Struct RandomWalkKernel 

pub struct RandomWalkKernel {
    pub lambda: f64,
    pub max_steps: usize,
}

Random Walk kernel for graphs

Fields

lambda: f64

max_steps: usize

Implementations

impl RandomWalkKernel

pub fn new(lambda: f64, max_steps: usize) -> Self

pub fn compute_graph_kernel(&self, g1: &Graph, g2: &Graph) -> f64

Compute the random-walk graph kernel (Gärtner / Kashima et al.).

The geometric random-walk kernel between graphs G1 and G2 is

K(G1, G2) = Σ_{i,j} [ (I - λ A_×)^{-1} ]_{ij}

where A_× is the adjacency matrix of the direct (tensor) product graph G1 × G2, whose nodes are pairs (u, v) with u ∈ G1, v ∈ G2, and A_×[(u,v),(u',v')] = A1[u,u'] · A2[v,v']. The closed form sums the geometric series Σ_t λ^t A_×^t = (I - λ A_×)^{-1} over all start/end pairs (uniform start/stop probabilities).

We form A_× of size (n1·n2) × (n1·n2), then solve the linear system (I - λ A_×) s = 1 for s and return Σ_i s_i. The kernel is well-defined when λ < 1 / ρ(A_×); if the system is singular or the product graph is empty we fall back to 0.0.

Trait Implementations

impl Clone for RandomWalkKernel

fn clone(&self) -> RandomWalkKernel

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for RandomWalkKernel

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.