Suppose a given set of input data specified as SET I$\{$Xi$\}$ is used to train the net of

Fig. C and it consists of four sets of input data $\{$x$1,$ x$2\}$ as follows:

$\{$x$1=+1\mathrm{.}10$; x$2=0\mathrm{.}98\}$;

$\{$x$1=+0\mathrm{.}92$; x$2=1\mathrm{.}08\}$;

$\{$x$1=+1\mathrm{.}21$; x$2=1\mathrm{.}20\}$;

$\{$x$1=+0\mathrm{.}85$; x$2=0\mathrm{.}82\}$

$5$

Further, assume the following:

Assume: $2$ input neurons, $2$ hidden neurons, bias b $=0$ and Oi $=$f$($Zi$)=$ tanh$($Zi$).$

Teacher value $=0\mathrm{.}5$

Scaling constant: K $=1$

Sigmoid: tanh$(.)$

Error: $|$Ti $$ Oi$|$

Learning coefficient, $$: $0\mathrm{.}001$

Learning rule: Perceptron rule New wij $=$ Old wij $+(\backslash$times Error$)\backslash$times xi

Stop criterion on error $<=0\mathrm{.}01$ towards terminating iteration in backpropagation

Bias value, b $=0$

Statement of the Problem

The net of Fig. C is first trained with the given $4$ data sets of $\{$x$1,$ x$2\}$ specified as: SET I$$

$\{$Xi$\}$; and, after the net is trained to convergence, suppose a new input data set: SET II$$

$\{$Xi$\}$ is supplied.

SET II$\{$Xi: a$,$ b$,$ c$\}$ as follows:

$($a$)\{$x$1=+1\mathrm{.}50$; x$2=1\mathrm{.}08\}$

$($b$)\{$x$1=+0\mathrm{.}98$; x$2=1\mathrm{.}39\}$

$($c$)\{$x$1=+1\mathrm{.}35$; x$2=0\mathrm{.}01\}$

$($d$)\{$x$1=+0\mathrm{.}95$; x$2=1\mathrm{.}56\}$

The required exercise is that the net should classify whether the given new set SET II$$

$\{$Xi$\}$belong to SET I $($or it is an outlier of the SET I$).$

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