First Component in 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.
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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.
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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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user3656142 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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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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1 Answer
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1 Answer
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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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