Ranga Rodrigo February 8, 2014

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Presentation transcript:

Ranga Rodrigo February 8, 2014 The Artificial Neuron Ranga Rodrigo February 8, 2014

Introduction The basic building block of a artificial neural network is the artificial neuron. The neuron sums the weighted inputs. If this sum exceeds a threshold value, the neuron fires and a signal is transmitted via the axon to other neurons. In this lecture, we learn about the artificial neuron.

Artificial Neuron x1 x2 x3 xD f a y w1 w2 w3 wD  w0 x0 = 1 Activation function

Activation Functions f

Perceptron Perception is a single-layer NN with a step activation function. The perceptron, due to its activation function, takes only two different output values, so it may classify signals applied at its input in the form of vectors to one of two classes.

Question Sketch the perceptron for a two-dimensional (2-D) data of the form . How many weight parameters are there to be learned in this case?

Learning Learning means adjusting the weights. We adjust the weights by presenting a set of input vectors with known desired (target) values. If the desired value and the out output of the NN are different, there is an error. We present these vectors one at a time. We may adjust the weights, if the output of the NN differs from the desired. We repeat the process until the sum of errors becomes smaller than a threshold.

Objective Function (Error) Here we consider sum of squared errors as the objective function and an identity activation func. Given a training set comprising a set of input vectors where together with a corresponding set of target vectors , we minimize the error function True value for the nth input vector Output of the NN for nth input vector

dth component of the nth input vector identity activation func

Output of the NN for nth input vector

Gradient Descent Rule Given a single training pattern, weights are updated using Widrow-Hoff Learning Rule

Homework Plot the activation functions as shown in slide 4. Slide 12 shows the perceptron algorithm. What are the expression that fill the blanks in this flow chart? Write the perceptron algorithm as shown in slide 12.