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.23
References
References
- Duda R, Hart P, Stork D (2001) Pattern Classification, Second Edition. New York, NY, Uand Sons.
- 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.
- 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.