Struct GraphSampling 

pub struct GraphSampling {
    pub bandwidth: usize,
}

Optimal graph signal sampling set selection.

Selects a set of k nodes from which a k-bandlimited graph signal can be uniquely reconstructed. The greedy algorithm maximises the cut-off frequency achievable from the selected nodes by greedily picking nodes that maximise the determinant (volume) of the submatrix formed by the k smoothest eigenvectors restricted to the sampling set.

The greedy maximisation of the log-determinant is equivalent to maximising the minimum singular value of the restricted eigenvector matrix, which directly determines the stability of the reconstruction.

Fields

bandwidth: usize

Number of frequency components (bandwidth) of the signal.

Implementations

impl GraphSampling

pub fn new(bandwidth: usize) -> Self

Create a GraphSampling instance for signals with bandwidth components.

pub fn greedy_sampling_set( &self, gft: &GraphFourierTransform, ) -> Result<Vec<usize>>

Greedy sampling set selection.

Returns a list of bandwidth node indices that form a valid sampling set (i.e. the restriction of the first bandwidth eigenvectors to these rows has full column rank).

The algorithm iteratively adds the node that maximises the volume (log-det of Aᵀ A where A is the current restricted eigenvector submatrix). This is a classic D-optimal experimental design step.

pub fn is_valid_sampling_set( &self, gft: &GraphFourierTransform, set: &[usize], tol: f64, ) -> Result<bool>

Check whether a given node set is a valid bandwidth-sampling set, i.e. the restricted eigenvector matrix has full column rank.

Validity is checked by verifying that the minimum singular value of the restricted matrix exceeds tol.

Trait Implementations

impl Clone for GraphSampling

fn clone(&self) -> GraphSampling

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for GraphSampling

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

Formats the value using the given formatter.