Requiring number of data samples in order to learn a dictionary
$begingroup$
I have a sparse representation problem where I have the linear model
$ mathbf{x} approx DA $,
where $D$ $in$ $mathbb{R}^{N times K}$ is the dictionary I want to learn and $A=[alpha_{1}, ..., alpha_{M}]$ $in$ $mathbb{R}^{K times M}$ is a matrix of representations of x $in$ $mathbb{R}^{N times M}$. x is the observation data with sparsity level $L$ (means that $|| mathbf{x}||_{0} leq L)$. We have an underdetermined system which means that $N<K$.
What is the absolute requirement of samples (how big does $M$ have to be) in order to be able to learn $D$?
machine-learning sparse-matrices
$endgroup$
add a comment |
$begingroup$
I have a sparse representation problem where I have the linear model
$ mathbf{x} approx DA $,
where $D$ $in$ $mathbb{R}^{N times K}$ is the dictionary I want to learn and $A=[alpha_{1}, ..., alpha_{M}]$ $in$ $mathbb{R}^{K times M}$ is a matrix of representations of x $in$ $mathbb{R}^{N times M}$. x is the observation data with sparsity level $L$ (means that $|| mathbf{x}||_{0} leq L)$. We have an underdetermined system which means that $N<K$.
What is the absolute requirement of samples (how big does $M$ have to be) in order to be able to learn $D$?
machine-learning sparse-matrices
$endgroup$
add a comment |
$begingroup$
I have a sparse representation problem where I have the linear model
$ mathbf{x} approx DA $,
where $D$ $in$ $mathbb{R}^{N times K}$ is the dictionary I want to learn and $A=[alpha_{1}, ..., alpha_{M}]$ $in$ $mathbb{R}^{K times M}$ is a matrix of representations of x $in$ $mathbb{R}^{N times M}$. x is the observation data with sparsity level $L$ (means that $|| mathbf{x}||_{0} leq L)$. We have an underdetermined system which means that $N<K$.
What is the absolute requirement of samples (how big does $M$ have to be) in order to be able to learn $D$?
machine-learning sparse-matrices
$endgroup$
I have a sparse representation problem where I have the linear model
$ mathbf{x} approx DA $,
where $D$ $in$ $mathbb{R}^{N times K}$ is the dictionary I want to learn and $A=[alpha_{1}, ..., alpha_{M}]$ $in$ $mathbb{R}^{K times M}$ is a matrix of representations of x $in$ $mathbb{R}^{N times M}$. x is the observation data with sparsity level $L$ (means that $|| mathbf{x}||_{0} leq L)$. We have an underdetermined system which means that $N<K$.
What is the absolute requirement of samples (how big does $M$ have to be) in order to be able to learn $D$?
machine-learning sparse-matrices
machine-learning sparse-matrices
edited Dec 15 '18 at 17:47
Johan Abrahamsson
asked Dec 15 '18 at 15:10
Johan AbrahamssonJohan Abrahamsson
63
63
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