Multiple Discriminant Analysis (MDA) is a multivariate
dimensionality reduction
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally ...
technique. It has been used to predict signals as diverse as
neural
In biology, the nervous system is the highly complex part of an animal that coordinates its actions and sensory information by transmitting signals to and from different parts of its body. The nervous system detects environmental changes th ...
memory traces and corporate failure.
MDA is not directly used to perform classification. It merely supports
classification Classification is a process related to categorization, the process in which ideas and objects are recognized, differentiated and understood.
Classification is the grouping of related facts into classes.
It may also refer to:
Business, organizat ...
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
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. Th ...
. In other words, when signals are represented in very-high-dimensional spaces, the classifier's performance is catastrophically impaired by the
overfitting
mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". An overfitt ...
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.
[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.]
References
External links
DefinitionNCSU faculty
Statistical classification
Classification algorithms
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