Distance between finite sets of points
Clash Royale CLAN TAG#URR8PPP
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Denote the collection of all finite subsets in $mathbbR^d$ as $mathcalS = S subseteq mathbbR^d: $. What are ways to define distance metrics on $mathcalS$ that can be efficiently computed? For instance, one could define
$$
d(A, B) = frac1 sum_xin Asum_yin B |x - y|_2^2
$$
but I'm not sure if the triangle inequality is satisfied?
metric-spaces
asked Aug 9 at 21:47
p-value
19910
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up vote
1
down vote
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Denote the collection of all finite subsets in $mathbbR^d$ as $mathcalS = S subseteq mathbbR^d: $. What are ways to define distance metrics on $mathcalS$ that can be efficiently computed? For instance, one could define
$$
d(A, B) = frac1 sum_xin Asum_yin B |x - y|_2^2
$$
but I'm not sure if the triangle inequality is satisfied?
metric-spaces
asked Aug 9 at 21:47
p-value
19910
Could you be precise about what you mean by a distance metric?
– Matt
Aug 9 at 21:54
@Matt: I mean a metric that satisfies the requirements: en.wikipedia.org/wiki/Metric_(mathematics)
– p-value
Aug 9 at 21:59
Could you use the discrete metric?
– Matt
Aug 9 at 22:02
@Matt: What to is your definition of the discrete metric?
– p-value
Aug 9 at 22:03
If $x = y$ then $d(x,y) = 0$. Otherwise, $d(x,y) = 1$.
– Matt
Aug 9 at 22:04
 |Â
show 4 more comments
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Denote the collection of all finite subsets in $mathbbR^d$ as $mathcalS = S subseteq mathbbR^d: $. What are ways to define distance metrics on $mathcalS$ that can be efficiently computed? For instance, one could define
$$
d(A, B) = frac1 sum_xin Asum_yin B |x - y|_2^2
$$
but I'm not sure if the triangle inequality is satisfied?
metric-spaces
asked Aug 9 at 21:47
p-value
19910
Denote the collection of all finite subsets in $mathbbR^d$ as $mathcalS = S subseteq mathbbR^d: $. What are ways to define distance metrics on $mathcalS$ that can be efficiently computed? For instance, one could define
$$
d(A, B) = frac1 sum_xin Asum_yin B |x - y|_2^2
$$
but I'm not sure if the triangle inequality is satisfied?
metric-spaces
asked Aug 9 at 21:47
p-value
19910
asked Aug 9 at 21:47
p-value
19910
asked Aug 9 at 21:47
p-value
19910
asked Aug 9 at 21:47
p-value
19910
19910
Could you be precise about what you mean by a distance metric?
– Matt
Aug 9 at 21:54
@Matt: I mean a metric that satisfies the requirements: en.wikipedia.org/wiki/Metric_(mathematics)
– p-value
Aug 9 at 21:59
Could you use the discrete metric?
– Matt
Aug 9 at 22:02
@Matt: What to is your definition of the discrete metric?
– p-value
Aug 9 at 22:03
If $x = y$ then $d(x,y) = 0$. Otherwise, $d(x,y) = 1$.
– Matt
Aug 9 at 22:04
 |Â
show 4 more comments
Could you be precise about what you mean by a distance metric?
– Matt
Aug 9 at 21:54
@Matt: I mean a metric that satisfies the requirements: en.wikipedia.org/wiki/Metric_(mathematics)
– p-value
Aug 9 at 21:59
Could you use the discrete metric?
– Matt
Aug 9 at 22:02
@Matt: What to is your definition of the discrete metric?
– p-value
Aug 9 at 22:03
If $x = y$ then $d(x,y) = 0$. Otherwise, $d(x,y) = 1$.
– Matt
Aug 9 at 22:04
Could you be precise about what you mean by a distance metric?
– Matt
Aug 9 at 21:54
Could you be precise about what you mean by a distance metric?
– Matt
Aug 9 at 21:54
@Matt: I mean a metric that satisfies the requirements: en.wikipedia.org/wiki/Metric_(mathematics)
– p-value
Aug 9 at 21:59
@Matt: I mean a metric that satisfies the requirements: en.wikipedia.org/wiki/Metric_(mathematics)
– p-value
Aug 9 at 21:59
Could you use the discrete metric?
– Matt
Aug 9 at 22:02
Could you use the discrete metric?
– Matt
Aug 9 at 22:02
@Matt: What to is your definition of the discrete metric?
– p-value
Aug 9 at 22:03
@Matt: What to is your definition of the discrete metric?
– p-value
Aug 9 at 22:03
If $x = y$ then $d(x,y) = 0$. Otherwise, $d(x,y) = 1$.
– Matt
Aug 9 at 22:04
If $x = y$ then $d(x,y) = 0$. Otherwise, $d(x,y) = 1$.
– Matt
Aug 9 at 22:04
 |Â
show 4 more comments
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Could you be precise about what you mean by a distance metric?
– Matt
Aug 9 at 21:54
@Matt: I mean a metric that satisfies the requirements: en.wikipedia.org/wiki/Metric_(mathematics)
– p-value
Aug 9 at 21:59
Could you use the discrete metric?
– Matt
Aug 9 at 22:02
@Matt: What to is your definition of the discrete metric?
– p-value
Aug 9 at 22:03
If $x = y$ then $d(x,y) = 0$. Otherwise, $d(x,y) = 1$.
– Matt
Aug 9 at 22:04