Non-negative matrix factorization: Difference between revisions

Revision as of 03:39, 25 January 2022

Revision as of 08:39, 30 January 2022

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When the orthogonality constraint <math> \mathbf{H}\mathbf{H}^T = I </math> is not explicitly imposed, the orthogonality holds to a large extent, and the clustering property holds too. Clustering is the main objective of most [[data mining]] applications of NMF.{{citation needed|date=April 2015}}

When the error function to be used is [[Kullback–Leibler divergence]], NMF is identical to the [[Probabilistic latent semantic analysis]], a popular document clustering method.<ref>{{cite journal |vauthors=Ding C, Li Y, Peng W |url=http://users.cis.fiu.edu/~taoli/pub/NMFpLSIequiv.pdf |title=On the equivalence between non-negative matrix factorization and probabilistic latent semantic indexing |archive-url=https://web.archive.org/web/20160304070027/http://users.cis.fiu.edu/~taoli/pub/NMFpLSIequiv.pdf |archive-date=2016-03-04 |url-status=dead |journal=Computational Statistics & Data Analysis |year=2008 |volume=52 |issue=8 |pages=3913-39273913–3927|doi=10.1016/j.csda.2008.01.011 }}</ref>

== Types ==

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Arora, Ge, Halpern, Mimno, Moitra, Sontag, Wu, & Zhu (2013) have given polynomial-time algorithms to learn topic models using NMF. The algorithm assumes that the topic matrix satisfies a separability condition that is often found to hold in these settings.<ref name=Arora2013 />

Hassani, Iranmanesh and Mansouri (2019) proposed a feature agglomeration method for term-document matrices which operates using NMF. The algorithm reduces the term-document matrix into a smaller matrix more suitable for text clustering.<ref>{{cite arxivarXiv|last1=Hassani|first1=Ali|last2=Iranmanesh|first2=Amir|last3=Mansouri|first3=Najme|date=2019-11-12|title=Text Mining using Nonnegative Matrix Factorization and Latent Semantic Analysis|eprint=1911.04705|class=cs.LG}}</ref>

=== Spectral data analysis ===

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| title = Algorithms and Applications for Approximate Nonnegative Matrix Factorization

|journal=Computational Statistics & Data Analysis |volume=52 |issue=1 |date=15 September 2007 |pages=155–173

|doi=10.1016/j.csda.2006.11.006 }}</ref>

}}</ref>

=== Scalable Internet distance prediction ===

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| last1 = Ding|last2 = Li|last3 = Peng|last4 = Park

| title = Orthogonal nonnegative matrix t-factorizations for clustering

| journal = Proceedings of the 12th ACM SIGKDD internationalInternational conferenceConference on Knowledge discoveryDiscovery and dataData miningMining

| year = 2006

| pages = 126&ndash;135

| doi = 10.1145/1150402.1150420

|isbn = 1595933395|s2cid = 165018}}</ref> as been use for drug repurposing tasks in order to predict novel protein targets and therapeutic indications for approved drugs <ref>{{Cite journal

| last1 = Ceddia|last2 = Pinoli|last3 = Ceri|last4 = Masseroli

| title = Matrix factorization-based technique for drug repurposing predictions

| journal = IEEE journalJournal of biomedicalBiomedical and healthHealth informaticsInformatics

| year = 2020

|volume = 24|issue = 11| pages = 3162&ndash;3172

| doi = 10.1109/JBHI.2020.2991763

|pmid = 32365039|s2cid = 218504587}}</ref> and to infer pair of synergic anticancer drugs.<ref>{{Cite journal

| last1 = Pinoli|last2 = Ceddia|last3 = Ceri|last4 = Masseroli

| title = Predicting drug synergism by means of non-negative matrix tri-factorization

| journal = IEEE/ACM Transactions on Computational Biology and Bioinformatics

| year = 2021

|volume = PP|page = 1| doi = 10.1109/TCBB.2021.3091814

|pmid = 34166199|s2cid = 235634059}}</ref>

}}</ref>

=== Nuclear imaging ===