How does minimizing the rank of a matrix help us impute missing values in it?
up vote
3
down vote
favorite
I am not really a math guru myself, but I know that many estimation or approximation problems can be reformulated as minimizing the rank of a matrix. Although that is really hard, we can try to minimize the nuclear norm instead, which turns out to be a convex optimization problem that is easier to solve.
Let's say I have a sparse matrix X which I need to fill and somehow I've found the minimal nuclear norm. How can I impute the missing values now? And how the whole idea of minimizing the rank relate to that? Can you provide me with a simple(visual, if possible) example, please?
linear-algebra norm svd sparse-matrices nuclear-norm
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41853
asked Jan 16 at 22:49
MLearner
161
add a comment |
up vote
3
down vote
favorite
I am not really a math guru myself, but I know that many estimation or approximation problems can be reformulated as minimizing the rank of a matrix. Although that is really hard, we can try to minimize the nuclear norm instead, which turns out to be a convex optimization problem that is easier to solve.
Let's say I have a sparse matrix X which I need to fill and somehow I've found the minimal nuclear norm. How can I impute the missing values now? And how the whole idea of minimizing the rank relate to that? Can you provide me with a simple(visual, if possible) example, please?
linear-algebra norm svd sparse-matrices nuclear-norm
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41853
asked Jan 16 at 22:49
MLearner
161
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I am not really a math guru myself, but I know that many estimation or approximation problems can be reformulated as minimizing the rank of a matrix. Although that is really hard, we can try to minimize the nuclear norm instead, which turns out to be a convex optimization problem that is easier to solve.
Let's say I have a sparse matrix X which I need to fill and somehow I've found the minimal nuclear norm. How can I impute the missing values now? And how the whole idea of minimizing the rank relate to that? Can you provide me with a simple(visual, if possible) example, please?
linear-algebra norm svd sparse-matrices nuclear-norm
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41853
asked Jan 16 at 22:49
MLearner
161
I am not really a math guru myself, but I know that many estimation or approximation problems can be reformulated as minimizing the rank of a matrix. Although that is really hard, we can try to minimize the nuclear norm instead, which turns out to be a convex optimization problem that is easier to solve.
Let's say I have a sparse matrix X which I need to fill and somehow I've found the minimal nuclear norm. How can I impute the missing values now? And how the whole idea of minimizing the rank relate to that? Can you provide me with a simple(visual, if possible) example, please?
linear-algebra norm svd sparse-matrices nuclear-norm
linear-algebra norm svd sparse-matrices nuclear-norm
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41853
asked Jan 16 at 22:49
MLearner
161
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41853
asked Jan 16 at 22:49
MLearner
161
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41853
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41853
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41853
12.8k41853
asked Jan 16 at 22:49
MLearner
161
asked Jan 16 at 22:49
MLearner
161
asked Jan 16 at 22:49
MLearner
161
161
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32
add a comment |
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32
add a comment |
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',
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%2f2608445%2fhow-does-minimizing-the-rank-of-a-matrix-help-us-impute-missing-values-in-it%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f2608445%2fhow-does-minimizing-the-rank-of-a-matrix-help-us-impute-missing-values-in-it%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
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32