Computer Science Homework Help

Let and be the attribute vectors of two objects. State whether the following proximity measures—cosine, correlation, and Euclidean distance—are invariant (unchanged) under the following transformations. Specifically, if → ′ and → ′, would cosine( , ) = cosine( ′, ′), correlation( , ) = correlation( ′, ′), and Euclidean( , ) = Euclidean( ′, ′). Please explain your answers by referring to the formula for each proximity measure. Simple yes or no would not be accepted.

I.Translation: → + and → + , where is a constant added to each attribute value in and .

II.Scaling: → and → , where is a constant multiplied to each attribute value in and .

III.Standardization: →(x – c)/d and →(y – c)/d where and are constants.