Create a multidimensional points cloud with given only the distance between the points
$begingroup$
as the title says, I am trying to get the most accurate multidimensional points cloud with the leas dimensions needed given only the distance between all the points. The dimension of the solution is not given either.
e.g. I have given three points A, B and C:
Points AB have the Distance 1
Points AC have the Distance 1
Points BC have the Distance 1.41 (sqrt(2))
In this simple case, the best solution would be 2 dimensional like this:
A – – – C
| – – – |
| – – – |
| – – – |
B – – – .
As there are more points and more dimension, this problem gets more complicated. The input distance between the points will be empirical values and will therefore never give a unique solution.
But I think the best solution could be narrowed down, this would be the solution with the least error.
I guess there must already be an approach to this problem, but I did not yet find any solution. Do you have any suggestions?
Thank you a lot!
geometry algebraic-geometry
asked Dec 18 '18 at 10:01
StarStar
1
$endgroup$
add a comment |
$begingroup$
as the title says, I am trying to get the most accurate multidimensional points cloud with the leas dimensions needed given only the distance between all the points. The dimension of the solution is not given either.
e.g. I have given three points A, B and C:
Points AB have the Distance 1
Points AC have the Distance 1
Points BC have the Distance 1.41 (sqrt(2))
In this simple case, the best solution would be 2 dimensional like this:
A – – – C
| – – – |
| – – – |
| – – – |
B – – – .
As there are more points and more dimension, this problem gets more complicated. The input distance between the points will be empirical values and will therefore never give a unique solution.
But I think the best solution could be narrowed down, this would be the solution with the least error.
I guess there must already be an approach to this problem, but I did not yet find any solution. Do you have any suggestions?
Thank you a lot!
geometry algebraic-geometry
asked Dec 18 '18 at 10:01
StarStar
1
$endgroup$
$begingroup$
This is the classical multidimensional scaling problem. See e.g. sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/…
$endgroup$
– Rahul
Dec 18 '18 at 12:40
add a comment |
$begingroup$
as the title says, I am trying to get the most accurate multidimensional points cloud with the leas dimensions needed given only the distance between all the points. The dimension of the solution is not given either.
e.g. I have given three points A, B and C:
Points AB have the Distance 1
Points AC have the Distance 1
Points BC have the Distance 1.41 (sqrt(2))
In this simple case, the best solution would be 2 dimensional like this:
A – – – C
| – – – |
| – – – |
| – – – |
B – – – .
As there are more points and more dimension, this problem gets more complicated. The input distance between the points will be empirical values and will therefore never give a unique solution.
But I think the best solution could be narrowed down, this would be the solution with the least error.
I guess there must already be an approach to this problem, but I did not yet find any solution. Do you have any suggestions?
Thank you a lot!
geometry algebraic-geometry
asked Dec 18 '18 at 10:01
StarStar
1
$endgroup$
as the title says, I am trying to get the most accurate multidimensional points cloud with the leas dimensions needed given only the distance between all the points. The dimension of the solution is not given either.
e.g. I have given three points A, B and C:
Points AB have the Distance 1
Points AC have the Distance 1
Points BC have the Distance 1.41 (sqrt(2))
In this simple case, the best solution would be 2 dimensional like this:
A – – – C
| – – – |
| – – – |
| – – – |
B – – – .
As there are more points and more dimension, this problem gets more complicated. The input distance between the points will be empirical values and will therefore never give a unique solution.
But I think the best solution could be narrowed down, this would be the solution with the least error.
I guess there must already be an approach to this problem, but I did not yet find any solution. Do you have any suggestions?
Thank you a lot!
geometry algebraic-geometry
geometry algebraic-geometry
asked Dec 18 '18 at 10:01
StarStar
1
asked Dec 18 '18 at 10:01
StarStar
1
asked Dec 18 '18 at 10:01
StarStar
1
asked Dec 18 '18 at 10:01
StarStar
1
asked Dec 18 '18 at 10:01
StarStar
1
1
$begingroup$
This is the classical multidimensional scaling problem. See e.g. sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/…
$endgroup$
– Rahul
Dec 18 '18 at 12:40
add a comment |
$begingroup$
This is the classical multidimensional scaling problem. See e.g. sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/…
$endgroup$
– Rahul
Dec 18 '18 at 12:40
$begingroup$
This is the classical multidimensional scaling problem. See e.g. sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/…
$endgroup$
– Rahul
Dec 18 '18 at 12:40
$begingroup$
This is the classical multidimensional scaling problem. See e.g. sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/…
$endgroup$
– Rahul
Dec 18 '18 at 12:40
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3044973%2fcreate-a-multidimensional-points-cloud-with-given-only-the-distance-between-the%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3044973%2fcreate-a-multidimensional-points-cloud-with-given-only-the-distance-between-the%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
This is the classical multidimensional scaling problem. See e.g. sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/…
$endgroup$
– Rahul
Dec 18 '18 at 12:40