In this problem, we will train a Multi$-$class perceptron on data of the form $($f$($X$)$ in R$2,$Y in $\{$A$,$B$,$C$\}).$ In particular, we will use training data to update three weight vectors, Wy in R$2,$y$=$A$,$B$,$C$.$

We begin with the following set of randomly$-$initialized weight vectors:

yWy$,1$Wy$,2$A$-0\mathrm{.}82-0\mathrm{.}02$B$-1\mathrm{.}63-0\mathrm{.}88$C$0\mathrm{.}390\mathrm{.}65$

Q$1\mathrm{.}1)$ We will now incorporate the training data point f$($X$)=(1\mathrm{.}06,0\mathrm{.}95)$;Y$=$C$.$ First fill in the resulting weight$-$feature dot products.

WA$$f$($X$)$:

WB$$f$($X$)$:

WC$$f$($X$)$:

Q$1\mathrm{.}2)$Now update the weight values as necessary for the training point from part $1.$

Note: For all of these questions, if a weight vector doesn't get updated, make sure to still write its value in the blank provided.

new WA$,1$:

new$$WA$,2$:

new$$WB$,1$:

new$$WB$,2$:

new$$WC$,1$:

new$$WC$,2$:

Q$1\mathrm{.}3)$We will now incorporate the training data point f$($X$)=(0\mathrm{.}09,1\mathrm{.}48)$;Y$=$A$$Fill in the resulting weight$-$feature dot product, and update the weight values as necessary.

WA$$f$($X$)=$

WB$$f$($X$)=$

WC$$f$($X$)=$

Q$1\mathrm{.}4)$

new WA$,1$:

new$$WA$,2$:

new$$WB$,1$:

new$$WB$,2$:

new$$WC$,1$:

new$$WC$,2$:

$$