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Non-negative matrix factorization (NMF)

Non-negative matrix factorization (NMF)

A matrix factorization method where all of the values in matrices are constrained to be non-negative so that they are easier to inspect. It is useful in data mining because it has the effect of clustering the input data.

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Daniel Frumkin"Changed to use more general terms."
Daniel Frumkin edited on 12 Mar 2019 3:05 pm
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Several NMF variants have been shown to be well-performing alternatives to clustering algorithms.



Several NMF variants have been shown to be well-performing alternatives to clustering algorithms. Clustering, or cluster analysis, is an unsupervised learning problem. Clustering algorithms aim to find partitioningsgroups of a data set such that the similarity within each partitiongroup is maximized and the similarity between different partitionsgroups is minimized. 

Daniel Frumkin
Daniel Frumkin edited on 12 Mar 2019 2:49 pm
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Several NMF variants have been shown to be well-performing alternatives to clusteringclustering algorithms.

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Daniel Frumkin"Added original journal entry and creators"
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Daniel D. Lee

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H. Sebastian Seung

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Author
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Learning the parts of objects by non-negative matrix factorization

Daniel D. Lee, H. Sebastian Seung

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Daniel Frumkin"Added section on clustering"
Daniel Frumkin edited on 11 Mar 2019 9:06 pm
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One of the common techniques used to perform matrix factorization is called gradient descent, which itself has many variations such as SGD, Momentum method, Adagrad, Adadelta, RMSprop, Adam, and others.



One of the common techniques used to perform matrix factorization is called gradient descent, which itself has many variations such as SGD, Momentum method, Adagrad, Adadelta, RMSprop, Adam, and others. Another widely used technique is singular value decomposition (SVD), which includes the Funk SVD, SVD++, Iterative SVD, Regularized SVD, and Asymmetric SVD algorithms. Funk SVD was first introduced in a 2006 blog post by Simon Funk titled Netflix Update: Try This at Home, in which Funk outlined a method that could be used by Netflix to recommend relevant shows and movies to its users.

NMF Methods for Clustering

Several NMF variants have been shown to be well-performing alternatives to clustering algorithms.



Clustering, or cluster analysis, is an unsupervised learning problem. Clustering algorithms aim to find partitionings of a data set such that the similarity within each partition is maximized and the similarity between different partitions is minimized. 

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Researchers have developed a variety of difference methods in applying NMF for clustering, including Sparse NMF, Projective NMF, Non-negative Spectral Clustering, and Cluster-NMF.

Daniel Frumkin"Added citation"
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One of the common techniques used to perform matrix factorization is called gradient descent, which itself has many variations such as SGD, Momentum method, Adagrad, Adadelta, RMSprop, Adam, and others. Another widely used technique is singular value decomposition (SVD), which includes the Funk SVD, SVD++, Iterative SVD, Regularized SVD, and Asymmetric SVD algorithms. Funk SVD was first introduced in a 2006 blog post by Simon Funk titled Netflix Update: Try This at Home, in which Funk outlined a method that could be used by Netflix to recommend relevant shows and movies to its users.

Daniel Frumkin"Corrected inaccuracy and added information"
Daniel Frumkin edited on 11 Mar 2019 8:40 pm
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The technique used to actually perform the matrix factorization is called gradient descent, which itself has many variations such as SGD, Momentum method, Adagrad, Adadelta, RMSprop, Adam, and others.

One of the common techniques used to perform matrix factorization is called gradient descent, which itself has many variations such as SGD, Momentum method, Adagrad, Adadelta, RMSprop, Adam, and others. Another widely used technique is singular value decomposition (SVD), which includes the Funk SVD, SVD++, Iterative SVD, Regularized SVD, and Asymmetric SVD algorithms. Funk SVD was first introduced in a 2006 blog post by Simon Funk titled Netflix Update: Try This at Home, in which Funk outlined a method that could be used by Netflix to recommend relevant shows and movies to its users.

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Title
Author
Link
Type

Netflix Update: Try This at Home

Simon Funk

Web

Michael Mangus
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Non-negative matrix factorization (NMF)

A matrix factorization method where all of the values in matrices are constrained to be non-negative so that they are easier to inspect. It is useful in data mining because it has the effect of clustering the input data.

Edits on 10 Mar 2019
Daniel Frumkin
Daniel Frumkin edited on 10 Mar 2019 12:20 pm
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Non-negative matrix factorization Non-negative matrix factorization (NMF)

A matrix factorization method where all of the values in matrices are constrained to be non-negative so that they are easier to inspect. It is useful in data mining because it has the effect of clustering the input data.

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Non-negative matrix factorization (NMF)

A matrix factorization method where all of the values in matrices are constrained to be nonnegativenon-negative so that they are easier to inspect.

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NonnegativeNon-negative Matrix Factorization (NMF or NNMF) is a matrix factorization method where theall of values in matrices are constrained to be nonnegativenon-negative so that they are easier to inspect.



Matrix factorization is also sometimes referred to as matrix decomposition because it is the process of taking one matrix (V) and finding two smaller matrices (W and H) such that their product approximates the original matrix. 



When NMF is used in machine learning, W is the weights matrix and H is the features matrix. This means that W has a column for each feature and a row for each row in the original matrix, while H has a row for each feature and a column for each column in the original matrix. The dot product of W and H then produces the sum of the latent features by the weights for each element in the original matrix.



The utility of NMF in machine learning is that it can be used to predict values that were zero values in the original matrix. NMF is closely related to both supervised learning and unsupervised learning methodologies, particularly the latter. 



The technique used to actually perform the matrix factorization is called gradient descent, which itself has many variations such as SGD, Momentum method, Adagrad, Adadelta, RMSprop, Adam, and others.

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Edits on 9 Mar 2019
Daniel Frumkin"Added image, description, resources, category, and related topics."
Daniel Frumkin edited on 9 Mar 2019 8:58 pm
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Non-negative matrix factorization (NMF)

A matrix factorization method where the matrices are constrained to be nonnegative.

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Nonnegative Matrix Factorization (NMF) is a matrix factorization method where the matrices are constrained to be nonnegative.

Further reading

Title
Author
Link
Type

A Practical Introduction to NMF (nonnegative matrix factorization)



Web

Beginners Guide to Non-Negative Matrix Factorization

Benjamin Bengfort

Web

Documentaries, videos and podcasts

Title
Date
Link

10701: Non-Negative Matrix Factorization

December 11th, 2013

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 Non-negative matrix factorization

A matrix factorization method where all of the values in matrices are constrained to be non-negative so that they are easier to inspect. It is useful in data mining because it has the effect of clustering the input data.

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