Question $1(3$ points$)$

LVQ is used to classify $4$ input vectors $xk$ and their respective classes $Tk$ for $k=1$ to

$4$ into $2$ classes such that $T1=T2=C1=1$ and $T3=T4=C2=2.$ Let the $2$ initial weights

for classes $C1$ and $C2$ be selected as $W1=x2$ and $W2=x3.$ Assuming that $($i$)$ all the $4$

input vectors are to be presented orderly as $x1,x2,x3,$ and $x4$ in each iteration, $($ii$)$

an immediate update is applied to each weight vector within each iteration, and $($iii$)$

updates are carried out in all the weight vectors with equal minimum distances

from an input vector.

Given the initial gain value $g(1)$ is $0\mathrm{.}9$ and $g(t+1)=\{v\}g(t)$ for $t1,$ show the step$-$

by$-$step calculation for the value of the sum of all the differences between elements

obtained by subtracting W$2$ from W$1$ as $($W$1-$ W$2)$ at the end of the first iteration

$($using g$(1))$ in the Answer Book and submit Your Answer rounded to $2$ decimal places

to the rectangular box below for grading. Given

$0$ X$4=\left[\begin{array}{ccc}1& 0& 0\end{array}\right].$

Your Answer:

Answer

D Add attachments to support your workQuestion $1(3$ points$)$

Given a $2-$input $1-$output RBF network with two RBF centers at T$1=[0,0]$ and T$2=$

$1,0$ with two weights $w1$ and $w2,$ and one bias $w0,$ four input vectors $x1=[0,0],$

$x2=[0,0\mathrm{.}6],x3=[1,0],x4=[1,0\mathrm{.}6]$ with the corresponding desired output vector $D=$

$1,0,0,0,$ and the Gaussian function consisting of the squared I$2-$norm operator is

used as the radial basis function.

Show the step$-$by$-$step calculation to obtain the combined weights $[$w$0,$w$1,$w$2]$ to

recall the four corresponding outputs $Y1,Y2,Y3,Y4$ and submit the sum of the $3$

weight values as Your Answer by typing its numerical value $($rounded to $4$ decimal

places$)$ into the Answer Box below. Hint: A minimum resolution of $6$ decimal places

for step$-$by$-$step calculation is required.

Your Answer:

Answer

D Add attachments to support your work