matrix decomposition (not quite non-negative matrix decomposition)
I'm interested in finding a good approximation of the mxn matrix $Y$ as $Yapprox XB$ where the mxn matrix $X$ has only non-negative elements and $B$ is an invertable nxn matrix. Are there algorithms available for this task?
Context: I am trying to classify a set of images containing n atoms that are either in a fluorescing or non-fluorescing state. The matrix $Y$ results from a principal component analysis of pixel correlations and contains the $n$ most relevant eigenvectors. These eigenvectors enable a dimensional reduction by projecting images onto $Y$; however, I'm not really interested in representing an image as a linear superposition of a few eigenvectors but rather as a linear superposition of n (non-orthogonal) vectors, each of which representing exactly one atom in the fluorescing state; these vectors only have non-negative elements.
matrix-decomposition
asked Dec 9 '18 at 23:31
felix
11
add a comment |
I'm interested in finding a good approximation of the mxn matrix $Y$ as $Yapprox XB$ where the mxn matrix $X$ has only non-negative elements and $B$ is an invertable nxn matrix. Are there algorithms available for this task?
Context: I am trying to classify a set of images containing n atoms that are either in a fluorescing or non-fluorescing state. The matrix $Y$ results from a principal component analysis of pixel correlations and contains the $n$ most relevant eigenvectors. These eigenvectors enable a dimensional reduction by projecting images onto $Y$; however, I'm not really interested in representing an image as a linear superposition of a few eigenvectors but rather as a linear superposition of n (non-orthogonal) vectors, each of which representing exactly one atom in the fluorescing state; these vectors only have non-negative elements.
matrix-decomposition
asked Dec 9 '18 at 23:31
felix
11
add a comment |
I'm interested in finding a good approximation of the mxn matrix $Y$ as $Yapprox XB$ where the mxn matrix $X$ has only non-negative elements and $B$ is an invertable nxn matrix. Are there algorithms available for this task?
Context: I am trying to classify a set of images containing n atoms that are either in a fluorescing or non-fluorescing state. The matrix $Y$ results from a principal component analysis of pixel correlations and contains the $n$ most relevant eigenvectors. These eigenvectors enable a dimensional reduction by projecting images onto $Y$; however, I'm not really interested in representing an image as a linear superposition of a few eigenvectors but rather as a linear superposition of n (non-orthogonal) vectors, each of which representing exactly one atom in the fluorescing state; these vectors only have non-negative elements.
matrix-decomposition
asked Dec 9 '18 at 23:31
felix
11
I'm interested in finding a good approximation of the mxn matrix $Y$ as $Yapprox XB$ where the mxn matrix $X$ has only non-negative elements and $B$ is an invertable nxn matrix. Are there algorithms available for this task?
Context: I am trying to classify a set of images containing n atoms that are either in a fluorescing or non-fluorescing state. The matrix $Y$ results from a principal component analysis of pixel correlations and contains the $n$ most relevant eigenvectors. These eigenvectors enable a dimensional reduction by projecting images onto $Y$; however, I'm not really interested in representing an image as a linear superposition of a few eigenvectors but rather as a linear superposition of n (non-orthogonal) vectors, each of which representing exactly one atom in the fluorescing state; these vectors only have non-negative elements.
matrix-decomposition
matrix-decomposition
asked Dec 9 '18 at 23:31
felix
11
asked Dec 9 '18 at 23:31
felix
11
asked Dec 9 '18 at 23:31
felix
11
asked Dec 9 '18 at 23:31
felix
11
asked Dec 9 '18 at 23:31
felix
11
11
add a comment |
add a comment |
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