Multiple discriminant analysis

Multiple Discriminant Analysis (MDA) is a multivariate dimensionality reduction technique. It has been used to predict signals as diverse as neural memory traces and corporate failure.[1]

MDA is not directly used to perform classification. It merely supports classification by yielding a compressed signal amenable to classification. The method described in Duda et al. (2001) §3.8.3 projects the multivariate signal down to an M−1 dimensional space where M is the number of categories.

MDA is useful because most classifiers are strongly affected by the curse of dimensionality. In other words, when signals are represented in very-high-dimensional spaces, the classifier's performance is catastrophically impaired by the overfitting problem. This problem is reduced by compressing the signal down to a lower-dimensional space as MDA does.

MDA has been used to reveal neural codes.[2][3]

References
  1. Duda R, Hart P, Stork D (2001) Pattern Classification, Second Edition. New York, NY, Uand Sons.
  2. Lin L et al. (2005) Identification of network-level coding units for real-time representation of episodic experiences in the hippocampus. PNAS 102(17):6125-6130.
  3. Lin L, Osan R, and Tsien JZ (2006) Organizing principles of real-time memory encoding: neural clique assemblies and universal neural codes. Trends in Neurosciences 29(1):48-57.


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