Editing Linear discriminant analysis (section)

==Incremental LDA==
The typical implementation of the LDA technique requires that all the samples are available in advance. However,  there are situations where the entire data set is not available and the input data are observed as a stream. In this case, it is desirable for the LDA feature extraction to have the ability to update the computed LDA features by observing the new samples without running the algorithm on the whole data set. For example, in many real-time applications such as mobile robotics or on-line face recognition, it is important to update the extracted LDA features as soon as new observations are available. An LDA feature extraction technique that can update the LDA features by simply observing new samples is an ''incremental LDA algorithm'', and this idea has been extensively studied over the last two decades.<ref name=":0">{{Cite journal|title = Fast incremental LDA feature extraction|journal = Pattern Recognition|date = 2015-06-01|pages = 1999–2012|volume = 48|issue = 6|doi = 10.1016/j.patcog.2014.12.012|first1 = Youness|last1 = Aliyari Ghassabeh|first2 = Frank|last2 = Rudzicz|first3 = Hamid Abrishami|last3 = Moghaddam|bibcode = 2015PatRe..48.1999A}}</ref> Chatterjee and Roychowdhury proposed an incremental self-organized LDA algorithm for updating the LDA features.<ref name=":1">{{Cite journal|title = On self-organizing algorithms and networks for class-separability features|journal = IEEE Transactions on Neural Networks|date = 1997-05-01|issn = 1045-9227|pages = 663–678|volume = 8|issue = 3|doi = 10.1109/72.572105|pmid = 18255669|first1 = C.|last1 = Chatterjee|first2 = V.P.|last2 = Roychowdhury}}</ref> In other work, Demir and Ozmehmet proposed online local learning algorithms for updating LDA features incrementally using error-correcting and the Hebbian learning rules.<ref>{{Cite journal|title = Online Local Learning Algorithms for Linear Discriminant Analysis|journal = Pattern Recognit. Lett.|date = 2005-03-01|issn = 0167-8655|pages = 421–431|volume = 26|issue = 4|doi = 10.1016/j.patrec.2004.08.005|first1 = G. K.|last1 = Demir|first2 = K.|last2 = Ozmehmet|bibcode = 2005PaReL..26..421D}}</ref> Later, Aliyari et al. derived fast incremental algorithms to update the LDA features by observing the new samples.<ref name=":0" />