how to verify that N points are on the same plane (but may not be perfectly)
Given a collection of points in 3d. The value of each dimension can be visualized
When we visualize these points in 3d. They clearly are actually only live on a plane (but not perfectly), visualized bellow
My question is, what is a general approach to verify that any number of collection of points live on the same plane. Or more generally, any collection of points of dimenion m, actually live on n dimension space where n < m.
One way of doing such a job is to find 3 points to make a plane and iteratively test every point. However, this is not what I am looking for due to the fact that it is not generalizable for more than 3->2 dimension and if there is a slight amount of noise, the method falls apart. One approach I have tried is to find the SVD decomposition and decide by the eigenvalues. I am certain this problem has been solved principally but I am not sure how, I appreciate any opinion.
linear-algebra matrices linear-transformations
asked 2 days ago
Scicare
1134
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add a comment |
Given a collection of points in 3d. The value of each dimension can be visualized
When we visualize these points in 3d. They clearly are actually only live on a plane (but not perfectly), visualized bellow
My question is, what is a general approach to verify that any number of collection of points live on the same plane. Or more generally, any collection of points of dimenion m, actually live on n dimension space where n < m.
One way of doing such a job is to find 3 points to make a plane and iteratively test every point. However, this is not what I am looking for due to the fact that it is not generalizable for more than 3->2 dimension and if there is a slight amount of noise, the method falls apart. One approach I have tried is to find the SVD decomposition and decide by the eigenvalues. I am certain this problem has been solved principally but I am not sure how, I appreciate any opinion.
linear-algebra matrices linear-transformations
asked 2 days ago
Scicare
1134
New contributor
Scicare is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Pick 3 points, find the plane between them, then check whether the rest satisfy the plane equation.
– Don Thousand
2 days ago
If you can make a matrix 3 by 3 with the coords of 3 of these points, with rank 3, then they lay not in the same plane.
– dmtri
2 days ago
Hi @DonThousand and dmtri , I have just edited and add additional info. Thanks for your opinion and I'd appreciate any additional insight.
– Scicare
2 days ago
2
Are you sure you're not looking to do Principal Component Analysis instead? Applied to your example data, it would yield an orthonormal transform (rotation) around the coordinate mean, with the figure being on the $xy$ plane (with all $z$ coordinates being almost the same).
– Nominal Animal
2 days ago
add a comment |
Given a collection of points in 3d. The value of each dimension can be visualized
When we visualize these points in 3d. They clearly are actually only live on a plane (but not perfectly), visualized bellow
My question is, what is a general approach to verify that any number of collection of points live on the same plane. Or more generally, any collection of points of dimenion m, actually live on n dimension space where n < m.
One way of doing such a job is to find 3 points to make a plane and iteratively test every point. However, this is not what I am looking for due to the fact that it is not generalizable for more than 3->2 dimension and if there is a slight amount of noise, the method falls apart. One approach I have tried is to find the SVD decomposition and decide by the eigenvalues. I am certain this problem has been solved principally but I am not sure how, I appreciate any opinion.
linear-algebra matrices linear-transformations
asked 2 days ago
Scicare
1134
New contributor
Scicare is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Given a collection of points in 3d. The value of each dimension can be visualized
When we visualize these points in 3d. They clearly are actually only live on a plane (but not perfectly), visualized bellow
My question is, what is a general approach to verify that any number of collection of points live on the same plane. Or more generally, any collection of points of dimenion m, actually live on n dimension space where n < m.
One way of doing such a job is to find 3 points to make a plane and iteratively test every point. However, this is not what I am looking for due to the fact that it is not generalizable for more than 3->2 dimension and if there is a slight amount of noise, the method falls apart. One approach I have tried is to find the SVD decomposition and decide by the eigenvalues. I am certain this problem has been solved principally but I am not sure how, I appreciate any opinion.
linear-algebra matrices linear-transformations
linear-algebra matrices linear-transformations
asked 2 days ago
Scicare
1134
New contributor
Scicare is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Scicare
1134
New contributor
Scicare is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 2 days ago
asked 2 days ago
Scicare
1134
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Scicare is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 2 days ago
Scicare
1134
asked 2 days ago
Scicare
1134
1134
New contributor
Scicare is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Scicare 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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Check out our Code of Conduct.
2
Pick 3 points, find the plane between them, then check whether the rest satisfy the plane equation.
– Don Thousand
2 days ago
If you can make a matrix 3 by 3 with the coords of 3 of these points, with rank 3, then they lay not in the same plane.
– dmtri
2 days ago
Hi @DonThousand and dmtri , I have just edited and add additional info. Thanks for your opinion and I'd appreciate any additional insight.
– Scicare
2 days ago
2
Are you sure you're not looking to do Principal Component Analysis instead? Applied to your example data, it would yield an orthonormal transform (rotation) around the coordinate mean, with the figure being on the $xy$ plane (with all $z$ coordinates being almost the same).
– Nominal Animal
2 days ago
add a comment |
2
Pick 3 points, find the plane between them, then check whether the rest satisfy the plane equation.
– Don Thousand
2 days ago
If you can make a matrix 3 by 3 with the coords of 3 of these points, with rank 3, then they lay not in the same plane.
– dmtri
2 days ago
Hi @DonThousand and dmtri , I have just edited and add additional info. Thanks for your opinion and I'd appreciate any additional insight.
– Scicare
2 days ago
2
Are you sure you're not looking to do Principal Component Analysis instead? Applied to your example data, it would yield an orthonormal transform (rotation) around the coordinate mean, with the figure being on the $xy$ plane (with all $z$ coordinates being almost the same).
– Nominal Animal
2 days ago
2
2
Pick 3 points, find the plane between them, then check whether the rest satisfy the plane equation.
– Don Thousand
2 days ago
Pick 3 points, find the plane between them, then check whether the rest satisfy the plane equation.
– Don Thousand
2 days ago
If you can make a matrix 3 by 3 with the coords of 3 of these points, with rank 3, then they lay not in the same plane.
– dmtri
2 days ago
If you can make a matrix 3 by 3 with the coords of 3 of these points, with rank 3, then they lay not in the same plane.
– dmtri
2 days ago
Hi @DonThousand and dmtri , I have just edited and add additional info. Thanks for your opinion and I'd appreciate any additional insight.
– Scicare
2 days ago
Hi @DonThousand and dmtri , I have just edited and add additional info. Thanks for your opinion and I'd appreciate any additional insight.
– Scicare
2 days ago
2
2
Are you sure you're not looking to do Principal Component Analysis instead? Applied to your example data, it would yield an orthonormal transform (rotation) around the coordinate mean, with the figure being on the $xy$ plane (with all $z$ coordinates being almost the same).
– Nominal Animal
2 days ago
Are you sure you're not looking to do Principal Component Analysis instead? Applied to your example data, it would yield an orthonormal transform (rotation) around the coordinate mean, with the figure being on the $xy$ plane (with all $z$ coordinates being almost the same).
– Nominal Animal
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
Total Least Squares technique is what you need.
If the points are almost layered into one plane (in any dimension), that method will reveal it
and will give you the measure of the noise.
But if the points layer into multiple planes, then you would need more sophisticated methods
ranging through SVD , low-rank approximation or other methods.
In general, the problem falls into the category of Point Cloud analysis.
answered 2 days ago
G Cab
18k31237
So SVD was one of the right track. Thanks :D
– Scicare
yesterday
@Scicare Yes, indeed there is a strict connection between SVD and Least Squares.
– G Cab
22 hours ago
add a comment |
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1 Answer
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votes
Total Least Squares technique is what you need.
If the points are almost layered into one plane (in any dimension), that method will reveal it
and will give you the measure of the noise.
But if the points layer into multiple planes, then you would need more sophisticated methods
ranging through SVD , low-rank approximation or other methods.
In general, the problem falls into the category of Point Cloud analysis.
answered 2 days ago
G Cab
18k31237
So SVD was one of the right track. Thanks :D
– Scicare
yesterday
@Scicare Yes, indeed there is a strict connection between SVD and Least Squares.
– G Cab
22 hours ago
add a comment |
Total Least Squares technique is what you need.
If the points are almost layered into one plane (in any dimension), that method will reveal it
and will give you the measure of the noise.
But if the points layer into multiple planes, then you would need more sophisticated methods
ranging through SVD , low-rank approximation or other methods.
In general, the problem falls into the category of Point Cloud analysis.
answered 2 days ago
G Cab
18k31237
So SVD was one of the right track. Thanks :D
– Scicare
yesterday
@Scicare Yes, indeed there is a strict connection between SVD and Least Squares.
– G Cab
22 hours ago
add a comment |
Total Least Squares technique is what you need.
If the points are almost layered into one plane (in any dimension), that method will reveal it
and will give you the measure of the noise.
But if the points layer into multiple planes, then you would need more sophisticated methods
ranging through SVD , low-rank approximation or other methods.
In general, the problem falls into the category of Point Cloud analysis.
answered 2 days ago
G Cab
18k31237
Total Least Squares technique is what you need.
If the points are almost layered into one plane (in any dimension), that method will reveal it
and will give you the measure of the noise.
But if the points layer into multiple planes, then you would need more sophisticated methods
ranging through SVD , low-rank approximation or other methods.
In general, the problem falls into the category of Point Cloud analysis.
answered 2 days ago
G Cab
18k31237
edited 2 days ago
answered 2 days ago
G Cab
18k31237
answered 2 days ago
G Cab
18k31237
answered 2 days ago
G Cab
18k31237
18k31237
So SVD was one of the right track. Thanks :D
– Scicare
yesterday
@Scicare Yes, indeed there is a strict connection between SVD and Least Squares.
– G Cab
22 hours ago
add a comment |
So SVD was one of the right track. Thanks :D
– Scicare
yesterday
@Scicare Yes, indeed there is a strict connection between SVD and Least Squares.
– G Cab
22 hours ago
So SVD was one of the right track. Thanks :D
– Scicare
yesterday
So SVD was one of the right track. Thanks :D
– Scicare
yesterday
@Scicare Yes, indeed there is a strict connection between SVD and Least Squares.
– G Cab
22 hours ago
@Scicare Yes, indeed there is a strict connection between SVD and Least Squares.
– G Cab
22 hours ago
add a comment |
Scicare is a new contributor. Be nice, and check out our Code of Conduct.
Scicare is a new contributor. Be nice, and check out our Code of Conduct.
Scicare is a new contributor. Be nice, and check out our Code of Conduct.
Scicare is a new contributor. Be nice, and check out our Code of Conduct.
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2
Pick 3 points, find the plane between them, then check whether the rest satisfy the plane equation.
– Don Thousand
2 days ago
If you can make a matrix 3 by 3 with the coords of 3 of these points, with rank 3, then they lay not in the same plane.
– dmtri
2 days ago
Hi @DonThousand and dmtri , I have just edited and add additional info. Thanks for your opinion and I'd appreciate any additional insight.
– Scicare
2 days ago
2
Are you sure you're not looking to do Principal Component Analysis instead? Applied to your example data, it would yield an orthonormal transform (rotation) around the coordinate mean, with the figure being on the $xy$ plane (with all $z$ coordinates being almost the same).
– Nominal Animal
2 days ago