Perceptron $(\{(x^{(i)},y^{(i)}),i=1,$dots,$n\},T)$:

initialize $=0(vector)$;

for $t=1,$dots,$T$

for $i=1,$dots,$n$

$if{y}^{(i)}(*x^{(i)})0$

then update $=+y^{(i)}{x}^{(i)}$

In the lecture, it was introduced that we can always express $$ as

$={\displaystyle \underset{j=1}{\overset{n}{}}}{}_j{y}^{(j)}(x^{(j)})$

where values of ${}_1,$dots,${}_n$ may vary at each step of the algorithm. In other words,

we can reformulate the algorithm so that we somehow initialize and update ${}_j\text{'}$s$,$

instead of $.$

The reformulated algorithm, or kernel perceptron, can be given in the following

form:

Look at the initialization statement of the algorithm. Which of the following is an

equivalent way to initialize ${}_1,{}_2,$dots,${}_n,$ if we want the same result as initializing

$=0?$

${}_1=$dots$={}_n=$

${}_1=$dots$={}_n=1$

${}_1=$dots$={}_n=0$

${}_1=$dots$={}_n=-1$