This is a very simple question as I am new to the concepts.
I have a 4-4-1 neural network that I am running on 16x4 binary data to predict a 16x1 column of outputs.
I have utilized random weights and biases to generate a rough predicted output vector. I then calculate a vector of errors (actual-output) which is 16x1.
When back propagating, I am trying to update my weights. But how do I update the single value of a weight if my error is a 16x1 list of errors? That is, how do I implement:
weight = weight + learning_rate * error * input
if 'error' is 16x1 and input is 16x4?
Related
So I have something like this,
y=l3*[sin(theta1)*cos(theta2)*cos(theta3)+cos(theta1)*sin(theta2)*cos(theta3)-sin(theta1)*sin(theta2)*sin(theta3)+cos(theta1)*cos(theta2)sin(theta3)]+l2[sin(theta1)*cos(theta2)+cos(theta1)*sin(theta2)]+l1*sin(theta1)+l0;
and something similar for x. Where thetai is angles from specified interval and li some coeficients. Task is approximate inversion of equation, so you set x and y and result will be appropriate theta. So I random generate thetas from specified intervals, compute x and y. Then I norm x and y between <-1,1> and thetas between <0,1>. This data I used as training set in such way, inputs of network are normalized x and y, outputs are normalized thetas.
I train the network, tried different configuration and absolute error of network was still around 24.9% after whole night of training. It's so much, so I don't know what to do.
Bigger training set?
Bigger network?
Experiment with learning rate?
Longer training?
Technical info
As training algorithm was used error back propagation. Neurons have sigmoid activation function, units are biased. I tried topology: [2 50 3], [2 100 50 3], training set has length 1000 and training duration was 1000 cycle(in one cycle I go through all dataset). Learning rate has value 0.2.
Error of approximation was computed as
sum of abs(desired_output - reached_output)/dataset_lenght.
Used optimizer is stochastic gradient descent.
Loss function,
1/2 (desired-reached)^2
Network was realized in my Matlab template for NN. I know that is weak point, but I'm sure my template is right because(successful solution of XOR problem, approximation of differential equations, approximation of state regulator). But I show this template, because this information may be useful.
Neuron class
Network class
EDIT:
I used 2500 unique data within theta ranges.
theta1<0, 180>, theta2<-130, 130>, theta3<-150, 150>
I also experiment with larger dataset, but accuracy doesn't improve.
I have a 2x147 matrix as an input and a 3x147 matrix as an output, and I trained the NN pattern recognition with the input matrix and output matrix. I then generated a Simulink model of the trained NN, and now I want to test the new dataset of same size (2x147).
I am getting the following errors:
Error in port widths or dimensions. Output port 1 of NN_Trail/Constant is a [2x147] matrix.
Error in port widths or dimensions. Input port 1 of NN_Trail/Pattern Recognition Neural Network is a one dimensional vector with 2 elements.
If I give a constant value of 2 elements, then the Simulink runs for the mentioned time and gives the desired output. How can I get it to work with the data I've described?
My idea in future is to connect the trained neural network to a simulated plant and find the abnormal data from the plant.
So your model has an input of dimenstion 2 and an output of dimenson 3.
And you have an calculated signal of 147 timesteps that you want to run on the inputs.
To import that signal to your model you can use a Matlab time series object.
http://ch.mathworks.com/help/simulink/ug/importing-matlab-timeseries-data-to-a-root-level-input-port.html
I am trying to train a linear SVM on a data which has 100 dimensions. I have 80 instances for training. I train the SVM using fitcsvm function in MATLAB and check the function using predict on the training data. When I classify the training data with the SVM all the data points are being classified into only one class.
SVM = fitcsvm(votes,b,'ClassNames',unique(b)');
predict(SVM,votes);
This gives outputs as all 0's which corresponds to 0th class. b contains 1's and 0's indicating the class to which each data point belongs.
The data used, i.e. matrix votes and vector b are given the following link
Make sure you use a non-linear kernel, such as a gaussian kernel and that the parameters of the kernel are tweaked. Just as a starting point:
SVM = fitcsvm(votes,b,'KernelFunction','RBF', 'KernelScale','auto');
bp = predict(SVM,votes);
that said you should split your set in a training set and a testing set, otherwise you risk overfitting
I have to use NAR network to train a time-series for my project. To have an idea of how time-series tool (ntstool) works in MATLAB , I used the GUI of ntstool in matlab with a dataset containing 427 timesteps of one element. While training I used a neural network with 10 hidden layers and delay value = 5.
Now I have following Three questions :
What does the **delay value (d) ** in the GUI means. Does it mean that while training the network assumes that each timestep value is dependent on last 'd' timesteps' values ?
how to predict the values at future timesteps in ntstool?
Delay value means that neural network inputs are current input value and N delay values of input signals, in your case N=5. Hope this will help you.
I'm trying to implement gradient checking for a simple feedforward neural network with 2 unit input layer, 2 unit hidden layer and 1 unit output layer. What I do is the following:
Take each weight w of the network weights between all layers and perform forward propagation using w + EPSILON and then w - EPSILON.
Compute the numerical gradient using the results of the two feedforward propagations.
What I don't understand is how exactly to perform the backpropagation. Normally, I compare the output of the network to the target data (in case of classification) and then backpropagate the error derivative across the network. However, I think in this case some other value have to be backpropagated, since in the results of the numerical gradient computation are not dependent of the target data (but only of the input), while the error backpropagation depends on the target data. So, what is the value that should be used in the backpropagation part of gradient check?
Backpropagation is performed after computing the gradients analytically and then using those formulas while training. A neural network is essentially a multivariate function, where the coefficients or the parameters of the functions needs to be found or trained.
The definition of a gradient with respect to a specific variable is the rate of change of the function value. Therefore, as you mentioned, and from the definition of the first derivative we can approximate the gradient of a function, including a neural network.
To check if your analytical gradient for your neural network is correct or not, it is good to check it using the numerical method.
For each weight layer w_l from all layers W = [w_0, w_1, ..., w_l, ..., w_k]
For i in 0 to number of rows in w_l
For j in 0 to number of columns in w_l
w_l_minus = w_l; # Copy all the weights
w_l_minus[i,j] = w_l_minus[i,j] - eps; # Change only this parameter
w_l_plus = w_l; # Copy all the weights
w_l_plus[i,j] = w_l_plus[i,j] + eps; # Change only this parameter
cost_minus = cost of neural net by replacing w_l by w_l_minus
cost_plus = cost of neural net by replacing w_l by w_l_plus
w_l_grad[i,j] = (cost_plus - cost_minus)/(2*eps)
This process changes only one parameter at a time and computes the numerical gradient. In this case I have used the (f(x+h) - f(x-h))/2h, which seems to work better for me.
Note that, you mentiond: "since in the results of the numerical gradient computation are not dependent of the target data", this is not true. As when you find the cost_minus and cost_plus above, the cost is being computed on the basis of
The weights
The target classes
Therefore, the process of backpropagation should be independent of the gradient checking. Compute the numerical gradients before backpropagation update. Compute the gradients using backpropagation in one epoch (using something similar to above). Then compare each gradient component of the vectors/matrices and check if they are close enough.
Whether you want to do some classification or have your network calculate a certain numerical function, you always have some target data. For example, let's say you wanted to train a network to calculate the function f(a, b) = a + b. In that case, this is the input and target data you want to train your network on:
a b Target
1 1 2
3 4 7
21 0 21
5 2 7
...
Just as with "normal" classification problems, the more input-target pairs, the better.