Softmax Regression Classification Algorithm

Question

I'm following the Stanford Machine Learning course while simultaneously developing my Mathematica abilities. I'm having issues with my Softmax Classifier implementation (for ref, have a look at these notes, the last four pages).

Using my own dataset, when performing softmax classification on it, I get the following plot.

As seen, I believe the hand-drawn red lines is a better fit, so how come the algorithm doesn't converge to that? I have gone over my code several times, but I can't find what I am doing wrong.

I define the hypothesis function

Hyp[x_, θ_, l_] := Exp[θ[[l]].x] / Sum[Exp[θ[[j]].x], {j, 1, Length[θ]}]

and the log likelihood function

l[θ_] := 
   Sum[Log[Product[Hyp[multiX[[i]], θ, l]^Boole[multiY[[i]] == l], 
   {l, Length[Tally[multiY]]}]], {i, Length[multiX]}]

where multiX and multiY constitute my data in the format

multiX = {{10.5, 3}, {11, 5}, ...}
multiY = {1, 3, ...}

with labels 1 through 3.

I then define the Hessian matrix and the first derivate, such that I can perform Newton's Method

$$\theta:=\theta - H^{-1}\nabla_{\theta}l(\theta)$$

(* Hessian *)
Hessian[θ_] := 
 Partition[
  Derivative[##][l]@θ & /@ 
   Partition[
    Partition[
     Flatten[(Table[#, {6}] + IdentityMatrix[6] & /@ 
        IdentityMatrix[6])], 2], 3], 6]

(* First Order Derivative *)
d[θ_] := 
 Derivative[##][l]@θ & /@ Partition[Partition[Flatten[IdentityMatrix[6]], 2], 3]

followed by the update rule

Step[θ_] := Partition[(Flatten[θ] - PseudoInverse[Hessian[θ]].d[θ]), 2]

Lastly, to obtain the optimal parameters, I step through the function

optimal = Nest[Step, {{1, 1}, {1, 1}, {1, 1}}, 100]

whose parameters I use for the hypothesis function, when I subsequently plot it.

Any clue as to why I don't get the optimal fit? I looked into this duplicate, but I couldn't make sense of it.

The data I used is the following:

multiX = {{10.5, 3}, {11, 5}, {8.4, 1}, {7.9, 3}, {9.1, 4}, {9.8, 2}, {8.7, 4.5}, {9.5, 8}, {10.5, 6}, {13.3, 11.2}, {12.7, 9.5}, {11.51, 6.8}, {12, 3.2}, {11.31, 3.24}, {14, 2.1}, {12.51, 4.41}, {13.6, 6.4}}
multiY = {1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3}