Euclidean Distance and Attribute Vectors Data Mining Short Question

Description

Let ??and ??be the attribute vectors of two objects. State whether the following proximity measurescosine, correlation, and Euclidean distanceare 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.

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