How to sort incidence matrix by the number of ones in two dimensions?
$begingroup$
I have a set of "machines", each "machine" is described by a set of "tags". Not all tags present in all machines.
How to find largest subset of tags and largest subset of machines, where each tag is present in each machine?
I drew an incidence matrix like this:
now I want to sort its rows and cols to maximize area of "black" elements, something like this
(it is not guaranteed that the picture is well done)
How to do this?
I am trying to implement maximal biclique enumeration algorith from the paper and getting bicliques like this
Is it maximal in the sense? I.e. it is impossible to add one node and remain biclique?
Or it is erroneous output?
Code is here: https://github.com/dims12/iMBEA
matrices graph-theory algorithms sorting
asked Dec 22 '18 at 11:05
DimsDims
4271516
$endgroup$
add a comment |
$begingroup$
I have a set of "machines", each "machine" is described by a set of "tags". Not all tags present in all machines.
How to find largest subset of tags and largest subset of machines, where each tag is present in each machine?
I drew an incidence matrix like this:
now I want to sort its rows and cols to maximize area of "black" elements, something like this
(it is not guaranteed that the picture is well done)
How to do this?
I am trying to implement maximal biclique enumeration algorith from the paper and getting bicliques like this
Is it maximal in the sense? I.e. it is impossible to add one node and remain biclique?
Or it is erroneous output?
Code is here: https://github.com/dims12/iMBEA
matrices graph-theory algorithms sorting
asked Dec 22 '18 at 11:05
DimsDims
4271516
$endgroup$
2
$begingroup$
This problem (if I've understood it correctly) is equivalent to finding the maximum biclique of a bipartite graph. After some searching, I found this post on SO that you may find useful.
$endgroup$
– Omnomnomnom
Dec 22 '18 at 11:19
$begingroup$
@Omnomnomnom We can improve on Bron-Kerbosch considerably for cliques if we don't have to list all maximal cliques as in that post, and probably the same thing can be done for bicliques.
$endgroup$
– Misha Lavrov
Dec 22 '18 at 16:13
add a comment |
$begingroup$
I have a set of "machines", each "machine" is described by a set of "tags". Not all tags present in all machines.
How to find largest subset of tags and largest subset of machines, where each tag is present in each machine?
I drew an incidence matrix like this:
now I want to sort its rows and cols to maximize area of "black" elements, something like this
(it is not guaranteed that the picture is well done)
How to do this?
I am trying to implement maximal biclique enumeration algorith from the paper and getting bicliques like this
Is it maximal in the sense? I.e. it is impossible to add one node and remain biclique?
Or it is erroneous output?
Code is here: https://github.com/dims12/iMBEA
matrices graph-theory algorithms sorting
asked Dec 22 '18 at 11:05
DimsDims
4271516
$endgroup$
I have a set of "machines", each "machine" is described by a set of "tags". Not all tags present in all machines.
How to find largest subset of tags and largest subset of machines, where each tag is present in each machine?
I drew an incidence matrix like this:
now I want to sort its rows and cols to maximize area of "black" elements, something like this
(it is not guaranteed that the picture is well done)
How to do this?
I am trying to implement maximal biclique enumeration algorith from the paper and getting bicliques like this
Is it maximal in the sense? I.e. it is impossible to add one node and remain biclique?
Or it is erroneous output?
Code is here: https://github.com/dims12/iMBEA
matrices graph-theory algorithms sorting
matrices graph-theory algorithms sorting
asked Dec 22 '18 at 11:05
DimsDims
4271516
asked Dec 22 '18 at 11:05
DimsDims
4271516
edited Dec 24 '18 at 21:54
Dims
asked Dec 22 '18 at 11:05
DimsDims
4271516
asked Dec 22 '18 at 11:05
DimsDims
4271516
asked Dec 22 '18 at 11:05
DimsDims
4271516
4271516
2
$begingroup$
This problem (if I've understood it correctly) is equivalent to finding the maximum biclique of a bipartite graph. After some searching, I found this post on SO that you may find useful.
$endgroup$
– Omnomnomnom
Dec 22 '18 at 11:19
$begingroup$
@Omnomnomnom We can improve on Bron-Kerbosch considerably for cliques if we don't have to list all maximal cliques as in that post, and probably the same thing can be done for bicliques.
$endgroup$
– Misha Lavrov
Dec 22 '18 at 16:13
add a comment |
2
$begingroup$
This problem (if I've understood it correctly) is equivalent to finding the maximum biclique of a bipartite graph. After some searching, I found this post on SO that you may find useful.
$endgroup$
– Omnomnomnom
Dec 22 '18 at 11:19
$begingroup$
@Omnomnomnom We can improve on Bron-Kerbosch considerably for cliques if we don't have to list all maximal cliques as in that post, and probably the same thing can be done for bicliques.
$endgroup$
– Misha Lavrov
Dec 22 '18 at 16:13
2
2
$begingroup$
This problem (if I've understood it correctly) is equivalent to finding the maximum biclique of a bipartite graph. After some searching, I found this post on SO that you may find useful.
$endgroup$
– Omnomnomnom
Dec 22 '18 at 11:19
$begingroup$
This problem (if I've understood it correctly) is equivalent to finding the maximum biclique of a bipartite graph. After some searching, I found this post on SO that you may find useful.
$endgroup$
– Omnomnomnom
Dec 22 '18 at 11:19
$begingroup$
@Omnomnomnom We can improve on Bron-Kerbosch considerably for cliques if we don't have to list all maximal cliques as in that post, and probably the same thing can be done for bicliques.
$endgroup$
– Misha Lavrov
Dec 22 '18 at 16:13
$begingroup$
@Omnomnomnom We can improve on Bron-Kerbosch considerably for cliques if we don't have to list all maximal cliques as in that post, and probably the same thing can be done for bicliques.
$endgroup$
– Misha Lavrov
Dec 22 '18 at 16:13
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%2f3049319%2fhow-to-sort-incidence-matrix-by-the-number-of-ones-in-two-dimensions%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%2f3049319%2fhow-to-sort-incidence-matrix-by-the-number-of-ones-in-two-dimensions%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
2
$begingroup$
This problem (if I've understood it correctly) is equivalent to finding the maximum biclique of a bipartite graph. After some searching, I found this post on SO that you may find useful.
$endgroup$
– Omnomnomnom
Dec 22 '18 at 11:19
$begingroup$
@Omnomnomnom We can improve on Bron-Kerbosch considerably for cliques if we don't have to list all maximal cliques as in that post, and probably the same thing can be done for bicliques.
$endgroup$
– Misha Lavrov
Dec 22 '18 at 16:13