First Component in PCA Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)What do the first $k$ factors from factor analysis maximize?First principal component of 2D data forming a rectangle?Line that separates data partitioned by the first principal component of PCAWhy is linear regression different from PCA?Does the first principal component differ from simply computing the mean of all variables?Citation for total amount of variance explained in PCAQuiz: Determine first principal component from data-plotsIn PCA, is there an intuitive explanation for why the second principal component chosen must be orthogonal to the first component?PCA: How can the first principal component both maximize variance AND define the line that most closely fits the data?Principal component weights flipped after PCA
Pointing to problems without suggesting solutions
Are there any irrational/transcendental numbers for which the distribution of decimal digits is not uniform?
Why complex landing gears are used instead of simple, reliable and light weight muscle wire or shape memory alloys?
Found this skink in my tomato plant bucket. Is he trapped? Or could he leave if he wanted?
Understanding piped commands in GNU/Linux
Why do the Z-fighters hide their power?
Weaponising the Grasp-at-a-Distance spell
Did pre-Columbian Americans know the spherical shape of the Earth?
What is a more techy Technical Writer job title that isn't cutesy or confusing?
Can two people see the same photon?
How to get a flat-head nail out of a piece of wood?
Does the main washing effect of soap come from foam?
Can gravitational waves pass through a black hole?
What is the proper term for etching or digging of wall to hide conduit of cables
Is there a verb for listening stealthily?
Should man-made satellites feature an intelligent inverted "cow catcher"?
How do you cope with tons of web fonts when copying and pasting from web pages?
What did Turing mean when saying that "machines cannot give rise to surprises" is due to a fallacy?
Is there a spell that can create a permanent fire?
The Nth Gryphon Number
How do Java 8 default methods hеlp with lambdas?
Plotting a Maclaurin series
By what mechanism was the 2017 UK General Election called?
Noise in Eigenvalues plot
First Component in PCA
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)What do the first $k$ factors from factor analysis maximize?First principal component of 2D data forming a rectangle?Line that separates data partitioned by the first principal component of PCAWhy is linear regression different from PCA?Does the first principal component differ from simply computing the mean of all variables?Citation for total amount of variance explained in PCAQuiz: Determine first principal component from data-plotsIn PCA, is there an intuitive explanation for why the second principal component chosen must be orthogonal to the first component?PCA: How can the first principal component both maximize variance AND define the line that most closely fits the data?Principal component weights flipped after PCA
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
I was doing the Andrew Ng's ML course, and one of the solutions mentioned The first principal component is aligned with the direction of maximal variance.
I didn't get what it is trying to say.
machine-learning pca
asked 6 hours ago
user3656142user3656142
61
New contributor
user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I was doing the Andrew Ng's ML course, and one of the solutions mentioned The first principal component is aligned with the direction of maximal variance.
I didn't get what it is trying to say.
machine-learning pca
asked 6 hours ago
user3656142user3656142
61
New contributor
user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I was doing the Andrew Ng's ML course, and one of the solutions mentioned The first principal component is aligned with the direction of maximal variance.
I didn't get what it is trying to say.
machine-learning pca
asked 6 hours ago
user3656142user3656142
61
New contributor
user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I was doing the Andrew Ng's ML course, and one of the solutions mentioned The first principal component is aligned with the direction of maximal variance.
I didn't get what it is trying to say.
machine-learning pca
machine-learning pca
asked 6 hours ago
user3656142user3656142
61
New contributor
user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
user3656142user3656142
61
New contributor
user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
user3656142user3656142
61
New contributor
user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
user3656142user3656142
61
asked 6 hours ago
user3656142user3656142
61
61
New contributor
user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Welcome to CV!
PCA finds the linear combination of your original input variables that contains the largest possible variance among all input variables. This is the first principal component, and it will thus by definition "align with the direction of maximal variance". The second principal component is then a linear combination independent of the first PC, with the largest remaining variance, and so on.
Consider this mock example:
There are two input variables (bacterial colony size and relative expression of a fluorescent protein). However, it turns out that larger colonies express less fluorescent protein (i.e., the input variables are correlated). The first PC will then be in the direction of this combined variance of the two input variables, because this is the largest total variance that a linear combination can find. The second PC will do the same, but perpendicular to PC1.
answered 4 hours ago
Frans RodenburgFrans Rodenburg
3,6791529
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "65"
;
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: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
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
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
user3656142 is a new contributor. Be nice, and check out our Code of Conduct.
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%2fstats.stackexchange.com%2fquestions%2f404334%2ffirst-component-in-pca%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Welcome to CV!
PCA finds the linear combination of your original input variables that contains the largest possible variance among all input variables. This is the first principal component, and it will thus by definition "align with the direction of maximal variance". The second principal component is then a linear combination independent of the first PC, with the largest remaining variance, and so on.
Consider this mock example:
There are two input variables (bacterial colony size and relative expression of a fluorescent protein). However, it turns out that larger colonies express less fluorescent protein (i.e., the input variables are correlated). The first PC will then be in the direction of this combined variance of the two input variables, because this is the largest total variance that a linear combination can find. The second PC will do the same, but perpendicular to PC1.
answered 4 hours ago
Frans RodenburgFrans Rodenburg
3,6791529
$endgroup$
add a comment |
$begingroup$
Welcome to CV!
PCA finds the linear combination of your original input variables that contains the largest possible variance among all input variables. This is the first principal component, and it will thus by definition "align with the direction of maximal variance". The second principal component is then a linear combination independent of the first PC, with the largest remaining variance, and so on.
Consider this mock example:
There are two input variables (bacterial colony size and relative expression of a fluorescent protein). However, it turns out that larger colonies express less fluorescent protein (i.e., the input variables are correlated). The first PC will then be in the direction of this combined variance of the two input variables, because this is the largest total variance that a linear combination can find. The second PC will do the same, but perpendicular to PC1.
answered 4 hours ago
Frans RodenburgFrans Rodenburg
3,6791529
$endgroup$
add a comment |
$begingroup$
Welcome to CV!
PCA finds the linear combination of your original input variables that contains the largest possible variance among all input variables. This is the first principal component, and it will thus by definition "align with the direction of maximal variance". The second principal component is then a linear combination independent of the first PC, with the largest remaining variance, and so on.
Consider this mock example:
There are two input variables (bacterial colony size and relative expression of a fluorescent protein). However, it turns out that larger colonies express less fluorescent protein (i.e., the input variables are correlated). The first PC will then be in the direction of this combined variance of the two input variables, because this is the largest total variance that a linear combination can find. The second PC will do the same, but perpendicular to PC1.
answered 4 hours ago
Frans RodenburgFrans Rodenburg
3,6791529
$endgroup$
Welcome to CV!
PCA finds the linear combination of your original input variables that contains the largest possible variance among all input variables. This is the first principal component, and it will thus by definition "align with the direction of maximal variance". The second principal component is then a linear combination independent of the first PC, with the largest remaining variance, and so on.
Consider this mock example:
There are two input variables (bacterial colony size and relative expression of a fluorescent protein). However, it turns out that larger colonies express less fluorescent protein (i.e., the input variables are correlated). The first PC will then be in the direction of this combined variance of the two input variables, because this is the largest total variance that a linear combination can find. The second PC will do the same, but perpendicular to PC1.
answered 4 hours ago
Frans RodenburgFrans Rodenburg
3,6791529
answered 4 hours ago
Frans RodenburgFrans Rodenburg
3,6791529
answered 4 hours ago
Frans RodenburgFrans Rodenburg
3,6791529
answered 4 hours ago
Frans RodenburgFrans Rodenburg
3,6791529
3,6791529
add a comment |
add a comment |
user3656142 is a new contributor. Be nice, and check out our Code of Conduct.
user3656142 is a new contributor. Be nice, and check out our Code of Conduct.
user3656142 is a new contributor. Be nice, and check out our Code of Conduct.
user3656142 is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Cross Validated!
- 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%2fstats.stackexchange.com%2fquestions%2f404334%2ffirst-component-in-pca%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
