find(trainset_label==2);
idx_ex_of_c3 = find(trainset_label==3);
[~,~,post] = cluster(GMModel,trainset);
cita_c_k = zeros(3,k_component);
for id_k = 1:k_component
cita_c_k(1,id_k) = sum(post(idx_ex_of_c1,id_k))/numel(idx_ex_of_c1);
cita_c_k(2,id_k) = sum(post(idx_ex_of_c2,id_k))/numel(idx_ex_of_c2);
cita_c_k(3,id_k) = sum(post(idx_ex_of_c3,id_k))/numel(idx_ex_of_c3);
end
cita_c_k is a (3*9) matrix to store the relationships. idx_ex_of_c1 is the index of examples, whose label is '1' in the trainset.
For the testing process. I first apply the GMModel to testset
[P,~] = posterior(GMModel,testset); % P is a m*9 matrix
And then, sum all components,
P_testset = P*cita_c_k';
[a,b] = max(P_testset,3);
imagesc(b);
The result is ok, But not good enough. Can anyone give me some tips?
Thanks!
You can take following steps:
Increase target error and/or use optimal network size in training, but over-training and network size increase usually won't help
Most important, shuffle training data while training and use only important data points for a label to train (ignore data points that may belong to more than one labels)
SEPARABILITY
Verify separability of data using properties using correlation.
Correlation of all data in a label (X) should be high (near to one)
Cross-correlation of all data in label (X) with data in label (!=X) should be low (near zero).
If you observe that data points in a label have low correlation and data points across labels have high correlation - It puts a question on selection of properties (there could be properties which actually won't make data separable). Being so do follows:
Add more relevant properties to data points and remove less relevant properties (technique to use this is PCA)
Use derived parameters like top frequency component etc. from data points to train rather than direct points
Use a time delay network to train time series (always)

Using Linear Prediction Over Time Series to Determine Next K Points

I have a time series of N data points of sunspots and would like to predict based on a subset of these points the remaining points in the series and then compare the correctness.
I'm just getting introduced to linear prediction using Matlab and so have decided that I would go the route of using the following code segment within a loop so that every point outside of the training set until the end of the given data has a prediction:
%x is the data, training set is some subset of x starting from beginning
%'unknown' is the number of points to extend the prediction over starting from the
%end of the training set (i.e. difference in length of training set and data vectors)
%x_pred is set to x initially
p = length(training_set);
coeffs = lpc(training_set, p);
for i=1:unknown
nextValue = -coeffs(2:end) * x_pred(end-unknown-1+i:-1:end-unknown-1+i-p+1)';
x_pred(end-unknown+i) = nextValue;
end
error = norm(x - x_pred)
I have three questions regarding this:
1) Does this appropriately do what I have described? I ask because my error seems rather large (>100) when predicting over only the last 20 points of a dataset that has hundreds of points.
2) Am I interpreting the second argument of lpc correctly? Namely, that it means the 'order' or rather number of points that you want to use in predicting the next point?
3) If this is there a more efficient, single line function in Matlab that I can call to replace the looping and just compute all necessary predictions for me given some subset of my overall data as a training set?
I tried looking through the lpc Matlab tutorial but it didn't seem to do the prediction as I have described my needs require. I have also been using How to use aryule() in Matlab to extend a number series? as a reference.
So after much deliberation and experimentation I have found the above approach to be correct and there does not appear to be any single Matlab function to do the above work. The large errors experienced are reasonable since I am using a linear prediction algorithm for a problem (i.e. sunspot prediction) that has inherent nonlinear behavior.
Hope this helps anyone else out there working on something similar.

Naïve Bayes Classifier -- is normalization necessary?

We recently studied the Naïve Bayesian Classifier in our Machine Learning class and now I'm trying to implement it on the Fisher Iris dataset as a self-exercise. The concept is easy and straightforward, with some trickiness involved for continuous attributes. I read up several literature resources which recommended using a Gaussian approximation to compute probability of test data values, so I'm going with it in my code.
Now I'm trying to run it initially for 50% training and 50% test data samples, but something is missing. The current code is always predicting class 1 (I used integers to represent the classes) for all test samples, which is obviously wrong.
My guess is that the problem may be due to normalization being omitted by the code? Though I think adding normalization would still yield proportionate results, and so far my attempts to normalize have produced the same classification results.
Can someone please suggest if there is anything obvious missing here? Or if I'm not approaching this right? Since most of the code is 'mechanics', I have made prominent (****************) the 2 lines that are responsible for the calculations. Any help is appreciated, thanks!
nsamples=75; % 50% samples
% acquire training set and test set
[trainingSample,idx] = datasample(data,nsamples,'Replace',false);
testData = data(setdiff(1:150,idx),:);
% define Gaussian function
%***********************************************************%
Phi=#(mu,sig2,x) (1/sqrt(2*pi*sig2))*exp(-((x-mu)^2)/2*sig2);
%***********************************************************%
for c=1:3 % for 3 classes in training set
clear y x mu sig2;
index=1;
for i=1 : length(trainingSample)
if trainingSample(i,5)==c
y(index,:)=trainingSample(i,:); % filter current class samples
index=index+1; % for conditional probabilities
end
end
for j=1:size(testData,1) % iterate over test samples
clear pf p;
for i=1:4 % iterate over columns
x=testData(j,i); % representing attributes
mu=mean(y(:,i));
sig2=var(y(:,i));
pf(i) = Phi(mu,sig2,x); % calc conditional probability
end
% calc class likelihood; prior * posterior
%*****************************************************%
pc(j,c) = size(y,1)/nsamples * pf(1)*pf(2)*pf(3)*pf(4);
%*****************************************************%
end
end
% find the predicted class for each test sample
% by taking the max probability calculated
for i=1:size(pc,1)
[~,q]=max(pc(i,:));
predicted(i)=q;
actual(i)=testData(i,5);
end
Normalization shouldn't be necessary since the features are only compared to each other.
p(class|thing) = p(class)p(thing|class) =
= p(class)p(feature_1|class)p(feature_2|class)...p(feature_N|class)
So when fitting the parameters for the distribution feature_i|class it will just rescale the parameters (for the new "scale") in this case (mu, sigma2), but the probabilities will remain the same.
It's hard to read the matlab code due to alot of indexing and splitting of training/testing etc. Which is a possible problem source.
You should try something with a lot less non-necessary stuff around it (I would recommend python with scikit-learn for example, alot of helpers for splitting data and such http://scikit-learn.org/).
It's really important that you separate the training and test data, and only train the model with training data and test the trained model with the test data. (Is this done?)
Next step is to check the parameters which is easiest done with either printing them out (sanity check) or..
for each feature render the gaussian bells fitted next to a histogram of the data to see that they match (remember that each histogram bar must be of height number_of_samples_within_range/total_number_of_samples.
Visualising the data and the model is really important to know what is happening.

How to use SVM in Matlab?

I am new to Matlab. Is there any sample code for classifying some data (with 41 features) with a SVM and then visualize the result? I want to classify a data set (which has five classes) using the SVM method.
I read the "A Practical Guide to Support Vector Classication" article and I saw some examples. My dataset is kdd99. I wrote the following code:
%% Load Data
[data,colNames] = xlsread('TarainingDataset.xls');
groups = ismember(colNames(:,42),'normal.');
TrainInputs = data;
TrainTargets = groups;
%% Design SVM
C = 100;
svmstruct = svmtrain(TrainInputs,TrainTargets,...
'boxconstraint',C,...
'kernel_function','rbf',...
'rbf_sigma',0.5,...
'showplot','false');
%% Test SVM
[dataTset,colNamesTest] = xlsread('TestDataset.xls');
TestInputs = dataTset;
groups = ismember(colNamesTest(:,42),'normal.');
TestOutputs = svmclassify(svmstruct,TestInputs,'showplot','false');
but I don't know that how to get accuracy or mse of my classification, and I use showplot in my svmclassify but when is true, I get this warning:
The display option can only plot 2D training data
Could anyone please help me?
I recommend you to use another SVM toolbox,libsvm. The link is as follow:
http://www.csie.ntu.edu.tw/~cjlin/libsvm/
After adding it to the path of matlab, you can train and use you model like this:
model=svmtrain(train_label,train_feature,'-c 1 -g 0.07 -h 0');
% the parameters can be modified
[label, accuracy, probablity]=svmpredict(test_label,test_feaure,model);
train_label must be a vector,if there are more than two kinds of input(0/1),it will be an nSVM automatically.
train_feature is n*L matrix for n samples. You'd better preprocess the feature before using it. In the test part, they should be preprocess in the same way.
The accuracy you want will be showed when test is finished, but it's only for the whole dataset.
If you need the accuracy for positive and negative samples separately, you still should calculate by yourself using the label predicted.
Hope this will help you!
Your feature space has 41 dimensions, plotting more that 3 dimensions is impossible.
In order to better understand your data and the way SVM works is to begin with a linear SVM. This tybe of SVM is interpretable, which means that each of your 41 features has a weight (or 'importance') associated with it after training. You can then use plot3() with your data on 3 of the 'best' features from the linear svm. Note how well your data is separated with those features and choose a basis function and other parameters accordingly.