I am making 8 x 8 tiles of Images and I want to train a RBF Neural Network in Matlab using those tiles as inputs. I understand that I can convert the matrix into a vector and use it. But is there a way to train them as matrices? (to preserve the locality) Or is there any other technique to solve this problem?
There is no way to use a matrix as an input to such a neural network, but anyway this won't change anything:
Assume you have any neural network with an image as input, one hidden layer, and the output layer. There will be one weight from every input pixel to every hidden unit. All weights are initialized randomly and then trained using backpropagation. The development of these weights does not depend on any local information - it only depends on the gradient of the output error with respect to the weight. Having a matrix input will therefore make no difference to having a vector input.
For example, you could make a vector out of the image, shuffle that vector in any way (as long as you do it the same way for all images) and the result would be (more or less, due to the random initialization) the same.
The way to handle local structures in the input data is using convolutional neural networks (CNN).
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In a neural network, for an intermediate layer, I need to threshold the output. The output of each neuron in the layer is a real value, but I need to binarize it (to 0 or 1). But with hard thresholding, backpropagation won't work. Is there a way to achieve this?
Details:
I have a GAN kind of network i.e. there are 2 neural networks trained end-to-end. The output of first neural network is real values. I need them to be binary values. I read that Gumbel Softmax (Categorical Reparameterization) is used to handle discrete variables in a neural network. Is there a way to use that for my use-case? If yes, how? If not, is there any other way?
From what I could gather in internet is that Gumbel is a probability distribution. Using that we can generate a discrete distribution. But for use-case, I need a function that can take a real input and output a binary value. So, I need an activation function of that form. How can I achieve that?
Thanks!
I found the picture below:
which is shown in this web page
I wonder how are this kind of images generated?
This picture is made by printing out the weights of first layer filters, later in that course there's a section about visualizing the networks.
For higher layers printing out the weights may not make sense, there's a paper that might be useful Visualizing Higher-Layer Features of a Deep Network.
Each convolutional kernel is just a matrix N x M (weight matrix), thus you can simply plot it (each square in the above plot is a single convoluational matrix). Color ones are probably taken from 3-channel convolution, thus each is encoded as one color.
I have trained a feedforward neural network in Matlab. Now I have to implement this neural network in C language (or simulate the model in Matlab using mathematical equations, without using direct functions). How do I do that? I know that I have to take the weights and bias and activation function. What else is required?
There is no point in representing it as a mathematical function because it won't save you any computations.
Indeed all you need is the weights, biases, activation and your architecture. I'm assuming it is a simple feedforward network as you said, you need to implement some kind of matrix multiplication and addition in C. Also, you'll need to implement the activation function. After that, you're ready to go. Your feed forward NN is ready to be implemented. If the C code will not be used for training, it won't be necessary to implement the backpropagation algorithm in C.
A feedforward layer would be implemented as follows:
Output = Activation_function(Input * weights + bias)
Where,
Input: (1 x number_of_input_parameters_for_this_layer)
Weights: (number_of_input_parameters_for_this_layer x number_of_neurons_for_this_layer)
Bias: (1 x number_of_neurons_for_this_layer)
Output: (1 x number_of_neurons_for_this_layer)
The output of a layer is the input to the next layer.
After some days of searching, I have found the following webpage to be very useful http://ufldl.stanford.edu/tutorial/supervised/MultiLayerNeuralNetworks/
The picture below shows a simple feedforward neural network. Picture taken from the above website.
In this figure, the circles denote the inputs to the network. The circles labeled “+1” are called bias units, and correspond to the intercept term. The leftmost layer of the network is called the input layer, and the rightmost layer the output layer (which, in this example, has only one node). The middle layer of nodes is called the hidden layer, because its values are not observed in the training set. In this example, the neural network has 3 input units (not counting the bias unit), 3 hidden units, and 1 output unit.
The mathematical equations representing this feedforward network are
This neural network has parameters (W,b)=(W(l),b(l),W(2),b(2)), where we write Wij(l) to denote the parameter (or weight) associated with the connection between unit j in layer l, and unit i in layer l+1. (Note the order of the indices.) Also, bi(l) is the bias associated with unit i in layer l+1.
So, from the trained model, as Mido mentioned in his answer, we have to take the input weight matrix which is W(1), the layer weight matrix which is W(2), biases, hidden layer transfer function and output layer transfer function. After this, use the above equations to estimate the output hW,b(x). A popular transfer function used for a regression problem is tan-sigmoid transfer function in the hidden layer and linear transfer function in the output layer.
Those who use Matlab, these links are highly useful
try to simulate neural network in Matlab by myself
Neural network in MATLAB
Programming a Basic Neural Network from scratch in MATLAB
Neural Networks are mostly used to classify. So, the activation of a neuron in the output layer indicates the class of whatever you are classifying.
Is it possible (and correct) to design a NN to get 3D coordinates? This is, three output neurons with values in ranges, for example [-1000.0, 1000.0], each one.
Yes. You can use a neural network to perform linear regression, and more complicated types of regression, where the output layer has multiple nodes that can be interpreted as a 3-D coordinate (or a much higher-dimensional tuple).
To achieve this in TensorFlow, you would create a final layer with three output neurons, each corresponding to a different dimension of your target coordinates, then minimize the root mean squared error between the current output and the known value for each example.
Can I input the SURF feature obtained by the MATLAB command (detectSURFFeature) as input to the neural network to train network in order to classify/detect the object in the image?.if yes how can I cop with the multidimensional data obtained by the descriptor? I am using image set of same resolution and almost similar orientation. I am using only MATLAB.
One way to do this is to use the bag of features approach. You discretize the space of the SURF descriptors, and then you compute a histogram of the descriptors in your image. This gives you a single vector that you can use at input to a neural network or any other classifier of your choice.