Sliced inverse regression (SIR) is a tool for dimensionality reduction in the field of multivariate statistics.[1]
In statistics, regression analysis is a method of studying the relationship between a response variable y and its input variable , which is a p-dimensional vector. There are several approaches in the category of regression. For example, parametric methods include multiple linear regression, and non-parametric methods include local smoothing.
As the number of observations needed to use local smoothing methods scales exponentially with high-dimensional data (as p grows), reducing the number of dimensions can make the operation computable. Dimensionality reduction aims to achieve this by showing only the most important dimension of the data. SIR uses the inverse regression curve, , to perform a weighted principal component analysis.
^Li, Ker-Chau (1991). "Sliced Inverse Regression for Dimension Reduction". Journal of the American Statistical Association. 86 (414): 316–327. doi:10.2307/2290563. ISSN 0162-1459.
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