In this problem, we will train a Multi-class perceptron on data of the form (f(X)∈R²,Y∈{A,B,C}). In particular, we will use training data to update three weight vectors, Wy ∈R² ,y=A,B,C.
We begin with the following set of randomly-initialized weight vectors:

y Wy,1 Wy,2
A -0.82 -0.02
B -1.63 -0.88
C 0.39 0.65

Note: For a multi-class perceptron, the label, Y, is chosen for a data point, X, as Y=argmaxyWy ⋅f(X)
When training a perceptron, if the label chosen by the perceptron matches the label provided with the training data, the weights do not change.
However, if the label differs, say the perceptron classified the data point as Y, but it should have been some other label, Y∗ , then the weights must be updated. This update is performed as:
Wy =Wy −f(X)
and
Wy∗=Wy∗ +f(X)

We will now incorporate the training data point f(X)=(−1.06,0.95);Y=C. What are the resulting weight-feature dot products?
a. WA ⋅f(X)
b. WB ⋅f(X)
c. WC ⋅f(X)

Q&A Education