Sliced inverse regression
Sliced inverse regression (SIR) is a tool for dimension reduction in the field of multivariate statistics.
In statistics, regression analysis is a popular way of studying the relationship between a response variable y and its explanatory variable , which is a p-dimensional vector. There are several approaches which come under the term of regression. For example parametric methods include multiple linear regression; non-parametric techniques include local smoothing.
With high-dimensional data (as p grows), the number of observations needed to use local smoothing methods escalates exponentially. Reducing the number of dimensions makes the operation computable. Dimension reduction aims to show only the most important directions of the data. SIR uses the inverse regression curve, to perform a weighted principal component analysis, with which one identifies the effective dimension reducing directions.
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