why dot product of normalized vector is always data size -1
up vote
0
down vote
favorite
I don't understand why dot product of normalized vector is always data size -1.
a <- scale(rnorm(100))
crossprod(a)
# equal = 100 - 1 = 99
b <- scale(runif(50))
crossprod(b)
# equal = 50 - 1 = 49
c <- scale(rchisq(30, 5))
crossprod(c)
# equal = 30 - 1 = 29
I want to know mathematical understanding.
r math linear-algebra
asked Nov 20 at 6:09
Rokmc1050
1881311
add a comment |
up vote
0
down vote
favorite
I don't understand why dot product of normalized vector is always data size -1.
a <- scale(rnorm(100))
crossprod(a)
# equal = 100 - 1 = 99
b <- scale(runif(50))
crossprod(b)
# equal = 50 - 1 = 49
c <- scale(rchisq(30, 5))
crossprod(c)
# equal = 30 - 1 = 29
I want to know mathematical understanding.
r math linear-algebra
asked Nov 20 at 6:09
Rokmc1050
1881311
Please read the documentation ofscale(), section Details: for the scaled data the standard deviation is 1.
– jogo
Nov 20 at 7:23
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I don't understand why dot product of normalized vector is always data size -1.
a <- scale(rnorm(100))
crossprod(a)
# equal = 100 - 1 = 99
b <- scale(runif(50))
crossprod(b)
# equal = 50 - 1 = 49
c <- scale(rchisq(30, 5))
crossprod(c)
# equal = 30 - 1 = 29
I want to know mathematical understanding.
r math linear-algebra
asked Nov 20 at 6:09
Rokmc1050
1881311
I don't understand why dot product of normalized vector is always data size -1.
a <- scale(rnorm(100))
crossprod(a)
# equal = 100 - 1 = 99
b <- scale(runif(50))
crossprod(b)
# equal = 50 - 1 = 49
c <- scale(rchisq(30, 5))
crossprod(c)
# equal = 30 - 1 = 29
I want to know mathematical understanding.
r math linear-algebra
r math linear-algebra
asked Nov 20 at 6:09
Rokmc1050
1881311
asked Nov 20 at 6:09
Rokmc1050
1881311
asked Nov 20 at 6:09
Rokmc1050
1881311
asked Nov 20 at 6:09
Rokmc1050
1881311
asked Nov 20 at 6:09
Rokmc1050
1881311
1881311
Please read the documentation ofscale(), section Details: for the scaled data the standard deviation is 1.
– jogo
Nov 20 at 7:23
add a comment |
Please read the documentation ofscale(), section Details: for the scaled data the standard deviation is 1.
– jogo
Nov 20 at 7:23
Please read the documentation of
scale(), section Details: for the scaled data the standard deviation is 1.– jogo
Nov 20 at 7:23
Please read the documentation of
scale(), section Details: for the scaled data the standard deviation is 1.– jogo
Nov 20 at 7:23
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Not in LaTex, but proof may help you to understand:
Your values are scaled, so: [x_i-mean(X)] / sd(X).
Crossprod does sum of squares of x_i = Sum_i ( [x_i-mean(X)])^2
Variance (squared sd): var(X) = sd^2(X) = 1/(n-1) * Sum_i ( [x_i-mean(X)])^2
Crossprod = Sum_i ([x_i-mean(X)] / sd(X))^2) = 1/sd(X)^2 * Sum_i ( [x_i-mean(X)]^2) = 1/(1/(n-1)) = n-1
answered Nov 20 at 7:59
emsinko
17115
Oh. I got it. Thank you.
– Rokmc1050
Nov 21 at 6:58
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
StackExchange.using("externalEditor", function () {
StackExchange.using("snippets", function () {
StackExchange.snippets.init();
});
});
}, "code-snippets");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "1"
};
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
},
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%2fstackoverflow.com%2fquestions%2f53387191%2fwhy-dot-product-of-normalized-vector-is-always-data-size-1%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
up vote
1
down vote
accepted
Not in LaTex, but proof may help you to understand:
Your values are scaled, so: [x_i-mean(X)] / sd(X).
Crossprod does sum of squares of x_i = Sum_i ( [x_i-mean(X)])^2
Variance (squared sd): var(X) = sd^2(X) = 1/(n-1) * Sum_i ( [x_i-mean(X)])^2
Crossprod = Sum_i ([x_i-mean(X)] / sd(X))^2) = 1/sd(X)^2 * Sum_i ( [x_i-mean(X)]^2) = 1/(1/(n-1)) = n-1
answered Nov 20 at 7:59
emsinko
17115
Oh. I got it. Thank you.
– Rokmc1050
Nov 21 at 6:58
add a comment |
up vote
1
down vote
accepted
Not in LaTex, but proof may help you to understand:
Your values are scaled, so: [x_i-mean(X)] / sd(X).
Crossprod does sum of squares of x_i = Sum_i ( [x_i-mean(X)])^2
Variance (squared sd): var(X) = sd^2(X) = 1/(n-1) * Sum_i ( [x_i-mean(X)])^2
Crossprod = Sum_i ([x_i-mean(X)] / sd(X))^2) = 1/sd(X)^2 * Sum_i ( [x_i-mean(X)]^2) = 1/(1/(n-1)) = n-1
answered Nov 20 at 7:59
emsinko
17115
Oh. I got it. Thank you.
– Rokmc1050
Nov 21 at 6:58
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Not in LaTex, but proof may help you to understand:
Your values are scaled, so: [x_i-mean(X)] / sd(X).
Crossprod does sum of squares of x_i = Sum_i ( [x_i-mean(X)])^2
Variance (squared sd): var(X) = sd^2(X) = 1/(n-1) * Sum_i ( [x_i-mean(X)])^2
Crossprod = Sum_i ([x_i-mean(X)] / sd(X))^2) = 1/sd(X)^2 * Sum_i ( [x_i-mean(X)]^2) = 1/(1/(n-1)) = n-1
answered Nov 20 at 7:59
emsinko
17115
Not in LaTex, but proof may help you to understand:
Your values are scaled, so: [x_i-mean(X)] / sd(X).
Crossprod does sum of squares of x_i = Sum_i ( [x_i-mean(X)])^2
Variance (squared sd): var(X) = sd^2(X) = 1/(n-1) * Sum_i ( [x_i-mean(X)])^2
Crossprod = Sum_i ([x_i-mean(X)] / sd(X))^2) = 1/sd(X)^2 * Sum_i ( [x_i-mean(X)]^2) = 1/(1/(n-1)) = n-1
answered Nov 20 at 7:59
emsinko
17115
edited Nov 20 at 9:02
answered Nov 20 at 7:59
emsinko
17115
answered Nov 20 at 7:59
emsinko
17115
answered Nov 20 at 7:59
emsinko
17115
17115
Oh. I got it. Thank you.
– Rokmc1050
Nov 21 at 6:58
add a comment |
Oh. I got it. Thank you.
– Rokmc1050
Nov 21 at 6:58
Oh. I got it. Thank you.
– Rokmc1050
Nov 21 at 6:58
Oh. I got it. Thank you.
– Rokmc1050
Nov 21 at 6:58
add a comment |
Thanks for contributing an answer to Stack Overflow!
- 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.
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%2fstackoverflow.com%2fquestions%2f53387191%2fwhy-dot-product-of-normalized-vector-is-always-data-size-1%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
Please read the documentation of
scale(), section Details: for the scaled data the standard deviation is 1.– jogo
Nov 20 at 7:23