Linear separation in 2-way partitioning. clustering a collection of vectors into k = 2 groups is called 2-way partitioning, since we are partitioning the vectors into 2 groups, with index sets g1 and g2. suppose we run k-means, with k = 2, on the n-vectors x1, . . , xn . show that there is a nonzero vector w and a scalar v that satisfy wtxi +v≥0fori∈g1, wtxi +v≤0fori∈g2. in other words, the affine function f (x) = wt x + v is greater than or equal to zero on the first group, and less than or equal to zero on the second group. this is called linear separation of the two groups (although affine separation would be more accurate). then, draw a representative picture and indicate where the vector w is in the picture. hint. consider the function ∥x − z2∥2 − ∥x − z1∥2, where z1 and z2 are the group representatives.