Suppose we have a origin centered circle, ie $x^2 + y^2 =1$, so it's in $\mathbb{R}^2$ (2D). It will be classified as 1 if it lies only on this arc, and will be labeled 0 otherwise. What is the VC dimension?

I think the answer is 2. Any two points can be shattered $(++, -+, +-, --)$. But if we have three points $\{(x1,y1),..,(x3,y3)\}$ that all have the label 1, with radius $r1 = r2 = 1$, and $r3 = 0$, it is impossible to shatter them. Is my intuition correct?

Or can I construct the sample points to my liking (to get the maximum VC dim) so that only the positive labels will be on the rim (have some combination of $x_i^2 + y_i^2 = 1$), and have 0 labels to not lie on the rim, therefore have infinite VC dimension?

Suppose we have an origin centered circle, ie $x^2 + y^2 =1$, so it's in $\mathbb{R}^2$ (2D). It will be classified as 1 if it lies only on this arc, and will be labeled 0 otherwise. What is the VC dimension?

I think the answer is 2. Any two points can be shattered $(++, -+, +-, --)$. But if we have three points $\{(x_1,y_1),\dots,(x_3,y_3)\}$ that all have the label 1, with radius $r_1 = r_2 = 1$, and $r_3 = 0$, it is impossible to shatter them. Is my intuition correct?

Or can I construct the sample points to my liking (to get the maximum VC dim) so that only the positive labels will be on the rim (have some combination of $x_i^2 + y_i^2 = 1$), and have 0 labels to not lie on the rim, therefore have infinite VC dimension?

Suppose we have a origin centered circle, ie x^2 + y^2 =1, so its in R^2 (2D). It will be classified as 1 if it lies only on this arc, and will be labeled 0 otherwise. What is the VC dimension?

I think the answer is 2. Any two points can be shattered (++, -+, +-, --). But if we have three points {(x1,y1),..,(x3,y3)} that all have the label 1, with radius r1 = r2 = 1, and r3 = 0, it is impossible to shatter them. Is my intuition correct?

Or can I construct the sample points to my liking (to get the maximum VC dim) so that only the positive labels will be on the rim (have some combination of x_i^2 + y_i^2 = 1), and have 0 labels to not lie on the rim, therefore have infinite VC dimension?

Suppose we have a origin centered circle, ie $x^2 + y^2 =1$, so it's in $\mathbb{R}^2$ (2D). It will be classified as 1 if it lies only on this arc, and will be labeled 0 otherwise. What is the VC dimension?

I think the answer is 2. Any two points can be shattered $(++, -+, +-, --)$. But if we have three points $\{(x1,y1),..,(x3,y3)\}$ that all have the label 1, with radius $r1 = r2 = 1$, and $r3 = 0$, it is impossible to shatter them. Is my intuition correct?

Or can I construct the sample points to my liking (to get the maximum VC dim) so that only the positive labels will be on the rim (have some combination of $x_i^2 + y_i^2 = 1$), and have 0 labels to not lie on the rim, therefore have infinite VC dimension?