A negative semi-definite (nsd) kernel is a symmetric functionk : X × X → R such that for all finite n-element sets X ⊆ X and for all vectors (2) Whereas positive semi-definite kernels correspond to inner products in a Hilbert space F, negative semi-definite kernels correspond to squared distances.
ifk(x, y) = 0 only when x = y then k is a metric.