I have come up with a solution for a classification problem using neural networks. I have got the weight vectors for the same too. The data is 5 dimensional and there are 5 neurons in the hidden layer.
Suppose neuron 1 has input weights w11, w12, ...w15
I have to explain the physical interpretation of these weights...like a combination of these weights, what does it represent in the problem.Does any such interpretation exist or is that the neuron has no specific interpretation as such?
A single neuron will not give you any interpretation, but looking at a combination of couple of neuron can tell you which pattern in your data is captured by that set of neurons (assuming your data is complicated enough to have multiple patterns and yet not too complicated that there is too many connections in the network).
The weights corresponding to neuron 1, in your case w11...w15, are the weights that map the 5 input features to that neuron. The weights quantify the extent to which each feature will effect its respective neuron (which is representing some higher dimensional feature, in turn). Each neuron is a matrix representation of these weights, usually after having an activation function applied.
The mathematical formula that determines the value of the neuron matrix is matrix multiplication of the feature matrix and the weight matrix, and using the loss function, which is most basically the sum of the square of the difference between the output from the matrix multiplication and the actual label.Stochastic Gradient Descent is then used to adjust the weight matrix's values to minimize the loss function.
Related
I would like to know what max pooling and mean pooling are for recurrent neural networks like LSTM while using them for sentiment analysis.
I think as far as I know we pooling is mostly used in convolution neural networks.
and it is a method of concentration of higher order matrix to lower order matrix which contains properties of inherent matrix...in pooling a matrix smaller size and is moved over the original matrix and max value or average value in smaller matrix is selected to form a new resultant matrix of further computation. link-https://machinelearningmastery.com/pooling-layers-for-convolutional-neural-networks/
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.
I have build a neural network model, with 3 classes. I understand that the best output for a classification process is the boolean 1 for a class and boolean zeros for the other classes , for example the best classification result for a certain class, where the output of a classifire that lead on how much this data are belong to this class is the first element in a vector is [1 , 0 , 0]. But the output of the testing data will not be like that,instead it will be a rational numbers like [2.4 ,-1 , .6] ,So how to interpret this result? How to decide to which class the testing data belong?
I have tried to take the absolute value and turn the maximum element to 1 and the other to zeros, so is this correct?
Learner.
It appears your neural network is bad designed.
Regardless your structure is -number of input-hidden-output- layers, when you are doing a multiple classification problem, you must ensure each of your output neurones are evaluating an individual class, that is, each them has a bounded output, in this case, between 0 and 1. Use almost any of the defined function on the output layer for performing this.
Nevertheles, for the Neural Network to work properly, you must strongly remember, that every single neuron loop -from input to output- operates as a classificator, this is, they define a region on your input space which is going to be classified.
Under this framework, every single neuron has a direct interpretable sense on the non-linear expansion the NN is defining, particularly when there are few hidden layers. This is ensured by the general expression of Neural Networks:
Y_out=F_n(Y_n-1*w_n-t_n)
...
Y_1=F_0(Y_in-1*w_0-t_0)
For example, with radial basis neurons -i.e. F_n=sqrt(sum(Yni-Rni)^2) and w_n=1 (identity):
Yn+1=sqrt(sum(Yni-Rni)^2)
a dn-dim spherical -being dn the dimension of the n-1 layer- clusters classification is induced from the first layer. Similarly, elliptical clusters are induced. When two radial basis neuron layers are added under that structure of spherical/elliptical clusters, unions and intersections of spherical/elliptical clusters are induced, three layers are unions and intersections of the previous, and so on.
When using linear neurons -i.e. F_n=(.) (identity), linear classificators are induced, that is, the input space is divided by dn-dim hyperplanes, and when adding two layers, union and intersections of hyperplanes are induced, three layers are unions and intersections of the previous, and so on.
Hence, you can realize the number of neurons per layer is the number of classificators per each class. So if the geometry of the space is -lets put this really graphically- two clusters for the class A, one cluster for the class B and three clusters for the class C, you will need at least six neurons per layer. Thus, assuming you could expect anything, you can consider as a very rough approximate, about n neurons per class per layer, that is, n neurons to n^2 minumum neurons per class per layer. This number can be increased or decreased according the topology of the classification.
Finally, the best advice here is for n outputs (classes), r inputs:
Have r good classificator neurons on the first layers, radial or linear, for segmenting the space according your expectations,
Have n to n^2 neurons per layer, or as per the dificulty of your problem,
Have 2-3 layers, only increase this number after getting clear results,
Have n thresholding networks on the last layer, only one layer, as a continuous function from 0 to 1 (make the crisp on the code)
Cheers...
I was wondering, MATLAB has a removeconstantrows function that should be applied to feedforward neural network input and target output data. This function removes constant rows from the data. For example if one input vector for a 5-input neural network is [1 1 1 1 1] then it is removed.
Googling, the best explanation I could find is that (paraphrasing) "constant rows are not needed and can be replaced by appropriate adjustments to the biases of the output layer".
Can someone elaborate?
Who does this adjustment?
From my book, the weight adjustment for simple gradient descent is:
Δ weight_i = learning_rate * local_gradient * input_i
Which means that all weights of a neuron at the first hidden layer are adjusted the same amount. But they ARE adjusted.
I think there is a misundertanding. The "row" is not an input pattern, but a feature, that is i-th component in all patterns. It's obvious that if some feature does not have big variance on all data set, it does not provide valuable information and does not play a noticable role for network training.
The comparison to a bias is feasible (though I don't agree, that this applies to output layer (only), bacause it depends on where the constant row is found - if it's in input data, then it is right as well for the first hidden layer, imho). If you remeber, it's recommended for each neuron in backpropagation network to have a special bias weight, connected to 1 constant signal. If, for example, a training set contains a row with all 1-th, then this is the same as additional bias. If the constant row has a different value, then the bias will have different effect, but in any case you can simply eliminate this row, and add the constant value of the row into the existing bias.
Disclaimer: I'm not a Matlab user. My background in neural networks comes solely from programming area.
I'm new to Neual Networks and I suppose I don't fully understand what 'bias' param does in Matlab's NN.
It simply means an additive term in the neuron computation. Typically you have the input vector to a neuron x, and you perform a dot product with the weights, w. Then you add on the bias term, b and apply a non-linear mapping.
The b number (per neuron) is part of the training and will change during training (unless you specifically disable it in training, but I know no reason to do this.)
The term bias is probably simply because it's an additive value in addition to the neuron's activation (that comes from the weighted inputs). Once trained, the bias is a fixed term that does not depend on the neuron inputs.
A neuron's bias is basically an extra input value that doesn't change. It is added to the normal inputs to get the total input to the neuron.