Finding attribution of coefficient in a matrix

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I have the following $d*n$ matrix in $0, 1$

beginbmatrix
x_11 & x_12 & x_13 & dots & x_1n \
x_21 & x_22 & x_23 & dots & x_2n \
vdots & vdots & vdots & ddots & vdots \
x_d1 & x_d2 & x_d3 & dots & x_dn
endbmatrix

And the following label in $mathbbW$

beginbmatrix
y_11 \
y_21 \
vdots \
y_d1
endbmatrix

Where the $d$ dimension is my data points and $n$ dimension is my feature.

I want to rank the feature that has the highest contribution to the label.

One way to do it is to solve this linear system, find out the coefficient of this feature.

Sort the coefficient and call it a day.

There is alot of issue with this method, such that there might be infinite solutions, or its not solvable.

I was also thinking about using SVD such that I distributed the label to my feature matrix like this

Given

beginbmatrix
1 & 0 & 1 & 0 \
0 & 0 & 1 & 1
endbmatrix

and label

beginbmatrix
100 \
50 \
endbmatrix

I will do SVD on the following matrix

beginbmatrix
50 & 0 & 50 & 0 \
0 & 0 & 25 & 25
endbmatrix

This will essentially return me the column that has the most contribution

Is there a better way to achieve my goal?

linear-algebra matrices linear-transformations

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edited Jul 24 at 17:22

asked Jul 24 at 1:10

python

1012

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up vote
0
down vote

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1

I have the following $d*n$ matrix in $0, 1$

beginbmatrix
x_11 & x_12 & x_13 & dots & x_1n \
x_21 & x_22 & x_23 & dots & x_2n \
vdots & vdots & vdots & ddots & vdots \
x_d1 & x_d2 & x_d3 & dots & x_dn
endbmatrix

And the following label in $mathbbW$

beginbmatrix
y_11 \
y_21 \
vdots \
y_d1
endbmatrix

Where the $d$ dimension is my data points and $n$ dimension is my feature.

I want to rank the feature that has the highest contribution to the label.

One way to do it is to solve this linear system, find out the coefficient of this feature.

Sort the coefficient and call it a day.

There is alot of issue with this method, such that there might be infinite solutions, or its not solvable.

I was also thinking about using SVD such that I distributed the label to my feature matrix like this

Given

beginbmatrix
1 & 0 & 1 & 0 \
0 & 0 & 1 & 1
endbmatrix

and label

beginbmatrix
100 \
50 \
endbmatrix

I will do SVD on the following matrix

beginbmatrix
50 & 0 & 50 & 0 \
0 & 0 & 25 & 25
endbmatrix

This will essentially return me the column that has the most contribution

Is there a better way to achieve my goal?

linear-algebra matrices linear-transformations

share|cite|improve this question

edited Jul 24 at 17:22

asked Jul 24 at 1:10

python

1012

add a comment | 

up vote
0
down vote

favorite

1

up vote
0
down vote

favorite

1

1

I have the following $d*n$ matrix in $0, 1$

beginbmatrix
x_11 & x_12 & x_13 & dots & x_1n \
x_21 & x_22 & x_23 & dots & x_2n \
vdots & vdots & vdots & ddots & vdots \
x_d1 & x_d2 & x_d3 & dots & x_dn
endbmatrix

And the following label in $mathbbW$

beginbmatrix
y_11 \
y_21 \
vdots \
y_d1
endbmatrix

Where the $d$ dimension is my data points and $n$ dimension is my feature.

I want to rank the feature that has the highest contribution to the label.

One way to do it is to solve this linear system, find out the coefficient of this feature.

Sort the coefficient and call it a day.

There is alot of issue with this method, such that there might be infinite solutions, or its not solvable.

I was also thinking about using SVD such that I distributed the label to my feature matrix like this

Given

beginbmatrix
1 & 0 & 1 & 0 \
0 & 0 & 1 & 1
endbmatrix

and label

beginbmatrix
100 \
50 \
endbmatrix

I will do SVD on the following matrix

beginbmatrix
50 & 0 & 50 & 0 \
0 & 0 & 25 & 25
endbmatrix

This will essentially return me the column that has the most contribution

Is there a better way to achieve my goal?

linear-algebra matrices linear-transformations

share|cite|improve this question

edited Jul 24 at 17:22

asked Jul 24 at 1:10

python

1012

I have the following $d*n$ matrix in $0, 1$

beginbmatrix
x_11 & x_12 & x_13 & dots & x_1n \
x_21 & x_22 & x_23 & dots & x_2n \
vdots & vdots & vdots & ddots & vdots \
x_d1 & x_d2 & x_d3 & dots & x_dn
endbmatrix

And the following label in $mathbbW$

beginbmatrix
y_11 \
y_21 \
vdots \
y_d1
endbmatrix

Where the $d$ dimension is my data points and $n$ dimension is my feature.

I want to rank the feature that has the highest contribution to the label.

One way to do it is to solve this linear system, find out the coefficient of this feature.

Sort the coefficient and call it a day.

There is alot of issue with this method, such that there might be infinite solutions, or its not solvable.

I was also thinking about using SVD such that I distributed the label to my feature matrix like this

Given

beginbmatrix
1 & 0 & 1 & 0 \
0 & 0 & 1 & 1
endbmatrix

and label

beginbmatrix
100 \
50 \
endbmatrix

I will do SVD on the following matrix

beginbmatrix
50 & 0 & 50 & 0 \
0 & 0 & 25 & 25
endbmatrix

This will essentially return me the column that has the most contribution

Is there a better way to achieve my goal?

linear-algebra matrices linear-transformations

share|cite|improve this question

edited Jul 24 at 17:22

asked Jul 24 at 1:10

python

1012

share|cite|improve this question

share|cite|improve this question

edited Jul 24 at 17:22

edited Jul 24 at 17:22

edited Jul 24 at 17:22

asked Jul 24 at 1:10

python

1012

asked Jul 24 at 1:10

python

1012

asked Jul 24 at 1:10

python

1012

1012

add a comment | 

add a comment | 

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