xvi Notation
Notation
U, u Domain, point on domain
x, x(u) ∈X(U, C) Signal on the domain of the form x : U →C
f (x) ∈F(X) Functions on signals on the domain of the form f :
X(U, C) →Y (when domain U and target C are clear from
the context)
G, g Group, element of the group
g.u, ρ(g) Group action, group representation
X ∈C
|U|×s
Matrix representing a signal on a discrete domain
x
u
∈C
s
Vector representing a discrete domain signal X on element
u ∈U
x
uj
∈C Scalar representing the jth component of a discrete domain
signal X on element u ∈U
F(X) Function on discrete domain signals that returns another
discrete domain signal, as a matrix
τ : U →U Automorphism of the domain
η : U →U
′
Isomorphism between two different domains
σ : C →C
′
Activation function (point-wise non-linearity)
G = (V, E) Graph with nodes V and edges E
M= (V, E, F) Mesh with nodes V, edges E, and faces F
x ⋆ θ Convolution with filter θ
S
v
Shift operator
φ
i
Basis function
T
u
U, TU Tangent space at u, tangent bundle
X ∈T
u
U Tangent vector
g
u
(X, Y) = ⟨X, Y⟩
u
Riemannian metric
ℓ(γ), ℓ
uv
Length of a curve γ, discrete metric on edge (u, v)
