Package 'Coreset'

Description

DropAdd() selects a maximally-dispersed subset of k points using the DropAdd tabu search algorithm, which comprises a greedy construction followed by a first-in, first-out drop-add tabu search, with streamlined neighbour-evaluation tricks (algorithms 1–4 in Porumbel et al. 2011).

Usage

DropAdd(
  k,
  d = NULL,
  plateau = 5000L,
  maxSeconds = Inf,
  points = NULL,
  maxCandidates = 46340L,
  seed = NULL,
  N = NULL
)

Arguments

Value

DropAdd() returns an integer vector of length k containing the selected indices, sorted ascending, with attributes:

score

numeric specifying the achieved MaxMin objective $\min_{i \ne j \in S} d_{ij}$.

secondary

numeric specifying the achieved (upper triangle) sum of pairwise distances over $S$.

seconds

numeric specifying wall-clock seconds spent.

iters

integer specifying main-loop iterations executed, excluding the construction phase.

The vector has class "MaxMinSelection" and prints as a one-line summary (see print.MaxMinSelection()).

Progress bar

In interactive sessions, status messages are shown. To toggle, set options("Coreset.progress" = FALSE) (or TRUE).

Parallelism

To parallelize computation when OpenMP is available, set the "mc.cores" option:

options(mc.cores = 2L)                       # use a fixed number of cores
options(mc.cores = parallel::detectCores())  # or all available cores

Distance function

When d is a function, d(i) must return the distances from element i to every element (length N, with the self-distance ignored), or to every element except i (length N - 1, in order). N is required, and memory is $O(N)$. This suits metrics where no stored matrix or coordinate embedding is available.

Because d is typically called many times; specifying a distance matrix (where memory permits) is likely to require less calculation than multiple calls to d, unless d implements efficient caching.

References

Porumbel D, Hao J, Glover F (2011). “A simple and effective algorithm for the MaxMin diversity problem.” Annals of Operations Research, 186, 275–293. doi:10.1007/s10479-011-0898-z.

Examples

set.seed(1)
pts <- matrix(rnorm(200), ncol = 2)
DropAdd(5L, dist(pts))

# Composable coreset: thin to 40 candidates with farthest-first, then run
# DropAdd on the coreset. Returned indices are original-space row indices.
suppressWarnings(DropAdd(5L, points = pts, maxCandidates = 40L))

# Disable thinning on the full problem
DropAdd(5L, points = pts, maxCandidates = 0L)

# Distance function; `cache` memoizes the columns to reduce computation.
data("USArrests")
ArrestDist <- function(dat) {
  scaled <- scale(as.matrix(dat))                 # derived once
  cache <- new.env(parent = emptyenv())
  function(i) {
    key <- as.character(i)
    if (is.null(cache[[key]])) {
      cache[[key]] <- sqrt(rowSums(sweep(scaled, 2, scaled[i, ], "-") ^ 2))
    }
    cache[[key]]
  }
}
arrests <- USArrests[, c("Murder", "Assault", "Rape")]
idx <- DropAdd(4L, ArrestDist(arrests), N = nrow(arrests), plateau = 200L)
USArrests[idx, ]

Description

ExactKCentre() finds an optimal solution to the discrete k-centre problem.

Usage

ExactKCentre(k, d, maxSeconds = 60)

ExactKCenter(k, d, maxSeconds = 60)

Arguments

Details

The optimum covering radius is the smallest threshold r, over the achieved distinct distances, for which k centres can cover every point within r.

Each probe asks whether k centres cover every point within a candidate radius. This is decided combinatorially via unit propagation and dominance reduction, then an exhaustive component-wise search. The search is warm-started from the KCentre() radius, then bisects downwards.

Value

ExactKCentre() returns an integer vector of length $\le k$ listing the chosen centres in ascending order. It has class c("KCentreExact", "KCentreSelection") and attributes:

radius

The covering radius achieved; the proven optimum when proven is TRUE, otherwise an upper bound.

proven

Logical: TRUE if optimality is certified.

seconds

Wall-clock seconds elapsed.

N, k

Instance size and centre budget.

Progress bar

In interactive sessions, a progress indicator is shown. To toggle, set options("Coreset.progress" = FALSE) (or TRUE).

See Also

KCentre() for the fast near-optimal heuristic; ExactMaxMin() for the dual MMDP optimum.

Examples

set.seed(1)
pts <- matrix(rnorm(40), ncol = 2)
d <- dist(pts)
ExactKCentre(3L, d)

Description

ExactMaxMin() finds the optimal solution to the Max-Min Diversity Problem (discrete p-dispersion) by iterated node-packing (Sayyady and Fathi 2016) (which may be slow or intractable on large sets).

Usage

ExactMaxMin(
  k,
  d,
  maxSeconds = 60,
  warmStart = NULL,
  nStart = 1L,
  graspPlateau = 50L,
  dropPlateau = 512L,
  boundSeconds = 0,
  upper = Inf
)

Arguments

Details

The search is warm-started from a heuristic lower bound (the best of nStart Grasp() restarts and a DropAdd() pass), then gallops upward from that bound to the first infeasible threshold and bisects the resulting bracket.

To parallelize computation when OpenMP is available, set the "mc.cores" option:

options(mc.cores = 2L)                       # use a fixed number of cores
options(mc.cores = parallel::detectCores())  # or all available cores

Parallelization returns identical results under a given seed.

Value

ExactMaxMin() returns an integer vector of length k (sorted ascending) with class "MaxMinSelection", carrying attributes:

score

The minimum pairwise distance within the selection. When proven is TRUE this is the optimum; otherwise a lower bound.

proven

Logical: TRUE if the search certified optimality within the budget, FALSE if it returned an unproven incumbent.

upper

An upper bound on the optimum: the largest distance below the smallest threshold proven infeasible, and no greater than the upper argument. Equals score when proven is TRUE.

seconds

Wall-clock seconds elapsed.

N, k

Instance size and target subset size.

Prints as a terse summary via print.MaxMinSelection().

Progress bar

In interactive sessions, a progress indicator is shown. To toggle, set options("Coreset.progress" = FALSE) (or TRUE).

References

Sayyady F, Fathi Y (2016). “An integer programming approach for solving the p-dispersion problem.” European Journal of Operational Research, 253(1), 216–225. doi:10.1016/j.ejor.2016.02.026.

Examples

set.seed(1)
pts <- matrix(rnorm(18), ncol = 2)
ExactMaxMin(3L, dist(pts))

Description

ExactMaxSum() finds the optimal solution to the Max-Sum Diversity Problem (the "maximum diversity problem"): it selects the k points that maximizes the total pairwise distance between points. As the problem is NP-hard, it is feasible only for small sets.

Usage

ExactMaxSum(k, d, maxSeconds = 30, warmStart = NULL)

Arguments

Details

The solver uses per-node integer-program linearisation (Kuo et al. 1993), starting from a multi-start 1-swap local search, whose result is returned when optimality cannot be proven within maxSeconds.

Value

ExactMaxSum() returns an integer vector of length k, sorted ascending, with class "MaxSumSelection", carrying attributes:

score

Numeric specifying the achieved total pairwise distance within the selection. When proven is TRUE this is the optimum; otherwise a lower bound.

proven

Logical: TRUE if optimality was certified.

seconds, N, k

Numerics reporting the wall-clock seconds elapsed; instance size; and target size.

References

Kuo C, Glover F, Dhir KS (1993). “Analyzing and modeling the maximum diversity problem by zero-one programming.” Decision Sciences, 24(6), 1171–1185. doi:10.1111/j.1540-5915.1993.tb00509.x.

Examples

set.seed(1)
pts <- matrix(rnorm(20), ncol = 2)
# Package 'highs' is required for ExactMaxSum
if (requireNamespace("highs", quietly = TRUE)) {
  ExactMaxSum(3L, dist(pts))
}

Description

Greedy farthest-first selection (González 1985; Hochbaum and Shmoys 1985) iteratively selects the point furthest from the current selection to yield a 2-approximation to the k-centre and Max Min Diversity problems.

Usage

FarFirst(
  k,
  d = NULL,
  points = NULL,
  N = NULL,
  strategy = "random_furthest",
  nSeeds = 3L
)

Arguments

Value

FarFirst() returns an integer vector with class MaxMinSelection, listing the selected indices in the order they were selected. Attributes report:

• score: the selection's minimum pairwise distance ($T_k$).

• winning_strategy: character vector listing strategies that attained the optimal score.

• strategy_results: results for each strategy.

Progress bar

In interactive sessions, the distance-column path shows a progress bar. To toggle, set options("Coreset.progress" = FALSE) (or TRUE).

Parallelism

To parallelize computation when OpenMP is available, set the "mc.cores" option:

options(mc.cores = 2L)                       # use a fixed number of cores
options(mc.cores = parallel::detectCores())  # or all available cores

The main use case for parallelization is when nSeeds is a multiple of mc.cores, so each seed point can be evaluated in parallel.

References

González TF (1985). “Clustering to minimize the maximum intercluster distance.” Theoretical Computer Science, 38, 293–306. doi:10.1016/0304-3975(85)90224-5.

Hochbaum DS, Shmoys DB (1985). “A best possible heuristic for the $k$-center problem.” Mathematics of Operations Research, 10(2), 180–184. doi:10.1287/moor.10.2.180.

See Also

PickPoint() for the seed indices alone; DropAdd() and ExactMaxMin() for higher-effort solvers.

Examples

set.seed(1)
pts <- matrix(rnorm(60), ncol = 2)
d <- dist(pts)

# Default: best of three random-furthest starts (set.seed for reproducibility):
FarFirst(5L, d)

# More random-furthest starts:
FarFirst(5L, d, nSeeds = 15L)

# Custom two-anchor ensemble:
FarFirst(5L, d, strategy = c("diameter", "anti_medoid"))

# A single strategy:
FarFirst(5L, d, strategy = "diameter")

# An explicit start index (integer strategy):
FarFirst(5L, d, strategy = 1L)

# Matrix-free coordinate path (identical result, O(N) memory):
FarFirst(5L, points = pts, strategy = 1L)

# Distance-column oracle: supply one column at a time, never the full matrix.
data("USArrests")
arrestTypes <- USArrests[, c("Murder", "Assault", "Rape")]
StateDist <- function(i) {
  diffs <- sweep(arrestTypes, 2, unlist(arrestTypes[i, ]), "-")
  sqrt(rowSums(diffs ^ 2))
}
idx <- FarFirst(4L, StateDist, N = nrow(arrestTypes), strategy = 1L)
arrestTypes[idx, ]

Description

Grasp() solves the Max-Min Diversity Problem (discrete p-dispersion) with the static variant of the GRASP / path-relinking metaheuristic (Resende et al. 2010, fig. 4). This expensive heuristic often attains high-quality selections.

Usage

Grasp(
  k,
  d,
  plateau = 100L,
  eliteSize = 10L,
  alpha = 0.8,
  maxSeconds = Inf,
  maxCandidates = 2000L
)

Arguments

Details

The GRASP with path-relinking algorithm conducts a randomised-greedy construction with extended-improvement local search builds; it identifies an elite set, then conducts a single pass of path relinking over all elite pairs (Resende et al. 2010).

The refinement loop stops after plateau consecutive GRASP iterations fail to improve the best elite objective, or once maxSeconds have elapsed.

This method will fail if the complete $N \times N$ distance matrix is too large to fit into memory.

Value

Grasp() returns an integer vector of length k specifying the indices of the selected points, with attributes:

score

Achieved MaxMin objective $T_k$.

seconds

Wall-clock seconds spent.

iters

Number of GRASP refinement iterations executed.

pr_calls

Number of path-relinking pair-applications run.

The vector has class "MaxMinSelection" and prints as a one-line summary (see print.MaxMinSelection()).

Parallelism

To parallelize computation when OpenMP is available, set the "mc.cores" option:

options(mc.cores = 2L)                       # use a fixed number of cores
options(mc.cores = parallel::detectCores())  # or all available cores

Progress bar

In interactive sessions, a bar tracks how close the search is to its plateau stopping criterion, snapping back each time a better solution is found. To toggle, set options("Coreset.progress" = FALSE) (or TRUE).

References

Resende MGC, Martí R, Gallego M, Duarte A (2010). “GRASP and path relinking for the max-min diversity problem.” Computers & Operations Research, 37(3), 498–508. doi:10.1016/j.cor.2008.05.011.

See Also

DropAdd() for scalable refinement; ExactMaxMin() for the proven optimum on small instances.

Examples

set.seed(1)
pts <- matrix(rnorm(60), ncol = 2)
Grasp(5L, dist(pts), plateau = 20L, eliteSize = 4L)

# Composable coreset: thin to 20 candidates with farthest-first, then run
# GRASP on the coreset. Returned indices are original-space row indices.
suppressWarnings(Grasp(5L, dist(pts), plateau = 20L, maxCandidates = 20L))

Description

KCentre() selects $k$ elements (centres) so as to minimize the largest distance from any point to its nearest centre (the covering radius), using the Critical Dominating Set heuristic (CDSh) (García-Díaz et al. 2017; García-Díaz et al. 2019).

Usage

KCentre(k, d, nstart = 1L, effort = 1L)

KCenter(k, d, nstart = 1L, effort = 1L)

Arguments

Details

On the benchmark instances of García-Díaz et al. (2019), the CDS heuristic reaches roughly 1–3.5% of the optimum at $O(N^2 \log N)$, far tighter than FarFirst().

Despite this good performance in practice, the CDSh is a 3-approximation. To guard against occasional cases where a better candidate is missed, KCentre() runs by default an exhaustive search of a small candidate grid (for n up to ~150); and an additional FarFirst() pass (controlled via the effort argument). These safeguards ensure that KCentre() always returns at least a 2-approximation.

Value

KCentre() returns an integer vector of length $\le k$ specifying the chosen centres in ascending order. The achieved covering radius is attached as attribute radius. The vector has class "KCentreSelection" and prints as a one-line summary.

References

García-Díaz J, Menchaca-Méndez R, Menchaca-Méndez R, Pomares Hernández S, Pérez-Sansalvador JC, Lakouari N (2019). “Approximation algorithms for the vertex $k$-center problem: survey and experimental evaluation.” IEEE Access, 7, 109228–109245. doi:10.1109/ACCESS.2019.2933875.

García-Díaz J, Sánchez-Hernández J, Menchaca-Méndez R, Menchaca-Méndez R (2017). “When a worse approximation factor gives better performance: a 3-approximation algorithm for the vertex $k$-center problem.” Journal of Heuristics, 23(5), 349–366. doi:10.1007/s10732-017-9345-x.

González TF (1985). “Clustering to minimize the maximum intercluster distance.” Theoretical Computer Science, 38, 293–306. doi:10.1016/0304-3975(85)90224-5.

See Also

ExactKCentre() for the proven optimum; KCentreRadius() for a selection's score; FarFirst() for the González (1985) 2-approximation baseline.

Examples

set.seed(1)
pts <- matrix(rnorm(120), ncol = 2)
d <- dist(pts)
centres <- KCentre(5L, d)
KCentreRadius(d, centres)
# Results will beat a Gonzalez 2-approximation:
KCentreRadius(d, FarFirst(5L, d, nSeeds = 1))

Description

KCentreRadius() computes the covering radius of a set of centres: the largest distance from any of the N points to its nearest centre, $R = \max_p \min_{c \in \mathrm{idx}} d(p, c)$. This is the min-max k-centre objective (González 1985) minimized by KCentre() and ExactKCentre().

Usage

KCentreRadius(d = NULL, idx, points = NULL)

KCenterRadius(d = NULL, idx, points = NULL)

Arguments

Value

KCentreRadius() returns a numeric denoting the covering radius.

References

González TF (1985). “Clustering to minimize the maximum intercluster distance.” Theoretical Computer Science, 38, 293–306. doi:10.1016/0304-3975(85)90224-5.

See Also

KCentre() and ExactKCentre() (which minimise this); MinDist() for the complementary MMDP objective.

Examples

set.seed(1)
pts <- matrix(rnorm(60), ncol = 2)
d <- dist(pts)
centres <- KCentre(4L, d)
KCentreRadius(d, centres)

Description

MaxEntropy() selects the k points that maximise the log-determinant of their kernel block, $\log\det K_S$. This is equivalent to finding the set of k points that span the largest volume, which corresponds to the maximum-entropy sampling criterion (Shewry and Wynn 1987) and the maximum-a-posteriori mode of a determinantal point process (Kulesza and Taskar 2012).

Usage

MaxEntropy(
  k,
  d,
  sigma = NULL,
  repair = c("clip", "shift", "truncate"),
  exact = NA,
  maxCombos = 300000L
)

Arguments

Details

A radial-basis kernel $K_{ij} = \exp(-d_{ij}^2 / 2\sigma^2)$ is built from the supplied distances and repaired to a positive-semidefinite matrix. The exact argmax is NP-hard (Kulesza and Taskar 2012). A greedy approximation is built by pivoted Cholesky, adding at each step the point of largest residual conditional variance. Ties are broken by selecting the more peripheral point.

Large instances run faster when R is linked to an optimised BLAS, such as OpenBLAS, Intel MKL or Apple Accelerate.

Value

MaxEntropy() returns an integer vector of length k (sorted ascending) with class "MaxEntropySelection", carrying attributes:

score

The retained $\log\det K_S$ of the selection. -Inf is returned for a degenerate selection where k exceeds the number of distinct points.

negMass

Fraction of spectral mass removed by the positive semi-definite repair.

sigma, repair, exact

The bandwidth, repair, and whether the optimum was certified by enumeration.

seed, N, k

The peripheral seed index, instance size, target size.

References

Kulesza A, Taskar B (2012). “Determinantal point processes for machine learning.” Foundations and Trends in Machine Learning, 5(2–3), 123–286. doi:10.1561/2200000044.

Shewry MC, Wynn HP (1987). “Maximum entropy sampling.” Journal of Applied Statistics, 14(2), 165–170. doi:10.1080/02664768700000020.

Examples

set.seed(1)
pts <- matrix(rnorm(40), ncol = 2)
MaxEntropy(4L, dist(pts))

Description

MaxMean() selects a maximally dispersed subset of elements from a pairwise distance matrix, maximising the max-mean objective:

$f(S) = \frac{\displaystyle\sum_{i < j,\, i,j \in S} d_{ij}}{|S|}$

The number of elements in the subset $|S| \ge 2$ is chosen so as to maximise the mean dispersion.

Usage

MaxMean(d, maxSeconds = 0.1, maxIter = 1000, useRL = TRUE)

Arguments

Details

MaxMean() implements the reinforcement-learning tabu search algorithm of (Nijimbere et al. 2020). An initial solution is constructed randomly for the first restart and via $Q$-learning thereafter; each initial solution is then refined by a tabu search using one-flip moves (adding or removing one element per step). Restarts continue until either the maxSeconds or maxIter budget is reached.

The reinforcement-learning and tabu hyperparameters are fixed at the tuned values reported by Nijimbere et al. (2020): greedy factor $\epsilon = 0.7$, learning rate $\alpha = 0.5$, discount $\gamma = 0.5$, maximum tabu tenure 120, search depth 50 000.

Value

MaxMean() returns an integer vector of selected 1-based indices (sorted ascending) with class "MaxMeanSelection" and attributes:

score

numeric, achieved objective $\sum_{i<j \in S} d_{ij} / |S|$.

size

integer, number of selected elements $|S|$.

seconds

numeric, wall-clock seconds spent.

iters

numeric, total tabu-search iterations across restarts.

The vector has class "MaxMeanSelection" and prints as a one-line summary (see print.MaxMeanSelection()); it is otherwise an ordinary integer vector that indexes the distance matrix directly.

Progress bar

In interactive sessions, status messages are shown. To toggle, set options("Coreset.progress" = FALSE) (or TRUE).

References

Nijimbere D, Zhao S, Gu X, Esangbedo MO, Dominique N (2020). “Tabu search guided by reinforcement learning for the max-mean dispersion problem.” Journal of Industrial & Management Optimization, 17, 3223–3254. doi:10.3934/jimo.2020115.

See Also

MeanDist() to score an arbitrary selection under this objective; FarFirst(), DropAdd() and Grasp() for fixed-cardinality max-min solvers.

Examples

# The max-mean problem is defined for signed dissimilarities; with these the
# optimal subset has an interior size, chosen to maximise mean dispersion.
set.seed(1)
x <- matrix(runif(100, -5, 5), 10)
d <- (x + t(x)) / 2          # symmetric, signed
selection <- MaxMean(d)
selection                    # 5 of the 10 elements: {2, 5, 6, 8, 10}
MeanDist(d, selection)       # 2.714 — equals attr(selection, "score")

Description

MeanDist() reports the sum of pairwise distances divided by the number of selected elements,

$f(S) = \frac{\displaystyle\sum_{i < j,\, i,j \in S} d_{ij}}{|S|}$

, the objective maximised by MaxMean().

Usage

MeanDist(d, idx)

Arguments

Value

MeanDist() returns a numeric scalar, or NA_real_ if length(idx) < 2.

See Also

MaxMean() which maximises this objective; MinDist() for the max-min (MMDP) analogue.

Examples

# The max-mean problem is defined for signed dissimilarities; with these the
# optimal subset has an interior size, chosen to maximise mean dispersion.
set.seed(1)
x <- matrix(runif(100, -5, 5), 10)
d <- (x + t(x)) / 2          # symmetric, signed
selection <- MaxMean(d)
selection                    # 5 of the 10 elements: {2, 5, 6, 8, 10}
MeanDist(d, selection)       # 2.714 — equals attr(selection, "score")

Description

Returns the minimum pairwise distance among selected points $T_k$. A set of points that is more dispersed will exhibit a higher value.

Usage

MinDist(d = NULL, idx, points = NULL)

Arguments

Details

The solvers in this package (FarFirst(), DropAdd(), Grasp()) already attach the achieved $T_k$ as a score attribute. MinDist() allows arbitrary selections to be scored, or an existing selection to be scored against a different distance matrix.

Value

MinDist() returns a numeric specifying the minimum distance between two selected points (or NA_real_, if length(idx) < 2).

See Also

FarFirst(), DropAdd(), Grasp() and ExactMaxMin().

Examples

set.seed(1)
pts <- matrix(rnorm(60), ncol = 2)
d <- dist(pts)
MinDist(d, FarFirst(5L, d))

Description

PickPoint() implements a range of strategies to select a seed for greedy farthest-first selection. Propitious seeds yield better solutions.

Usage

PickPoint(
  d = NULL,
  points = NULL,
  strategy = c("peripheral", "anti_centroid", "random_furthest", "diameter",
    "anti_medoid", "medoid", "rowsum", "rownorm"),
  N = NULL,
  nSeeds = 1L
)

Arguments

Value

PickPoint() returns an integer that identifies the index of a proposed seed in d or points; under "random_furthest" with nSeeds > 1, up to nSeeds distinct indices, in ascending order.

See Also

FarFirst(), which seeds and runs the greedy pass in one call.

Examples

set.seed(1)
pts <- matrix(rnorm(60), ncol = 2)
d <- dist(pts)
PickPoint(d, strategy = "diameter")
FarFirst(5L, d, strategy = PickPoint(d, strategy = "diameter"))

# Seeds for three starts, from distances computed one column at a time.
# The seeds drawn are identical to those selected by FarFirst().
Column <- function(i) sqrt(colSums((t(pts) - pts[i, ]) ^ 2))
set.seed(2)
PickPoint(Column, strategy = "random_furthest", N = nrow(pts), nSeeds = 3)
set.seed(2)
FarFirst(5L, Column, N = nrow(pts), strategy = "random_furthest", nSeeds = 3)

Description

Terse summaries of the objects returned by the Coreset solvers.

Usage

## S3 method for class 'MaxMinSelection'
format(x, ...)

## S3 method for class 'MaxMinSelection'
print(x, ...)

Arguments

Value

print.Coreset() returns x, invisibly. It is called for its side-effect of printing format(x) to the console. format.Coreset() returns a character string reporting the selection size, the selected indices, the algorithm (and if applicable strategy or proof status), and the achieved $T_k$.

See Also

Other reporting functions: print.KCentre, print.MaxEntropy, print.MaxMeanSelection(), print.MaxSum, summary.Coreset

Examples

set.seed(1)
pts <- matrix(rnorm(60), ncol = 2)
print(FarFirst(5L, dist(pts)))

Description

Terse summaries of the objects returned by KCentre() ("KCentreSelection") and ExactKCentre() ("KCentreExact")

Usage

## S3 method for class 'KCentreSelection'
format(x, ...)

## S3 method for class 'KCentreSelection'
print(x, ...)

## S3 method for class 'KCentreExact'
format(x, ...)

## S3 method for class 'KCentreExact'
print(x, ...)

Arguments

Value

print.KCentre() returns x, invisibly. It is called for its side-effect of printing format(x) to the console. format.KCentre() returns a character string describing a KCentreSelection; it reports the centre count, the chosen indices, the method, and the achieved covering radius (with proof status for the exact solver).

See Also

Other reporting functions: print.Coreset, print.MaxEntropy, print.MaxMeanSelection(), print.MaxSum, summary.Coreset

Examples

set.seed(1)
KCentre(4L, dist(matrix(rnorm(60), ncol = 2)))

Description

Terse summary of the object returned by MaxEntropy() ("MaxEntropySelection"), reporting the retained log-determinant ($\log\det K_S$, the maxdet objective) and the magnitude of the positive-semidefinite repair.

Usage

## S3 method for class 'MaxEntropySelection'
format(x, ...)

## S3 method for class 'MaxEntropySelection'
print(x, ...)

Arguments

Value

format.MaxEntropySelection() returns a one-line character summary; print.MaxEntropySelection() returns x invisibly, called for its side-effect.

See Also

Other reporting functions: print.Coreset, print.KCentre, print.MaxMeanSelection(), print.MaxSum, summary.Coreset

Examples

set.seed(1)
MaxEntropy(4L, dist(matrix(rnorm(40), ncol = 2)))

Description

Terse one-line and detailed summaries of the objects returned by MaxMean().

Usage

## S3 method for class 'MaxMeanSelection'
format(x, ...)

## S3 method for class 'MaxMeanSelection'
print(x, ...)

## S3 method for class 'MaxMeanSelection'
summary(object, ...)

Arguments

Value

print.MaxMeanSelection() returns x, invisibly. format.MaxMeanSelection() returns a character string reporting the selection size, the selected indices, and the achieved max-mean objective $f(S)$.

See Also

Other reporting functions: print.Coreset, print.KCentre, print.MaxEntropy, print.MaxSum, summary.Coreset

Examples

set.seed(1)
pts <- matrix(rnorm(60), ncol = 2)
print(MaxMean(dist(pts), maxSeconds = 1))

Description

Terse summary of the object returned by ExactMaxSum() ("MaxSumSelection"), reporting the achieved total pairwise distance (the max-sum objective) rather than the minimum distance of ExactMaxMin().

Usage

## S3 method for class 'MaxSumSelection'
format(x, ...)

## S3 method for class 'MaxSumSelection'
print(x, ...)

Arguments

Value

format.MaxSumSelection() returns a one-line character summary; print.MaxSumSelection() returns x invisibly, called for its side-effect.

See Also

Other reporting functions: print.Coreset, print.KCentre, print.MaxEntropy, print.MaxMeanSelection(), summary.Coreset

Examples

set.seed(1)
# Package 'highs' is required for ExactMaxSum()
if (requireNamespace("highs", quietly = TRUE)) {
  ExactMaxSum(3L, dist(matrix(rnorm(20), ncol = 2)))
}

Description

A fuller counterpart to print.MaxMinSelection(): the one-line headline, followed by the achieved objective(s), search effort, and – for a FarFirst() ensemble – the per-strategy $T_k$ table.

Usage

## S3 method for class 'MaxMinSelection'
summary(object, ...)

Arguments

Value

summary.Coreset() returns object, invisibly.

See Also

Other reporting functions: print.Coreset, print.KCentre, print.MaxEntropy, print.MaxMeanSelection(), print.MaxSum

Examples

set.seed(1)
pts <- matrix(rnorm(60), ncol = 2)
summary(FarFirst(5L, dist(pts)))