How the Kernel Perceptron Algorithm Works: Initalization

$1$ point possible $($graded$)$

Recall that the original Perceptron Algorithm is given as the following:

Perceptron

$$initialize $($vector$)$;

$$for $,$

$$for $,$

$$if $,$

$$then update

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

where values of may vary at each step of the algorithm. In other words, we can reformulate the algorithm so that we somehow initialize and update $\text{'}$s$,$ instead of $.$

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

Kernel Perceptron

$$Initialize to some values;

$$for

$$for

$$if

$$Update appropriately

Look at the initialization statement of the algorithm. Which of the following is an equivalent way to initialize $,$ if we want the same result as initializing $?$