I am reading
Bishop - Pattern Recognition and Machine Learning book. In Chapter 4 first page, there is a statement that
In this chapter, we consider linear models for classification, by which we mean that the decision surfaces are linear functions of the input vector x and hence are defined by (D − 1)-dimensional hyper planes within the D-dimensional input space.
If the input vector is of
D dimensions then the decision boundary should also be of
D dimensions. Why is it
D-1? For example, in 2-D plane, the line separating the points is also a straight line which is of 2 dimensions.
Am I thinking something terribly wrong? Can anyone explain me how is it
D-1 dimensions for decision boundary?