Singular Value Decomposition Basis? The 2019 Stack Overflow Developer Survey Results Are InSymmetric matrix decomposition with orthonormal basis of non-eigenvectorsProjection onto Singular Vector Subspace for Singular Value DecompositionEigenvalues and eigenvectorsIntuitively, what is the difference between Eigendecomposition and Singular Value Decomposition?Covariance- v. correlation-matrix based PCAon the Singular Value DecompositionRecovering eigenvectors from SVDSingular value decomposition, same matrix in different orthonormal basesChange of coordinates of a matrix $A$ to a basis formed by its eigenvectorsHow do you know what a matrix represents in matrix decomposition?
What is the closest word meaning "respect for time / mindful"
How to save as into a customized destination on macOS?
Can we generate random numbers using irrational numbers like π and e?
How can I autofill dates in Excel excluding Sunday?
Lightning Grid - Columns and Rows?
What do hard-Brexiteers want with respect to the Irish border?
Are there incongruent pythagorean triangles with the same perimeter and same area?
Is this app Icon Browser Safe/Legit?
What could be the right powersource for 15 seconds lifespan disposable giant chainsaw?
Did 3000BC Egyptians use meteoric iron weapons?
What to do when moving next to a bird sanctuary with a loosely-domesticated cat?
Time travel alters history but people keep saying nothing's changed
What does ひと匙 mean in this manga and has it been used colloquially?
Is three citations per paragraph excessive for undergraduate research paper?
Can someone be penalized for an "unlawful" act if no penalty is specified?
Shouldn't "much" here be used instead of "more"?
Is an up-to-date browser secure on an out-of-date OS?
Geography at the pixel level
Right tool to dig six foot holes?
How to support a colleague who finds meetings extremely tiring?
Output the Arecibo Message
Why can Shazam fly?
Return to UK after being refused entry years previously
Have you ever entered Singapore using a different passport or name?
Singular Value Decomposition Basis?
The 2019 Stack Overflow Developer Survey Results Are InSymmetric matrix decomposition with orthonormal basis of non-eigenvectorsProjection onto Singular Vector Subspace for Singular Value DecompositionEigenvalues and eigenvectorsIntuitively, what is the difference between Eigendecomposition and Singular Value Decomposition?Covariance- v. correlation-matrix based PCAon the Singular Value DecompositionRecovering eigenvectors from SVDSingular value decomposition, same matrix in different orthonormal basesChange of coordinates of a matrix $A$ to a basis formed by its eigenvectorsHow do you know what a matrix represents in matrix decomposition?
$begingroup$
I am unable to just understand one bit of SVD.
Given A=USV
where U is the eigenvectors of the correlation matrix between the entries S is the eigenvalue matrix and V the transpose of eigenvectors of correlation matrix between the features.
In the case of movie examples(from here at 9:52 https://www.youtube.com/watch?v=P5mlg91as1c&t=616s) U represents the relation of users to categories while V of movies to categories. How are they both expressed in the same basis i.e the same formulation of categories? If U comes from the covariance matrix of the users shouldn't it represent the principal direction of users?
While V represent the principal direction of movies? A user is written as a linear combination of a different user basis than the movie basis. I am not getting how they are in the exact same basis.
I understand that if I write every movie as a linear combination of some categories and users as a linear combination of their affinity to those same categories then we just do a dot product. But here the basis is different as it is of two different covariance matrices. What am I missing?
linear-algebra linear-transformations singularvalues
asked Mar 23 at 18:00
Rahul DeoraRahul Deora
316
$endgroup$
add a comment |
$begingroup$
I am unable to just understand one bit of SVD.
Given A=USV
where U is the eigenvectors of the correlation matrix between the entries S is the eigenvalue matrix and V the transpose of eigenvectors of correlation matrix between the features.
In the case of movie examples(from here at 9:52 https://www.youtube.com/watch?v=P5mlg91as1c&t=616s) U represents the relation of users to categories while V of movies to categories. How are they both expressed in the same basis i.e the same formulation of categories? If U comes from the covariance matrix of the users shouldn't it represent the principal direction of users?
While V represent the principal direction of movies? A user is written as a linear combination of a different user basis than the movie basis. I am not getting how they are in the exact same basis.
I understand that if I write every movie as a linear combination of some categories and users as a linear combination of their affinity to those same categories then we just do a dot product. But here the basis is different as it is of two different covariance matrices. What am I missing?
linear-algebra linear-transformations singularvalues
asked Mar 23 at 18:00
Rahul DeoraRahul Deora
316
$endgroup$
add a comment |
$begingroup$
I am unable to just understand one bit of SVD.
Given A=USV
where U is the eigenvectors of the correlation matrix between the entries S is the eigenvalue matrix and V the transpose of eigenvectors of correlation matrix between the features.
In the case of movie examples(from here at 9:52 https://www.youtube.com/watch?v=P5mlg91as1c&t=616s) U represents the relation of users to categories while V of movies to categories. How are they both expressed in the same basis i.e the same formulation of categories? If U comes from the covariance matrix of the users shouldn't it represent the principal direction of users?
While V represent the principal direction of movies? A user is written as a linear combination of a different user basis than the movie basis. I am not getting how they are in the exact same basis.
I understand that if I write every movie as a linear combination of some categories and users as a linear combination of their affinity to those same categories then we just do a dot product. But here the basis is different as it is of two different covariance matrices. What am I missing?
linear-algebra linear-transformations singularvalues
asked Mar 23 at 18:00
Rahul DeoraRahul Deora
316
$endgroup$
I am unable to just understand one bit of SVD.
Given A=USV
where U is the eigenvectors of the correlation matrix between the entries S is the eigenvalue matrix and V the transpose of eigenvectors of correlation matrix between the features.
In the case of movie examples(from here at 9:52 https://www.youtube.com/watch?v=P5mlg91as1c&t=616s) U represents the relation of users to categories while V of movies to categories. How are they both expressed in the same basis i.e the same formulation of categories? If U comes from the covariance matrix of the users shouldn't it represent the principal direction of users?
While V represent the principal direction of movies? A user is written as a linear combination of a different user basis than the movie basis. I am not getting how they are in the exact same basis.
I understand that if I write every movie as a linear combination of some categories and users as a linear combination of their affinity to those same categories then we just do a dot product. But here the basis is different as it is of two different covariance matrices. What am I missing?
linear-algebra linear-transformations singularvalues
linear-algebra linear-transformations singularvalues
asked Mar 23 at 18:00
Rahul DeoraRahul Deora
316
asked Mar 23 at 18:00
Rahul DeoraRahul Deora
316
asked Mar 23 at 18:00
Rahul DeoraRahul Deora
316
asked Mar 23 at 18:00
Rahul DeoraRahul Deora
316
asked Mar 23 at 18:00
Rahul DeoraRahul Deora
316
316
add a comment |
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%2f3159644%2fsingular-value-decomposition-basis%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%2f3159644%2fsingular-value-decomposition-basis%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
