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Neural Networks Neural Networks • Applications for neural networks – Speech recognition – Shape recognition – Financial prediction – The list goes on.. • The Idea behind neural networks is to make computer recognize patterns the way brain does it Touko Hallasmaa Perceptron • Perceptron takes several binary input and outputs a single binary output • Weight(w) represents the importance of its input to the output – Weights are real numbers • The perceptrons output(1 or 0) is determined by whether the weighted sum is less or greater than the threshold value. x 1 x 2 w1 w2 Σ wn Compare x n Output= { 0, 1, 𝑛 𝑖=0 𝑤𝑖𝑥𝑖 ≤ threshold 𝑛 𝑖=0 𝑤𝑖𝑥𝑖 > threshold Output – Threshold is a real number Touko Hallasmaa Perceptrons In Neural Networks • Neural networks can have several perceptrons • Output of one perceptron can be used as a input of another percepton • Output = 𝑛𝑖=0 𝑤𝑖𝑥𝑖 can be written as Output = w ◦ x (dot product) – In the dot product, W and X are vectors of weights and inputs • Perceptrons can be used to compute any logical function(laskentaoperaatiot) Touko Hallasmaa Sigmoid Neurons • It’s hard to make accurate learning neural network only with perceptrons. – For example, if we wanted to make change(determined by the output) to a weight of perceptron it might cause the output of that perceptron to completely change, which may cause the behaviour of the rest of the network to completely change. • The sigmoid neurons are similiar to perceptrons but their inputs can take any value between 0 and 1 and the output is provided by the sigmoid function σ(w ◦ x - b) – b is the bias ( complement of thershold ) – σ( x ) = 1 1+𝑒^(−𝑥) – The behaviour of sigmoid neurons is similiar to perceptons when x is very large or very small Sigmoid funtion Touko Hallasmaa Sigmoid Neurons • The shape of the sigmoid function makes learning neural networks possible – Therefore other functions may be used in neurons but the sigmoid function is most commonly used because it’s easy to work with(differientals) • As we stated before, with perceptons if we make even a small change to the weight of perceptron it might cause the output of that perceptron to completely flip but that’s not the case with sigmoid neurons(small change in the weight of the neuron will cause only small change in the output) Touko Hallasmaa Neural Networks - structure • Neural networks can be visualized as layers of neurons – First layer consists of inputs – The last layer is the output layer – Every neuron that’s not in the input nor in the output layer is in some hidden layer • For example in shape recognition application we could have a input neuron for every pixel of the pre-processed image (256x256 image would therefore have 65536 input neurons) • There may also be loops, neural networks which have loops are called recurrent(jatkuva) or feedback networks. If a network doesn’t have any loop it’s called feedforward neural network Touko Hallasmaa Neural Networks – Learning • Associative mapping - network learn to produce a pattern on the set of input units providing that another particular pattern is applied on the set of input units – Auto-association: can produce a pattern whenever a portion or distorted partion of it is presented. – Hetero-association - related to two recall mechanisms • Nearest-neightbour: stored pattern closest to the input pattern is recalled • Interpolative recall: the recalled pattern is a combination of outputs corresponding to the input training patterns nearest to the given input test pattern(input interpolation) • Regularity detection – units learn to respond to particular properties of the input patterns(whereas in associative mapping the network stores the relationship among patterns) performance x 1 x 2 X 0 w1 w2 Σ wn x n Touko Hallasmaa Neural Networks - Learning • Two categories of neural networks: – Fixed: weights cannot be changed(are fixed according to the problem) – Adaptive: weights can be changed • Learning can either be: – Supervised: each output unit is told what its desired response to input signals is supposed to be – Unsupervised: based only on local information Touko Hallasmaa Classification With Neural Networks • Classification systems make decisions – Decision are not pre-programmed – Rules are derived from data • Classification will use features of the object to be classified. Such features may include: – Size(Length, width, height), color, pattern, shape • Features usually objects contain lots of irrelevant data – Feature extraction has to be made(We need a preprocessor) – We will treat features as numeric values • When teaching the classifier we have to give the classifier the class of the object along with the feature data, whereas the test data is given without a class Touko Hallasmaa