How to calculate VC-dimension?
I am learning the VC dimension. How do I calculate the H in the VC dimension?
Let the domain set be $X = R2$, the label set be $Y = {0, 1}$ and the hypothesis class be $H = {h(a,b,c,d): a, b, c, d \in R}$, where for $(x, y) \in R2$ we have:
$h(a,b,c,d)(x, y) =$ \begin{cases} 1 \text{if $x \ge a$ and $y \ge b$} \\ \text{or $x \ge c$ and $y \ge d$} \\ 0 \text{otherwise} \end{cases}
Work out the VC-dimension of H.
Topic vc-theory machine-learning
Category Data Science