The Hidden Layer

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You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. Vote 0. How to choose number of hidden layers. Hi, I want to design a neural network with 3 input and 1 output. Samples are 21 Millions. For predictions and I don't know how many hidden layers and also the network parameters to use to get best results. Tags neural network.

See Also. Walter Roberson view profile. Answer by Walter Roberson Walter Roberson view profile. Accepted Answer.

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When you call patternnet, pass it a vector of the sizes of the hidden layers. Greg Heath Greg Heath view profile. I don't see it so I must have screwed it up. The jist was: She is designing for regression, not pattern recognition. Hope this helps. Greg Heath view profile.

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Vote 1. Answer by Greg Heath Greg Heath view profile. For 3 inputs and 1 output you only need 1 hidden layer. Minimize the number of hidden nodes subject to the maximum training error constraint. I use a double loop approach over. A reasonable choice to prevent overtraining an overfit net is.

machine learning, deep learning, nlp, data science

My experience is that for d-dimensional Gaussian distributions. There are zillions of examples of my double loop minimum H approach in. Just search on. Such a neural network is called a perceptron. However, real-world neural networks, capable of performing complex tasks such as image classification and stock market analysis, contain multiple hidden layers in addition to the input and output layer. In the previous article, we concluded that a Perceptron is capable of finding linear decision boundary. We used perceptron to predict whether a person is diabetic or not using a toy dataset.

However, a perceptron is not capable of finding non-linear decision boundaries. In this article, we will build upon the concepts that we studied in Part 1 of this series and will develop a neural network with one input layer, one hidden layer, and one output layer. We will see that the neural network that we will develop will be capable of finding non-linear boundaries. For this article, we need a non-linearly separable data. In other words, we need a dataset that cannot be classified using a straight line.

Luckily, Python's Scikit Learn library comes with a variety of tools that can be used to automatically generate different types of datasets. Execute the following script to generate the dataset that we are going to use, in order to train and test our neural network. In the script above we import the datasets class from the sklearn library. The method returns a dataset, which when plotted contains two interleaving half circles, as shown in the figure below:. You can clearly see that this data cannot be separated by a single straight line, hence the perceptron cannot be used to correctly classify this data.

Let's verify this concept. To do so, we'll use a simple perceptron with one input layer and one output layer the one we created in the last article and try to classify our "moons" dataset. Execute the following script:. You will see that the value of mean squared error will not converge beyond 4. This indicates to us that we can't possibly correctly classify all points of the dataset using this perceptron, no matter what we do.

In this section, we will create a neural network with one input layer, one hidden layer, and one output layer. The architecture of our neural network will look like this:. In the figure above, we have a neural network with 2 inputs, one hidden layer, and one output layer. The hidden layer has 4 nodes. The output layer has 1 node since we are solving a binary classification problem, where there can be only two possible outputs.

This neural network architecture is capable of finding non-linear boundaries. No matter how many nodes and hidden layers are there in the neural network, the basic working principle remains the same. You start with the feed-forward phase where inputs from the previous layer are multiplied with the corresponding weights and are passed through the activation function to get the final value for the corresponding node in the next layer.

This process is repeated for all the hidden layers until the output is calculated. In the back-propagation phase, the predicted output is compared with the actual output and the cost of error is calculated. The purpose is to minimize the cost function. This is pretty straight-forward if there is no hidden layer involved as we saw in the previous article.

However, if one or more hidden layers are involved, the process becomes a bit more complex because the error has to be propagated back to more than one layer since weights in all the layers are contributing towards the final output. In this article, we will see how to perform feed-forward and back-propagation steps for the neural network having one or more hidden layers. For each record, we have two features "x1" and "x2".

Creating a Neural Network from Scratch in Python: Adding Hidden Layers

To calculate the values for each node in the hidden layer, we have to multiply the input with the corresponding weights of the node for which we are calculating the value. We then pass the dot product through an activation function to get the final value. For instance to calculate the final value for the first node in the hidden layer, which is denoted by "ah1", you need to perform the following calculation:. This is the resulting value for the top-most node in the hidden layer. In the same way, you can calculate the values for the 2nd, 3rd, and 4th nodes of the hidden layer.

Similarly, to calculate the value for the output layer, the values in the hidden layer nodes are treated as inputs. Therefore, to calculate the output, multiply the values of the hidden layer nodes with their corresponding weights and pass the result through an activation function. Here "a0" is the final output of our neural network.

Remember that the activation function that we are using is the sigmoid function, as we did in the previous article. Note: For the sake of simplicity, we did not add a bias term to each weight. You will see that the neural network with hidden layer will perform better than the perceptron, even without the bias term. The feed forward step is relatively straight-forward. However, the back-propagation is not as straight-forward as it was in Part 1 of this series.

In the back-propagation phase, we will first define our loss function.

Unveiling the Hidden Layers of Deep Learning

We will be using the mean squared error cost function. It can be represented mathematically as:. In the first phase of back propagation, we need to update weights of the output layer i. So for the time being, just consider that our neural network has the following part:. This looks similar to the perceptron that we developed in the last article. The purpose of the first phase of back propagation is to update weights w9, w10, w11, and w12 in such a way that the final error is minimized. This is an optimization problem where we have to find the function minima for our cost function.

To find the minima of a function, we can use the gradient decent algorithm. The gradient decent algorithm can be mathematically represented as follows:. The details regarding how gradient decent function minimizes the cost have already been discussed in the previous article.

Here we will jus see the mathematical operations that we need to perform. In our neural network, the predicted output is represented by "ao".

Which means that we have to basically minimize this function:. From the previous article, we know that to minimize the cost function, we have to update weight values such that the cost decreases. To do so, we need to take derivative of the cost function with respect to each weight.

Since in this phase, we are dealing with weights of the output layer, we need to differentiate cost function with respect to w9, w10, w11, and w2. The differentiation of the cost function with respect to weights in the output layer can be mathematically represented as follows using the chain rule of differentiation. Here "wo" refers to the weights in the output layer. The letter "d" at the start of each term refers to derivative.

Here 2 and n are constant. If we ignore them, we have the following equation. Finally, we need to find "dzo" with respect to "dwo". The derivative is simply the inputs coming from the hidden layer as shown below:. Here "ah" refers to the 4 inputs from the hidden layers. Equation 1 can be used to find the updated weight values for the weights for the output layer.