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Apply a Metric Graph Low-Pass Filter Path

Source: R/metric_graph_lowpass.R
apply.metric.graph.lowpass.path.Rd

Applies every requested low-pass parameter to one response or a matrix of responses using a reusable spectral basis.

Usage

apply.metric.graph.lowpass.path(
  basis,
  y,
  eta.grid,
  filter.type = c("heat_kernel", "tikhonov", "cubic_spline", "gaussian", "exponential",
    "butterworth"),
  block.size = NULL,
  truncation.tol = 1e-04,
  unresolved.action = c("warn", "error", "allow"),
  exact.zero = TRUE
)

Arguments

basis

A "metric.graph.lowpass.basis" object.

y

Numeric response vector or matrix with one row per graph vertex.

eta.grid

Numeric filter-parameter grid.

filter.type

Spectral low-pass filter family.

block.size

Optional number of response columns processed together.

truncation.tol

Positive tolerance smaller than one used to classify truncated-basis candidates as spectrally resolved.

unresolved.action

Action when a truncated-basis candidate exceeds truncation.tol: "warn", "error", or "allow".

exact.zero

Logical. For heat filtering, return the input exactly at eta = 0. This avoids treating a truncated spectral projection as the identity.

Value

A list of class "metric.graph.lowpass.path". For one response, fitted.values is an \(N\) by \(J\) matrix. For multiple responses it is an \(N\) by \(J\) by \(S\) array.

Examples

adj <- list(2L, c(1L, 3L), c(2L, 4L), 3L)
lengths <- list(1, c(1, 1), c(1, 1), 1)
basis <- metric.graph.lowpass.basis(adj, lengths, n.eigenpairs = 4L,
                                    eigen.solver = "dense")
apply.metric.graph.lowpass.path(basis, 1:4, eta.grid = c(0, 0.1, 1))
#> $fitted.values
#>      0.0      0.1      1.0
#> [1,]   1 1.095310 1.687464
#> [2,]   2 2.004388 2.167428
#> [3,]   3 2.995612 2.832572
#> [4,]   4 3.904690 3.312536
#> 
#> $eta.grid
#> [1] 0.0 0.1 1.0
#> 
#> $filter.type
#> [1] "heat_kernel"
#> 
#> $effective.df
#> [1] 4.000000 3.472594 1.724905
#> 
#> $resolution
#>   eta retained.cutoff.weight spectrally.resolved exact.identity
#> 1 0.0             1.00000000                TRUE           TRUE
#> 2 0.1             0.71075936                TRUE          FALSE
#> 3 1.0             0.03290227                TRUE          FALSE
#> 
#> $n.responses
#> [1] 1
#> 
#> $response.names
#> NULL
#> 
#> $basis
#> $graph
#> $graph$n.vertices
#> [1] 4
#> 
#> $graph$n.edges
#> [1] 3
#> 
#> $graph$adj.list
#> $graph$adj.list[[1]]
#> [1] 2
#> 
#> $graph$adj.list[[2]]
#> [1] 1 3
#> 
#> $graph$adj.list[[3]]
#> [1] 2 4
#> 
#> $graph$adj.list[[4]]
#> [1] 3
#> 
#> 
#> $graph$weight.list
#> $graph$weight.list[[1]]
#> [1] 1
#> 
#> $graph$weight.list[[2]]
#> [1] 1 1
#> 
#> $graph$weight.list[[3]]
#> [1] 1 1
#> 
#> $graph$weight.list[[4]]
#> [1] 1
#> 
#> 
#> 
#> $operator
#> $graph
#> $graph$n.vertices
#> [1] 4
#> 
#> $graph$n.edges
#> [1] 3
#> 
#> $graph$adj.list
#> $graph$adj.list[[1]]
#> [1] 2
#> 
#> $graph$adj.list[[2]]
#> [1] 1 3
#> 
#> $graph$adj.list[[3]]
#> [1] 2 4
#> 
#> $graph$adj.list[[4]]
#> [1] 3
#> 
#> 
#> $graph$weight.list
#> $graph$weight.list[[1]]
#> [1] 1
#> 
#> $graph$weight.list[[2]]
#> [1] 1 1
#> 
#> $graph$weight.list[[3]]
#> [1] 1 1
#> 
#> $graph$weight.list[[4]]
#> [1] 1
#> 
#> 
#> 
#> $edge.table
#>   u v length conductance
#> 1 1 2      1           1
#> 2 2 3      1           1
#> 3 3 4      1           1
#> 
#> $conductance
#> $conductance$rule
#> [1] "inverse.length.power"
#> 
#> $conductance$values
#> [1] 1 1 1
#> 
#> $conductance$local.scales
#> [1] NA NA NA NA
#> 
#> $conductance$summary
#> $conductance$summary$min
#> [1] 1
#> 
#> $conductance$summary$q10
#> [1] 1
#> 
#> $conductance$summary$median
#> [1] 1
#> 
#> $conductance$summary$q90
#> [1] 1
#> 
#> $conductance$summary$max
#> [1] 1
#> 
#> $conductance$summary$mean
#> [1] 1
#> 
#> $conductance$summary$n.nonfinite
#> [1] 0
#> 
#> $conductance$summary$n.clipped
#> [1] 0
#> 
#> 
#> 
#> $degree
#> [1] 1 2 2 1
#> 
#> $laplacian
#> $laplacian$dim
#> [1] 4 4
#> 
#> $laplacian$i
#>  [1] 0 1 0 1 2 1 2 3 2 3
#> 
#> $laplacian$j
#>  [1] 0 0 1 1 1 2 2 2 3 3
#> 
#> $laplacian$x
#>  [1]  1 -1 -1  2 -1 -1  2 -1 -1  1
#> 
#> $laplacian$matrix
#> 4 x 4 sparse Matrix of class "dgCMatrix"
#>                 
#> [1,]  1 -1  .  .
#> [2,] -1  2 -1  .
#> [3,]  . -1  2 -1
#> [4,]  .  . -1  1
#> 
#> 
#> $laplacian.type
#> [1] "unnormalized"
#> 
#> $parameters
#> $parameters$conductance.epsilon
#> [1] 1e-08
#> 
#> $parameters$conductance.alpha
#> [1] 1
#> 
#> $parameters$conductance.sigma
#> [1] NA
#> 
#> $parameters$conductance.sigma.rule
#> [1] "edge.quantile"
#> 
#> $parameters$conductance.sigma.quantile
#> [1] 0.75
#> 
#> $parameters$conductance.local.k
#> [1] 5
#> 
#> $parameters$laplacian.type
#> [1] "unnormalized"
#> 
#> 
#> $diagnostics
#> $diagnostics$degree.summary
#> $diagnostics$degree.summary$min
#> [1] 1
#> 
#> $diagnostics$degree.summary$q10
#> [1] 1
#> 
#> $diagnostics$degree.summary$median
#> [1] 1.5
#> 
#> $diagnostics$degree.summary$q90
#> [1] 2
#> 
#> $diagnostics$degree.summary$max
#> [1] 2
#> 
#> $diagnostics$degree.summary$mean
#> [1] 1.5
#> 
#> $diagnostics$degree.summary$n.nonfinite
#> [1] 0
#> 
#> $diagnostics$degree.summary$n.clipped
#> [1] 0
#> 
#> 
#> $diagnostics$length.summary
#> $diagnostics$length.summary$min
#> [1] 1
#> 
#> $diagnostics$length.summary$q10
#> [1] 1
#> 
#> $diagnostics$length.summary$median
#> [1] 1
#> 
#> $diagnostics$length.summary$q90
#> [1] 1
#> 
#> $diagnostics$length.summary$max
#> [1] 1
#> 
#> $diagnostics$length.summary$mean
#> [1] 1
#> 
#> $diagnostics$length.summary$n.nonfinite
#> [1] 0
#> 
#> $diagnostics$length.summary$n.clipped
#> [1] 0
#> 
#> 
#> 
#> attr(,"class")
#> [1] "metric.graph.lowpass.operator" "list"                         
#> 
#> $conductance
#> $conductance$rule
#> [1] "inverse.length.power"
#> 
#> $conductance$values
#> [1] 1 1 1
#> 
#> $conductance$local.scales
#> [1] NA NA NA NA
#> 
#> $conductance$summary
#> $conductance$summary$min
#> [1] 1
#> 
#> $conductance$summary$q10
#> [1] 1
#> 
#> $conductance$summary$median
#> [1] 1
#> 
#> $conductance$summary$q90
#> [1] 1
#> 
#> $conductance$summary$max
#> [1] 1
#> 
#> $conductance$summary$mean
#> [1] 1
#> 
#> $conductance$summary$n.nonfinite
#> [1] 0
#> 
#> $conductance$summary$n.clipped
#> [1] 0
#> 
#> 
#> 
#> $laplacian
#> $laplacian$dim
#> [1] 4 4
#> 
#> $laplacian$i
#>  [1] 0 1 0 1 2 1 2 3 2 3
#> 
#> $laplacian$j
#>  [1] 0 0 1 1 1 2 2 2 3 3
#> 
#> $laplacian$x
#>  [1]  1 -1 -1  2 -1 -1  2 -1 -1  1
#> 
#> $laplacian$matrix
#> 4 x 4 sparse Matrix of class "dgCMatrix"
#>                 
#> [1,]  1 -1  .  .
#> [2,] -1  2 -1  .
#> [3,]  . -1  2 -1
#> [4,]  .  . -1  1
#> 
#> 
#> $laplacian.type
#> [1] "unnormalized"
#> 
#> $spectral
#> $spectral$eigenvalues
#> [1] -7.244401e-17  5.857864e-01  2.000000e+00  3.414214e+00
#> 
#> $spectral$eigenvectors
#>      [,1]       [,2] [,3]       [,4]
#> [1,] -0.5 -0.6532815 -0.5  0.2705981
#> [2,] -0.5 -0.2705981  0.5 -0.6532815
#> [3,] -0.5  0.2705981  0.5  0.6532815
#> [4,] -0.5  0.6532815 -0.5 -0.2705981
#> 
#> $spectral$backend
#> [1] "dense"
#> 
#> $spectral$n.vertices
#> [1] 4
#> 
#> $spectral$n.eigenpairs
#> [1] 4
#> 
#> $spectral$is.complete
#> [1] TRUE
#> 
#> $spectral$largest.retained.eigenvalue
#> [1] 3.414214
#> 
#> $spectral$smallest.positive.eigenvalue
#> [1] 0.5857864
#> 
#> $spectral$omitted.attenuation.bound.type
#> [1] "complete_spectrum"
#> 
#> 
#> $parameters
#> $parameters$conductance.rule
#> [1] "inverse.length.power"
#> 
#> $parameters$conductance.epsilon
#> [1] 1e-08
#> 
#> $parameters$conductance.alpha
#> [1] 1
#> 
#> $parameters$conductance.sigma
#> [1] NaN
#> 
#> $parameters$conductance.sigma.rule
#> [1] "edge.quantile"
#> 
#> $parameters$conductance.sigma.quantile
#> [1] 0.75
#> 
#> $parameters$conductance.local.k
#> [1] 5
#> 
#> $parameters$laplacian.type
#> [1] "unnormalized"
#> 
#> $parameters$verbose
#> [1] FALSE
#> 
#> $parameters$n.eigenpairs
#> [1] 4
#> 
#> $parameters$eigen.solver
#> [1] "dense"
#> 
#> $parameters$dense.eigen.threshold
#> [1] 200
#> 
#> $parameters$dense.fallback.threshold
#> [1] 5000
#> 
#> $parameters$dense.fallback
#> [1] "auto"
#> 
#> 
#> attr(,"class")
#> [1] "metric.graph.lowpass.basis" "list"                      
#> 
#> $parameters
#> $parameters$block.size
#> [1] NA
#> 
#> $parameters$truncation.tol
#> [1] 1e-04
#> 
#> $parameters$unresolved.action
#> [1] "warn"
#> 
#> $parameters$exact.zero
#> [1] TRUE
#> 
#> 
#> attr(,"class")
#> [1] "metric.graph.lowpass.path" "list"