NEURAL NET ALGORITHM UPDATE THE WEIGHTS

It comes with a simple example problem, and I include several results that you can compare with those that you find.I tried to make the design as straightforward as possible. This tutorial will tell you step by step how to implement a very basic neural network. It is not an explanation of how or why neural nets work, or when they should or should not be used. You can build one of these deep.This tutorial is an implementation guide. Neural networks are a biologically-inspired algorithm that attempt to mimic the functions of neurons in the brain. However, this approach is terrible for the poor implementer, neglecting many of the details that concern him or her.In 1: link.

This too can easily be addressed once a working neural net is in place against which you can verify correctness and measure performance improvements.The brief introduction below is a very superficial explanation of a neural net it is included mostly to establish terminology and help you map it to the concepts that are explained in more detail in other texts. Those are, in a sense, easy to add once you have a working neural net against which you can benchmark more elaborate designs.To keep the implementation simple, I did not bother with optimisation. There are no hidden layers (I will treat that in an upcoming tutorial), no momentum, no adaptive learning rates, and no sophisticated stopping conditions.

A neural net (one without any hidden layers) is parameterised by a weight matrix. A neural net is one possibility вЂ“ there are also others. So instead, we have to do with some approximation. Of course, we want a program for this.Now in heaven, there is a function for exactly that task вЂ“ we give the function the features, and it spits out the class.Down here on earth, we are not so lucky (well, not for most problems anyway). For example, if we are dealing with fruit, knowing the size, colour, and вЂњroughnessвЂќ of the skin, we might deduce which type the fruit is.

We use some of the known samples for this.Behind the scenes, the weight matrix and the feature vector are combined using some matrix operations to give the output vector, which is converted to a class. But not directly вЂ“ we have to use some kind of iterative scheme вЂ“ we have to вЂњtrainвЂќ our neural net. To solve our problem, we need to find a suitable matrix.If both our set of known samples and the problem itself are reasonable, we might expect to find such a matrix.

Neural Net Algorithm Update The Weights

The training set is used to update the weights iteratively the validation set is used to stop the training algorithm, and the test set is used to estimate how well our trained neural net will do in the wild.Each iteration of the training algorithm is called, quite poetically, an epoch. The training program is the difficult part most of the tutorial deals with training.It is common to divide the known samples in three sets, called the training set, validation set, and test set, typically divided in the ratio 50%, 25%, and 25%. Generally, the training and application programs are separate.

For instance, when dealing with colours, we might want to use RGB values, or we might want to make a list of colours (red, yellow, green, etc.), assign a number to each of these labels, and use the corresponding number.Classes, usually not being numbers, are similarly treated: we assign a number (often arbitrarily) to each class, and use that in our computations. RepresentationWe usually represent the features (our measurements) as a vector of numbers, like this:In cases of non-numeric values, we convert whatever we have to numbers with some scheme. In general, higher learning rate means faster learning (although, when it is set too high, the network might become unstable and not learn at all).

MatrixThe basic idea of the training algorithm is the following:First we load in the data: the training samples, the validation samples, and the test samples.Then we start to train: we run the backpropagation algorithm on random samples. The numbers are given in terms of the number of inputs (features) of the problem, the number of outputs. The following table will give dimensions of all the matrixes involved this will be helpful during implementation (especially for assert statements). This avoids many of the errors that can creep in loop-dense code. Similarly, outputs and classes are also put into matrices, with input sample in a row (say row number n) corresponds to output sample in row n, and also the class in row n.The implementation below makes use of high-level matrix operations. The output vector has a 1 in the position of the class number, and 0 everywhere else.Thus, if we are dealing with three classes of fruit (apple, pear, banana), and number the classes 1, 2, and 3 respectively, we will have the following output vectors: ClassIt is convenient to put all the inputs of a set together in a single matrix, where each row is a sample.

Hadamard multiplication (component-wise multiplication) Since neural nets do not require matrix inverses or long chains of matrix products, you need not worry (much) about numerical stability, thus the implementation is straightforward.The implementation needs to support the following matrix operations: A library that plots graphs (x versus y).If you canвЂ™t find a matrix library for your implementation language, then you can write a simple library yourself. A library that supports matrix algebra and Gather the necessary libraries (or write them)

For example, the matrices A and B below will be concatenated to form the new matrix C:A=eginA simple implementation simply constructs a new matrix whose components are given by if j < X_widthIf no graph libraries are available, simply write a function that will output a tab-separated list of the input and output sequences to plot. Each component of the new matrix is the product of corresponding components in the two multiplicands, that is: Z = X * YThe Kronecker product of a row vector and column vector is defined as a matrix whose components are given by: Z = X * YIt is possible to define the product for arbitrary matrices, but we donвЂ™t need it.The horizontal concatenation combines two matrices with the same number of rows. (Also check out the Wikipedia article on matrix multiplication вЂ“ it covers all the types of multiplication mentioned here.)Hadamard multiplication of matrices is defined for two matrices of equal dimensions.

Implement Output and Class conversion functionsThis is very simple: implement a function that converts an output matrix to a class number vector, and another that converts a class number to an output vector.