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by Homunculiheaded
4153 days ago
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I have a running joke with my machine learning friends that I will write a Data Science/ML book titled "A Thousand Ways to Say 'Singular Value Decomposition'". The number of papers and techniques out there that are SVD with a few minor tweaks and a unique philosophical interpretation of SVD is hilarious. Here are some examples: Principal Component Analysis - SVD does dimensionality reduction where some n% of variance should be accounted for. One layer Autoencoder - SVD done by a neural network Latent Semantic Analysis - SVD on td-idf matrix we interrupt lower dimensions as having semantic importance Matrix Factorization - SVD only now we interrupt lower dimensions as representing latent variables Collaborative Filtering - SVD where we interrupt lower dimensions as representing latent variables AND we use a a distance measure to determine similarity. |
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Not necessarily. Any serious user of autoencoders would apply some kind of L1 regularization or other sparsity constraint to the coefficients learned, so that the autoencoder does not learn the principal components of the data but instead learns an analogous sparse decomposition of the data (with the assumption that sparse representations have better generalization power).
Also I don't think any of the techniques you mentioned is being passed as "not SVD" by its practitioners. People know they're SVD. These names are just used as labels for use cases of SVD, each with their specific (and crucial) bells and whistles. And yes, these labels are useful.
Cognition is fundamentally dimensionality reduction over a space of information, so clearly most ML algorithms are going to be isomorphic to SVD in some way. More interesting to me are the really non-obvious ways in which that is happening (eg. RNNs learning word embeddings with skip-gram are actually factorizing a matrix of pairwise mutual information of words over a local context...)
That doesn't make these algorithms any less valuable.