Non-negative matrix factorization: Difference between revisions

Revision as of 09:33, 4 May 2023

Revision as of 20:09, 21 May 2023

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=== Online NMF ===

Many standard NMF algorithms analyze all the data together; i.e., the whole matrix is available from the start. This may be unsatisfactory in applications where there are too many data to fit into memory or where the data are provided in [[Data stream|streaming]] fashion. One such use is for [[collaborative filtering]] in [[recommender system|recommendation systems]], where there may be many users and many items to recommend, and it would be inefficient to recalculate everything when one user or one item is added to the system. The cost function for optimization in these cases may or may not be the same as for standard NMF, but the algorithms need to be rather different.<ref>http://www.ijcai.org/papers07/Papers/IJCAI07-432.pdf {{Bare URL PDF|date=March 2022}}</ref><ref>{{cite book|url=http://dl.acm.org/citation.cfm?id=1339264.1339709|title=Online Discussion Participation Prediction Using Non-negative Matrix Factorization |first1=Yik-Hing|last1=Fung|first2=Chun-Hung|last2=Li|first3=William K.|last3=Cheung|date=2 November 2007|publisher=IEEE Computer Society|pages=284–287|via=dl.acm.org|isbn=9780769530284|series=Wi-Iatw '07}}</ref><ref>{{Cite journal |author=Naiyang Guan|author2=Dacheng Tao|author3=Zhigang Luo|author4=Bo Yuan|name-list-style=amp|date=July 2012|title=Online Nonnegative Matrix Factorization With Robust Stochastic Approximation|journal=IEEE Transactions on Neural Networks and Learning Systems |issue=7 |doi=10.1109/TNNLS.2012.2197827|pmid=24807135|volume=23|pages=1087–1099|s2cid=8755408}}</ref>

=== Convolutional NMF ===

If the columns of {{math|'''V'''}} represent data sampled over spatial or temporal dimensions, e.g. time signals, images, or video, features that are equivariant w.r.t. shifts along these dimensions can be learned by Convolutional NMF. In this case, {{math|'''W'''}} is sparse with columns having local non-zero weight windows that are shared across shifts along the spatio-temporal dimensions of {{math|'''V'''}}, representing [[Kernel (image processing)|convolution kernels]]. By spatio-temporal pooling of {{math|'''H'''}} and repeatedly using the resulting representation as input to convolutional NMF, deep feature hierarchies can be learned.<ref>{{Cite journal |last=Behnke |first=S. |date=2003 |title=Discovering hierarchical speech features using convolutional non-negative matrix factorization |url=https://ieeexplore.ieee.org/document/1224004 |journal=Proceedings of the International Joint Conference on Neural Networks, 2003. |___location=Portland, Oregon USA |publisher=IEEE |volume=4 |pages=2758–2763 |doi=10.1109/IJCNN.2003.1224004 |isbn=978-0-7803-7898-8|s2cid=3109867 }}</ref>