1. The output of a single neuron is given by y = f(w_{1}x_{1} +w_{2}x_{2} +w_{0}x_{0}), where x_{1} and x_{2} are inputs, x_{0 }has the constant value 1, w_{0}, w_{1} and w_{2} are parameters (weights), and f : R ! R is a function. Suggest a function f typically used in this context. Explain how this neuron could be used to classify inputs (x_{1}; x_{2}) into one of two classes. The input data consists of 8 points:
(1:4; 5) (2:3; 9) (9:6; 9) (0:3; 1) (a_{0}; a_{1}) (a_{2}; a_{3}) (a_{4}; a_{5}) (a_{6}; a_{7})
where a_{0} a_{1} a_{2} a_{3} a_{4 }a_{5} a_{6} a_{7} is your student enrolment number. Assign these data points to classes, in such a way that the classification could be learnt by a single neuron. Suggest values for w_{0}, w_{1} and w_{2} that would achieve a correct classification, for your choice of function f. Draw a plot of the data points and the boundary line between the classes.
Explain in full detail how the weights of the single neuron in question 1 could be automatically adjusted using gradient descent i.e. how it could be trained to correctly distinguish the classes. Assume f to be the logistic function, and demonstrate why this choice simplifies the numerical calculation of the value of f'.