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)
