How does minimizing the rank of a matrix help us impute missing values in it?
I am not really a math guru myself, but I know that many estimation or approximation problems can be reformulated as minimizing the rank of a matrix. Although that is really hard, we can try to minimize the nuclear norm instead, which turns out to be a convex optimization problem that is easier to solve.
Let's say I have a sparse matrix X which I need to fill and somehow I've found the minimal nuclear norm. How can I impute the missing values now? And how the whole idea of minimizing the rank relate to that? Can you provide me with a simple(visual, if possible) example, please?
linear-algebra norm svd sparse-matrices nuclear-norm
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41854
asked Jan 16 at 22:49
MLearner
161
add a comment |
I am not really a math guru myself, but I know that many estimation or approximation problems can be reformulated as minimizing the rank of a matrix. Although that is really hard, we can try to minimize the nuclear norm instead, which turns out to be a convex optimization problem that is easier to solve.
Let's say I have a sparse matrix X which I need to fill and somehow I've found the minimal nuclear norm. How can I impute the missing values now? And how the whole idea of minimizing the rank relate to that? Can you provide me with a simple(visual, if possible) example, please?
linear-algebra norm svd sparse-matrices nuclear-norm
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41854
asked Jan 16 at 22:49
MLearner
161
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32
add a comment |
I am not really a math guru myself, but I know that many estimation or approximation problems can be reformulated as minimizing the rank of a matrix. Although that is really hard, we can try to minimize the nuclear norm instead, which turns out to be a convex optimization problem that is easier to solve.
Let's say I have a sparse matrix X which I need to fill and somehow I've found the minimal nuclear norm. How can I impute the missing values now? And how the whole idea of minimizing the rank relate to that? Can you provide me with a simple(visual, if possible) example, please?
linear-algebra norm svd sparse-matrices nuclear-norm
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41854
asked Jan 16 at 22:49
MLearner
161
I am not really a math guru myself, but I know that many estimation or approximation problems can be reformulated as minimizing the rank of a matrix. Although that is really hard, we can try to minimize the nuclear norm instead, which turns out to be a convex optimization problem that is easier to solve.
Let's say I have a sparse matrix X which I need to fill and somehow I've found the minimal nuclear norm. How can I impute the missing values now? And how the whole idea of minimizing the rank relate to that? Can you provide me with a simple(visual, if possible) example, please?
linear-algebra norm svd sparse-matrices nuclear-norm
linear-algebra norm svd sparse-matrices nuclear-norm
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41854
asked Jan 16 at 22:49
MLearner
161
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41854
asked Jan 16 at 22:49
MLearner
161
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41854
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41854
edited May 8 at 6:56
Rodrigo de Azevedo
12.8k41854
12.8k41854
asked Jan 16 at 22:49
MLearner
161
asked Jan 16 at 22:49
MLearner
161
asked Jan 16 at 22:49
MLearner
161
161
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32
add a comment |
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32
If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32
add a comment |
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If you know that the matrix has low rank that puts more constraints on how the entries relate to each other. As a simple example, if you know that two rows must sum up to a third row, that implies a bunch of linear equations between the entries in those rows that fill in some of the entries if you know the others.
– Qiaochu Yuan
Jan 16 at 23:32