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R/select.distance.R

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#'
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#' \subsection{Medoid-like Representative Sampling by Minimal Mean
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#' Distance}{Selects medoid-like representatives as accessions with the
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#' smallest average distance to all others within the group.
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#' smallest average distance to all others within the group
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#' \insertCite{kaufman_clustering_1987,kaufman_finding_1990}{SampleCore}.
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#'
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#' For each accession \mjseqn{g}, the mean distance to all other accessions
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#' \mjseqn{h} is computed as:
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#'
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#' Selects medoid-like representatives as accessions with the smallest median
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#' distance to all others within the group. This method is less influenced by
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#' outliers.
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#' outliers
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#' \insertCite{kaufman_clustering_1987,kaufman_finding_1990}{SampleCore}.
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#'
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#' For each accession \mjseqn{g}, the median distance to all other accessions
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#' \mjseqn{h} is computed as:
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#' \subsection{Representative Sampling by Proximity to Group
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#' Centroid}{Selects accessions closest to the group centroid in principal
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#' coordinate space, computed via multivariate dispersion analysis using
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#' \code{\link[vegan]{betadisper}}.
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#' \code{\link[vegan]{betadisper}}
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#' \insertCite{anderson_distance-based_2006,anderson_multivariate_2006}{SampleCore}.
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#'
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#' The distance of each accession \mjseqn{g} to the group centroid \mjseqn{C}
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#' in PCoA space is:
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#' \subsection{Representative Sampling by Proximity to Group Spatial Median}{
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#' Selects accessions closest to the group spatial median in principal
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#' coordinate space, computed via multivariate dispersion analysis using
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#' \code{\link[vegan]{betadisper}}.
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#' \code{\link[vegan]{betadisper}}
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#' \insertCite{oneill_theory_2000}{SampleCore}.
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#'
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#' The distance of each accession \mjseqn{g} to the group spatial median
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#' \mjseqn{M} is:
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#'
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#' \subsection{Peripheral Sampling by Maximal Mean Distance}{Selects the most
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#' peripheral accessions as those with the largest average distance to all
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#' others within the group.
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#' others within the group
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#' \insertCite{kaufman_clustering_1987,kaufman_finding_1990}{SampleCore}.
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#'
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#' \mjsdeqn{\bar{d}_g = \frac{1}{G} \sum_{h=1}^{G} d_{gh}}
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#'
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#'
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#' \subsection{Peripheral Sampling by Maximal Median Distance}{Selects the
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#' most peripheral accessions as those with the largest median distance to
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#' all others within the group.
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#' all others within the group
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#' \insertCite{kaufman_clustering_1987,kaufman_finding_1990}{SampleCore}.
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#'
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#' \mjsdeqn{\tilde{d}_g = \text{median}_{h=1,\dots,G}(d_{gh})}
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#'
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#'
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#' \subsection{Peripheral Sampling by Maximal Eccentricity}{Selects
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#' accessions with the largest eccentricity — the maximum distance to any
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#' other accession in the group.
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#' other accession in the group
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#' \insertCite{hage_eccentricity_1995}{SampleCore}.
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#'
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#' \mjsdeqn{e_g = \max_{h=1,\dots,G} d_{gh}}
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#'
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#'
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#' \subsection{Peripheral Sampling by Maximal Farness Centrality}{Selects
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#' accessions with the greatest total distance to all others, i.e. those most
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#' remote from the rest of the group.
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#' remote from the rest of the group
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#' \insertCite{sabidussi_centrality_1966}{SampleCore}.
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#'
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#' \mjsdeqn{f_g = \sum_{h=1}^{G} d_{gh}}
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#'
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#'
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#' \subsection{Space-Filling Sampling via the Kennard-Stone
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#' Algorithm}{Selects \mjseqn{n} accessions that maximally and uniformly
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#' cover the distance space via the Kennard-Stone algorithm (See
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#' cover the distance space via the Kennard-Stone algorithm
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#' \insertCite{kennard_computer_1969}{SampleCore} (See
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#' \code{\link[prospectr]{kenStone}}).
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#'
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#' Starting from the pair of accessions with the largest pairwise distance:
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#'
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#' \subsection{Space-Filling Sampling via the DUPLEX Algorithm}{Extends the
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#' Kennard-Stone algorithm to simultaneously construct a model set and a test
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#' set with similar distributions (\link[prospectr]{duplex}). Accessions are
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#' selected using Mahalanobis distance:
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#' set with similar distributions
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#' \insertCite{kennard_computer_1969,snee_validation_1977}{SampleCore}
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#' (\link[prospectr]{duplex}). Accessions are selected using Mahalanobis
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#' distance:
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#'
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#' \mjsdeqn{d_M(g, h) = \sqrt{(\mathbf{x}_g - \mathbf{x}_h)^\top \Sigma^{-1}
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#' (\mathbf{x}_g - \mathbf{x}_h)}}
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#'
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#' \subsection{Space-Filling Sampling via the Honigs Algorithm}{Selects
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#' \mjseqn{n} accessions sequentially by maximising dissimilarity to the
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#' already-selected set (\link[prospectr]{honigs})
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#' already-selected set \insertCite{honigs_unique-sample_1985}{SampleCore}
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#' (\link[prospectr]{honigs})
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#'
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#' At each step \mjseqn{k}, the accession \mjseqn{g_k} maximising total
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#' distance to all previously selected accessions \mjseqn{S} is chosen:
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#' \subsection{Space-Filling Sampling via Farthest-Point (Max-Min)
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#' Algorithm}{Selects \mjseqn{n} accessions by iteratively maximising the
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#' minimum distance to the current selected set — also known as the
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#' max-min or farthest-point sampling algorithm.
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#' max-min or farthest-point sampling algorithm
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#' \insertCite{gonzalez_clustering_1985,dyer_simple_1985,hochbaum_best_1985}{SampleCore}.
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#'
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#' \mjsdeqn{g_k = \underset{g \notin S}{\arg\max} \min_{s \in S} d_{gs}}
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#'
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#' \subsection{Density-Based Sampling by Minimal Nearest-Neighbour
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#' Distance}{Selects accessions residing in the densest regions of the
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#' distance space, identified as those with the smallest nearest-neighbour
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#' distance.
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#' distance
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#' \insertCite{cover_nearest_1967,fix_discriminatory_1989}{SampleCore}.
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#'
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#' For each accession \mjseqn{g}, the nearest-neighbour distance is:
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#'
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#' \subsection{Cluster-Based Sampling via K-means (Naes Method)}{Partitions
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#' accessions into \mjseqn{n} clusters via k-means applied to the distance
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#' matrix (See \code{\link[prospectr]{naes}}), then selects the accession
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#' closest to each cluster centre as the representative.
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#' closest to each cluster centre as the representative
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#' \insertCite{naes_design_1987,naes_user-friendly_2017}{SampleCore}.
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#'
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#' The k-means objective minimised is:
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#'
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#' \subsection{Cluster-Based Sampling via Hierarchical Clustering with
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#' Random Selection}{Partitions accessions into \mjseqn{n} clusters by
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#' cutting a hierarchical clustering dendrogram at height \mjseqn{k = n},
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#' then randomly samples one accession from each cluster.
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#' then randomly samples one accession from each cluster
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#' \insertCite{ward_Hierarchical_1963,li_studies_2002}{SampleCore}.
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#'
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#' The dendrogram is built by agglomerative hierarchical clustering using the
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#' linkage criterion specified by \code{\link[stats]{hclust}}. For
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#' \subsection{Cluster-Based Sampling via Hierarchical Clustering with Medoid
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#' Selection}{Partitions accessions into \mjseqn{n} clusters by cutting a
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#' hierarchical clustering dendrogram at height \mjseqn{k = n}, then selects
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#' the within-cluster medoid as the representative of each cluster.
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#' the within-cluster medoid as the representative of each cluster
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#' \insertCite{kaufman_clustering_1987,ward_Hierarchical_1963}{SampleCore}.
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#'
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#' For each cluster \mjseqn{C_k}, the medoid is the accession minimising
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#' total within-cluster distance:

R/select.random.R

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#' sampling according to allocation specified.
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#'
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#' For each cluster/group entries are selected randomly according to the
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#' allocation provided. Entries listed as \code{always.selected} are mandatorily
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#' included in the selection. Warnings are issued if requested allocation is
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#' smaller than the number of always-selected entries in a cluster/group and/or
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#' when the cluster/group does not contain enough remaining entries to fulfill
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#' the allocation.
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#' allocation provided \insertCite{brown_Core_1989;
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#' van_hintum_core_2000}{SampleCore}. Entries listed as \code{always.selected}
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#' are mandatorily included in the selection. Warnings are issued if requested
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#' allocation is smaller than the number of always-selected entries in a
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#' cluster/group and/or when the cluster/group does not contain enough remaining
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#' entries to fulfill the allocation.
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#'
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#' @template general-arg
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#' @template sel-arg

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