Parametric Data Reduction Techniques

Definition

A parametric data reduction technique is a data reduction technique that assumes a certain model for the data. The model contains some parameters and the technique fits the data into the model to determine the parameters. Then data reduction can be performed.

Key Points

Parametric data reduction (PDR) techniques is opposite to nonparametric data reduction (NDR) techniques. A model with parameters is used in a PDR technique and therefore some computation is required to determine these parameters, which may be costly. However, if a PDR technique is well-chosen, it may result in much more data reduction than NDR techniques. A representative example is linear regression [3]. Linear regression assumes that the data fall on a straight line, expressed by the following formula

$$ \mathrm{Y}=\mathrm{a}+\mathrm{bX} $$

(1)

Given a set of points (Assuming two dimensions.) {〈x₁, y₁〉, 〈x₂, y₂〉,…}, parameters a and b in Eq. (1) are determined from the points using the least squares...