Yes, that is reasonable. Thank you!28.09.2014, 19:45, "Alexandre Gramfort" <alexandre.gramf...@telecom-paristech.fr>:hi,
I am trying to make the K-SVD implementation consistent with the existing
sparse coding algorigthms (dict_learning and orthogonal_mp) and I am a bit
confused by the notations. I'll give a summary of the notations and explain
what I am not understanding.
1) sklearn.decomposition.dict_learning
Problem: X ~ CD, where
X : (n_samples, n_features) - training samples (as rows);
D : (n_components, n_features) - dictionary;
C : (n_samples, n_components) - sparse codes.
In the sparse coding papers the common notation is the following: X ~ DC,
where
X : (n_features_1, n_samples) - training samples (as columns);
D : (n_features_1, n_features_2) - dictionary;
C : (n_features_2, n_samples) - sparse codes.
If I understand correctly, the training samples are placed as rows for the
consistency with the rest of the library and machine learning papers'
notation. So all the matrices are just transposed and everything is ok.yes
2) sklearn.linear_model.orthogonal_mp
Problem: y ~ Xc, where
y : (n_samples,) - the input vector;
X : (n_samples, n_features) - dictionary;
c : (n_features,) - the sparse code.
Sparse coding papers notation: y ~ Xc, where
y : (n_features_1,) - the input vector;
X : (n_features_1, n_features_2) - dictionary;
c : (n_features_2,) - the sparse code.
To the contrary to the dict_learning function the matrices are not
transposed and the input vector is a column. Additionaly, the same entity
(features_1) is named differently in dict_learning (features) and
orthogonal_mp (samples).yes it's expected. orthogonal_mp is a standard regression model
so X is n_samples, n_features.
my advise is transpose the matrices as needed to keep the same API
as dictionary learning code.
A
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