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

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