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
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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
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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
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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
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user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1 Answer
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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
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$begingroup$
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 |
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