step cleansingintegratingand transforming data transforming the input variables greatly simplifies the estimation problem other times you might want to combine two variables into new variable reducing the number of variables sometimes you have too many variables and need to reduce the number because they don' add new information to the model having too many variables in your model makes the model difficult to handleand certain techniques don' perform well when you overload them with too many input variables for instanceall the techniques based on euclidean distance perform well only up to variables euclidean distance euclidean distance or "ordinarydistance is an extension to one of the first things anyone learns in mathematics about triangles (trigonometry)pythagoras' leg theorem if you know the length of the two sides next to the deg angle of right-angled triangle you can easily derive the length of the remaining side (hypotenusethe formula for this is hypotenuse side side the euclidean distance between two points in two-dimensional plane is calculated using similar formuladistance if you want to expand this distance calculation to more dimensionsadd the coordinates of the point within those higher dimensions to the formula for three dimensions we get distance data scientists use special methods to reduce the number of variables but retain the maximum amount of data we'll discuss several of these methods in figure shows how reducing the number of variables makes it easier to understand the component ( % - - - - - - - - component ( % figure variable reduction allows you to reduce the number of variables while maintaining as much information as possible