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
asked 2 hours ago
BrianBrian
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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
asked 2 hours ago
BrianBrian
61
New contributor
Brian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
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
asked 2 hours ago
BrianBrian
61
New contributor
Brian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
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
algorithms
asked 2 hours ago
BrianBrian
61
New contributor
Brian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
BrianBrian
61
New contributor
Brian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
BrianBrian
61
New contributor
Brian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
BrianBrian
61
asked 2 hours ago
BrianBrian
61
61
New contributor
Brian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Brian is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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2 Answers
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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 1 hour ago
Apass.JackApass.Jack
8,6451634
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+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
1 hour ago
add a comment |
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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 1 hour ago
SagnikSagnik
584319
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2 Answers
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2 Answers
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$begingroup$
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 1 hour ago
Apass.JackApass.Jack
8,6451634
$endgroup$
$begingroup$
+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
1 hour ago
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 1 hour ago
Apass.JackApass.Jack
8,6451634
$endgroup$
$begingroup$
+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
1 hour ago
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 1 hour ago
Apass.JackApass.Jack
8,6451634
$endgroup$
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 1 hour ago
Apass.JackApass.Jack
8,6451634
answered 1 hour ago
Apass.JackApass.Jack
8,6451634
answered 1 hour ago
Apass.JackApass.Jack
8,6451634
answered 1 hour ago
Apass.JackApass.Jack
8,6451634
8,6451634
$begingroup$
+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
1 hour ago
add a comment |
$begingroup$
+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
1 hour ago
$begingroup$
+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
1 hour ago
$begingroup$
+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
1 hour ago
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 1 hour ago
SagnikSagnik
584319
$endgroup$
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 1 hour ago
SagnikSagnik
584319
$endgroup$
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 1 hour ago
SagnikSagnik
584319
$endgroup$
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 1 hour ago
SagnikSagnik
584319
answered 1 hour ago
SagnikSagnik
584319
answered 1 hour ago
SagnikSagnik
584319
answered 1 hour ago
SagnikSagnik
584319
584319
add a comment |
add a comment |
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