Mixing
What is this data structure/concept where a plot of points defines a partition to a space
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I encountered an algorithm to solve a real world problem, and I remember a class I took where I made something very similar for some for a homework problem. 
Basically it's a plot of points, and the lines are drawn to be equidistant between two points. It forms a perfect partition where the lines around the point form the shape of area that is closest to that point. Does this ring a bell to anyone? I've had a tough time googling descriptions and getting results. And I don't know how else to describe it. Hopefully the picture helps.
algorithms data-structures terminology computational-geometry
edited Jan 22 at 14:14
Apass.Jack
12.4k1939
asked Jan 22 at 5:40
BrianBrian
763
$endgroup$
add a comment |
$begingroup$
I encountered an algorithm to solve a real world problem, and I remember a class I took where I made something very similar for some for a homework problem.
Basically it's a plot of points, and the lines are drawn to be equidistant between two points. It forms a perfect partition where the lines around the point form the shape of area that is closest to that point. Does this ring a bell to anyone? I've had a tough time googling descriptions and getting results. And I don't know how else to describe it. Hopefully the picture helps.
algorithms data-structures terminology computational-geometry
edited Jan 22 at 14:14
Apass.Jack
12.4k1939
asked Jan 22 at 5:40
BrianBrian
763
$endgroup$
$begingroup$
Viewed 1667 times since yesterday? Is SE being hacked?
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– HEKTO
Jan 23 at 18:35
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@HEKTO it was displayed as one of the "Hot Network Questions".
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– Apass.Jack
Jan 25 at 0:53
add a comment |
$begingroup$
I encountered an algorithm to solve a real world problem, and I remember a class I took where I made something very similar for some for a homework problem.
Basically it's a plot of points, and the lines are drawn to be equidistant between two points. It forms a perfect partition where the lines around the point form the shape of area that is closest to that point. Does this ring a bell to anyone? I've had a tough time googling descriptions and getting results. And I don't know how else to describe it. Hopefully the picture helps.
algorithms data-structures terminology computational-geometry
edited Jan 22 at 14:14
Apass.Jack
12.4k1939
asked Jan 22 at 5:40
BrianBrian
763
$endgroup$
I encountered an algorithm to solve a real world problem, and I remember a class I took where I made something very similar for some for a homework problem.
Basically it's a plot of points, and the lines are drawn to be equidistant between two points. It forms a perfect partition where the lines around the point form the shape of area that is closest to that point. Does this ring a bell to anyone? I've had a tough time googling descriptions and getting results. And I don't know how else to describe it. Hopefully the picture helps.
algorithms data-structures terminology computational-geometry
algorithms data-structures terminology computational-geometry
edited Jan 22 at 14:14
Apass.Jack
12.4k1939
asked Jan 22 at 5:40
BrianBrian
763
edited Jan 22 at 14:14
Apass.Jack
12.4k1939
asked Jan 22 at 5:40
BrianBrian
763
edited Jan 22 at 14:14
Apass.Jack
12.4k1939
edited Jan 22 at 14:14
Apass.Jack
12.4k1939
edited Jan 22 at 14:14
Apass.Jack
12.4k1939
12.4k1939
asked Jan 22 at 5:40
BrianBrian
763
asked Jan 22 at 5:40
BrianBrian
763
asked Jan 22 at 5:40
BrianBrian
763
763
$begingroup$
Viewed 1667 times since yesterday? Is SE being hacked?
$endgroup$
– HEKTO
Jan 23 at 18:35
$begingroup$
@HEKTO it was displayed as one of the "Hot Network Questions".
$endgroup$
– Apass.Jack
Jan 25 at 0:53
add a comment |
$begingroup$
Viewed 1667 times since yesterday? Is SE being hacked?
$endgroup$
– HEKTO
Jan 23 at 18:35
$begingroup$
@HEKTO it was displayed as one of the "Hot Network Questions".
$endgroup$
– Apass.Jack
Jan 25 at 0:53
$begingroup$
Viewed 1667 times since yesterday? Is SE being hacked?
$endgroup$
– HEKTO
Jan 23 at 18:35
$begingroup$
Viewed 1667 times since yesterday? Is SE being hacked?
$endgroup$
– HEKTO
Jan 23 at 18:35
$begingroup$
@HEKTO it was displayed as one of the "Hot Network Questions".
$endgroup$
– Apass.Jack
Jan 25 at 0:53
$begingroup$
@HEKTO it was displayed as one of the "Hot Network Questions".
$endgroup$
– Apass.Jack
Jan 25 at 0:53
add a comment |
2 Answers
2
active
oldest
votes
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What you described is Voronoi diagram.
Here is an excerpt from Wikipedia.
In the simplest case, shown in the first picture, we are given a finite set of points ${p_1, cdots, p_n}$ in the Euclidean plane. In this case each site $p_k$ is simply a point, and its corresponding Voronoi cell $R_k$ consists of every point in the Euclidean plane whose distance to $p_k$ is less than or equal to its distance to any other points. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The line segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites.
answered Jan 22 at 6:38
Apass.JackApass.Jack
12.4k1939
$endgroup$
4
$begingroup$
+1. I refrained from mentioning them and went for implementations because I remember my professors mentioning them with a footnote that Voronoi Diagrams are computationally quite complex to implement in higher dimensions. So simple kNN implementations get the job done much better. However the condition that "lines are drawn to be equidistant between two points" may not be fulfilled.
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– Sagnik
Jan 22 at 6:48
add a comment |
$begingroup$
You are looking for a Multi-Class Classification Algorithm. I suggest you have a look at:
- K-Nearest Neighbors algorithm (or KNN). Here is an introductory blog post.
- Support Vector Machines. You can start reading up on it here.
answered Jan 22 at 5:52
SagnikSagnik
669519
$endgroup$
add a comment |
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2 Answers
2
active
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2 Answers
2
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
What you described is Voronoi diagram.
Here is an excerpt from Wikipedia.
In the simplest case, shown in the first picture, we are given a finite set of points ${p_1, cdots, p_n}$ in the Euclidean plane. In this case each site $p_k$ is simply a point, and its corresponding Voronoi cell $R_k$ consists of every point in the Euclidean plane whose distance to $p_k$ is less than or equal to its distance to any other points. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The line segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites.
answered Jan 22 at 6:38
Apass.JackApass.Jack
12.4k1939
$endgroup$
4
$begingroup$
+1. I refrained from mentioning them and went for implementations because I remember my professors mentioning them with a footnote that Voronoi Diagrams are computationally quite complex to implement in higher dimensions. So simple kNN implementations get the job done much better. However the condition that "lines are drawn to be equidistant between two points" may not be fulfilled.
$endgroup$
– Sagnik
Jan 22 at 6:48
add a comment |
$begingroup$
What you described is Voronoi diagram.
Here is an excerpt from Wikipedia.
In the simplest case, shown in the first picture, we are given a finite set of points ${p_1, cdots, p_n}$ in the Euclidean plane. In this case each site $p_k$ is simply a point, and its corresponding Voronoi cell $R_k$ consists of every point in the Euclidean plane whose distance to $p_k$ is less than or equal to its distance to any other points. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The line segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites.
answered Jan 22 at 6:38
Apass.JackApass.Jack
12.4k1939
$endgroup$
4
$begingroup$
+1. I refrained from mentioning them and went for implementations because I remember my professors mentioning them with a footnote that Voronoi Diagrams are computationally quite complex to implement in higher dimensions. So simple kNN implementations get the job done much better. However the condition that "lines are drawn to be equidistant between two points" may not be fulfilled.
$endgroup$
– Sagnik
Jan 22 at 6:48
add a comment |
$begingroup$
What you described is Voronoi diagram.
Here is an excerpt from Wikipedia.
In the simplest case, shown in the first picture, we are given a finite set of points ${p_1, cdots, p_n}$ in the Euclidean plane. In this case each site $p_k$ is simply a point, and its corresponding Voronoi cell $R_k$ consists of every point in the Euclidean plane whose distance to $p_k$ is less than or equal to its distance to any other points. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The line segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites.
answered Jan 22 at 6:38
Apass.JackApass.Jack
12.4k1939
$endgroup$
What you described is Voronoi diagram.
Here is an excerpt from Wikipedia.
In the simplest case, shown in the first picture, we are given a finite set of points ${p_1, cdots, p_n}$ in the Euclidean plane. In this case each site $p_k$ is simply a point, and its corresponding Voronoi cell $R_k$ consists of every point in the Euclidean plane whose distance to $p_k$ is less than or equal to its distance to any other points. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The line segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites.
answered Jan 22 at 6:38
Apass.JackApass.Jack
12.4k1939
answered Jan 22 at 6:38
Apass.JackApass.Jack
12.4k1939
answered Jan 22 at 6:38
Apass.JackApass.Jack
12.4k1939
answered Jan 22 at 6:38
Apass.JackApass.Jack
12.4k1939
12.4k1939
4
$begingroup$
+1. I refrained from mentioning them and went for implementations because I remember my professors mentioning them with a footnote that Voronoi Diagrams are computationally quite complex to implement in higher dimensions. So simple kNN implementations get the job done much better. However the condition that "lines are drawn to be equidistant between two points" may not be fulfilled.
$endgroup$
– Sagnik
Jan 22 at 6:48
add a comment |
4
$begingroup$
+1. I refrained from mentioning them and went for implementations because I remember my professors mentioning them with a footnote that Voronoi Diagrams are computationally quite complex to implement in higher dimensions. So simple kNN implementations get the job done much better. However the condition that "lines are drawn to be equidistant between two points" may not be fulfilled.
$endgroup$
– Sagnik
Jan 22 at 6:48
4
4
$begingroup$
+1. I refrained from mentioning them and went for implementations because I remember my professors mentioning them with a footnote that Voronoi Diagrams are computationally quite complex to implement in higher dimensions. So simple kNN implementations get the job done much better. However the condition that "lines are drawn to be equidistant between two points" may not be fulfilled.
$endgroup$
– Sagnik
Jan 22 at 6:48
$begingroup$
+1. I refrained from mentioning them and went for implementations because I remember my professors mentioning them with a footnote that Voronoi Diagrams are computationally quite complex to implement in higher dimensions. So simple kNN implementations get the job done much better. However the condition that "lines are drawn to be equidistant between two points" may not be fulfilled.
$endgroup$
– Sagnik
Jan 22 at 6:48
add a comment |
$begingroup$
You are looking for a Multi-Class Classification Algorithm. I suggest you have a look at:
- K-Nearest Neighbors algorithm (or KNN). Here is an introductory blog post.
- Support Vector Machines. You can start reading up on it here.
answered Jan 22 at 5:52
SagnikSagnik
669519
$endgroup$
add a comment |
$begingroup$
You are looking for a Multi-Class Classification Algorithm. I suggest you have a look at:
- K-Nearest Neighbors algorithm (or KNN). Here is an introductory blog post.
- Support Vector Machines. You can start reading up on it here.
answered Jan 22 at 5:52
SagnikSagnik
669519
$endgroup$
add a comment |
$begingroup$
You are looking for a Multi-Class Classification Algorithm. I suggest you have a look at:
- K-Nearest Neighbors algorithm (or KNN). Here is an introductory blog post.
- Support Vector Machines. You can start reading up on it here.
answered Jan 22 at 5:52
SagnikSagnik
669519
$endgroup$
You are looking for a Multi-Class Classification Algorithm. I suggest you have a look at:
- K-Nearest Neighbors algorithm (or KNN). Here is an introductory blog post.
- Support Vector Machines. You can start reading up on it here.
answered Jan 22 at 5:52
SagnikSagnik
669519
answered Jan 22 at 5:52
SagnikSagnik
669519
answered Jan 22 at 5:52
SagnikSagnik
669519
answered Jan 22 at 5:52
SagnikSagnik
669519
669519
add a comment |
add a comment |
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$begingroup$
Viewed 1667 times since yesterday? Is SE being hacked?
$endgroup$
– HEKTO
Jan 23 at 18:35
$begingroup$
@HEKTO it was displayed as one of the "Hot Network Questions".
$endgroup$
– Apass.Jack
Jan 25 at 0:53