|
22 | 22 | #' |
23 | 23 | #' \subsection{Medoid-like Representative Sampling by Minimal Mean |
24 | 24 | #' Distance}{Selects medoid-like representatives as accessions with the |
25 | | -#' smallest average distance to all others within the group. |
| 25 | +#' smallest average distance to all others within the group |
| 26 | +#' \insertCite{kaufman_clustering_1987,kaufman_finding_1990}{SampleCore}. |
26 | 27 | #' |
27 | 28 | #' For each accession \mjseqn{g}, the mean distance to all other accessions |
28 | 29 | #' \mjseqn{h} is computed as: |
|
39 | 40 | #' |
40 | 41 | #' Selects medoid-like representatives as accessions with the smallest median |
41 | 42 | #' distance to all others within the group. This method is less influenced by |
42 | | -#' outliers. |
| 43 | +#' outliers |
| 44 | +#' \insertCite{kaufman_clustering_1987,kaufman_finding_1990}{SampleCore}. |
43 | 45 | #' |
44 | 46 | #' For each accession \mjseqn{g}, the median distance to all other accessions |
45 | 47 | #' \mjseqn{h} is computed as: |
|
54 | 56 | #' \subsection{Representative Sampling by Proximity to Group |
55 | 57 | #' Centroid}{Selects accessions closest to the group centroid in principal |
56 | 58 | #' coordinate space, computed via multivariate dispersion analysis using |
57 | | -#' \code{\link[vegan]{betadisper}}. |
| 59 | +#' \code{\link[vegan]{betadisper}} |
| 60 | +#' \insertCite{anderson_distance-based_2006,anderson_multivariate_2006}{SampleCore}. |
58 | 61 | #' |
59 | 62 | #' The distance of each accession \mjseqn{g} to the group centroid \mjseqn{C} |
60 | 63 | #' in PCoA space is: |
|
71 | 74 | #' \subsection{Representative Sampling by Proximity to Group Spatial Median}{ |
72 | 75 | #' Selects accessions closest to the group spatial median in principal |
73 | 76 | #' coordinate space, computed via multivariate dispersion analysis using |
74 | | -#' \code{\link[vegan]{betadisper}}. |
| 77 | +#' \code{\link[vegan]{betadisper}} |
| 78 | +#' \insertCite{oneill_theory_2000}{SampleCore}. |
75 | 79 | #' |
76 | 80 | #' The distance of each accession \mjseqn{g} to the group spatial median |
77 | 81 | #' \mjseqn{M} is: |
|
93 | 97 | #' |
94 | 98 | #' \subsection{Peripheral Sampling by Maximal Mean Distance}{Selects the most |
95 | 99 | #' peripheral accessions as those with the largest average distance to all |
96 | | -#' others within the group. |
| 100 | +#' others within the group |
| 101 | +#' \insertCite{kaufman_clustering_1987,kaufman_finding_1990}{SampleCore}. |
97 | 102 | #' |
98 | 103 | #' \mjsdeqn{\bar{d}_g = \frac{1}{G} \sum_{h=1}^{G} d_{gh}} |
99 | 104 | #' |
|
104 | 109 | #' |
105 | 110 | #' \subsection{Peripheral Sampling by Maximal Median Distance}{Selects the |
106 | 111 | #' most peripheral accessions as those with the largest median distance to |
107 | | -#' all others within the group. |
| 112 | +#' all others within the group |
| 113 | +#' \insertCite{kaufman_clustering_1987,kaufman_finding_1990}{SampleCore}. |
108 | 114 | #' |
109 | 115 | #' \mjsdeqn{\tilde{d}_g = \text{median}_{h=1,\dots,G}(d_{gh})} |
110 | 116 | #' |
|
115 | 121 | #' |
116 | 122 | #' \subsection{Peripheral Sampling by Maximal Eccentricity}{Selects |
117 | 123 | #' accessions with the largest eccentricity — the maximum distance to any |
118 | | -#' other accession in the group. |
| 124 | +#' other accession in the group |
| 125 | +#' \insertCite{hage_eccentricity_1995}{SampleCore}. |
119 | 126 | #' |
120 | 127 | #' \mjsdeqn{e_g = \max_{h=1,\dots,G} d_{gh}} |
121 | 128 | #' |
|
127 | 134 | #' |
128 | 135 | #' \subsection{Peripheral Sampling by Maximal Farness Centrality}{Selects |
129 | 136 | #' accessions with the greatest total distance to all others, i.e. those most |
130 | | -#' remote from the rest of the group. |
| 137 | +#' remote from the rest of the group |
| 138 | +#' \insertCite{sabidussi_centrality_1966}{SampleCore}. |
131 | 139 | #' |
132 | 140 | #' \mjsdeqn{f_g = \sum_{h=1}^{G} d_{gh}} |
133 | 141 | #' |
|
147 | 155 | #' |
148 | 156 | #' \subsection{Space-Filling Sampling via the Kennard-Stone |
149 | 157 | #' Algorithm}{Selects \mjseqn{n} accessions that maximally and uniformly |
150 | | -#' cover the distance space via the Kennard-Stone algorithm (See |
| 158 | +#' cover the distance space via the Kennard-Stone algorithm |
| 159 | +#' \insertCite{kennard_computer_1969}{SampleCore} (See |
151 | 160 | #' \code{\link[prospectr]{kenStone}}). |
152 | 161 | #' |
153 | 162 | #' Starting from the pair of accessions with the largest pairwise distance: |
|
166 | 175 | #' |
167 | 176 | #' \subsection{Space-Filling Sampling via the DUPLEX Algorithm}{Extends the |
168 | 177 | #' Kennard-Stone algorithm to simultaneously construct a model set and a test |
169 | | -#' set with similar distributions (\link[prospectr]{duplex}). Accessions are |
170 | | -#' selected using Mahalanobis distance: |
| 178 | +#' set with similar distributions |
| 179 | +#' \insertCite{kennard_computer_1969,snee_validation_1977}{SampleCore} |
| 180 | +#' (\link[prospectr]{duplex}). Accessions are selected using Mahalanobis |
| 181 | +#' distance: |
171 | 182 | #' |
172 | 183 | #' \mjsdeqn{d_M(g, h) = \sqrt{(\mathbf{x}_g - \mathbf{x}_h)^\top \Sigma^{-1} |
173 | 184 | #' (\mathbf{x}_g - \mathbf{x}_h)}} |
|
180 | 191 | #' |
181 | 192 | #' \subsection{Space-Filling Sampling via the Honigs Algorithm}{Selects |
182 | 193 | #' \mjseqn{n} accessions sequentially by maximising dissimilarity to the |
183 | | -#' already-selected set (\link[prospectr]{honigs}) |
| 194 | +#' already-selected set \insertCite{honigs_unique-sample_1985}{SampleCore} |
| 195 | +#' (\link[prospectr]{honigs}) |
184 | 196 | #' |
185 | 197 | #' At each step \mjseqn{k}, the accession \mjseqn{g_k} maximising total |
186 | 198 | #' distance to all previously selected accessions \mjseqn{S} is chosen: |
|
195 | 207 | #' \subsection{Space-Filling Sampling via Farthest-Point (Max-Min) |
196 | 208 | #' Algorithm}{Selects \mjseqn{n} accessions by iteratively maximising the |
197 | 209 | #' minimum distance to the current selected set — also known as the |
198 | | -#' max-min or farthest-point sampling algorithm. |
| 210 | +#' max-min or farthest-point sampling algorithm |
| 211 | +#' \insertCite{gonzalez_clustering_1985,dyer_simple_1985,hochbaum_best_1985}{SampleCore}. |
199 | 212 | #' |
200 | 213 | #' \mjsdeqn{g_k = \underset{g \notin S}{\arg\max} \min_{s \in S} d_{gs}} |
201 | 214 | #' |
|
216 | 229 | #' \subsection{Density-Based Sampling by Minimal Nearest-Neighbour |
217 | 230 | #' Distance}{Selects accessions residing in the densest regions of the |
218 | 231 | #' distance space, identified as those with the smallest nearest-neighbour |
219 | | -#' distance. |
| 232 | +#' distance |
| 233 | +#' \insertCite{cover_nearest_1967,fix_discriminatory_1989}{SampleCore}. |
220 | 234 | #' |
221 | 235 | #' For each accession \mjseqn{g}, the nearest-neighbour distance is: |
222 | 236 | #' |
|
256 | 270 | #' \subsection{Cluster-Based Sampling via K-means (Naes Method)}{Partitions |
257 | 271 | #' accessions into \mjseqn{n} clusters via k-means applied to the distance |
258 | 272 | #' matrix (See \code{\link[prospectr]{naes}}), then selects the accession |
259 | | -#' closest to each cluster centre as the representative. |
| 273 | +#' closest to each cluster centre as the representative |
| 274 | +#' \insertCite{naes_design_1987,naes_user-friendly_2017}{SampleCore}. |
260 | 275 | #' |
261 | 276 | #' The k-means objective minimised is: |
262 | 277 | #' |
|
271 | 286 | #' \subsection{Cluster-Based Sampling via Hierarchical Clustering with |
272 | 287 | #' Random Selection}{Partitions accessions into \mjseqn{n} clusters by |
273 | 288 | #' cutting a hierarchical clustering dendrogram at height \mjseqn{k = n}, |
274 | | -#' then randomly samples one accession from each cluster. |
| 289 | +#' then randomly samples one accession from each cluster |
| 290 | +#' \insertCite{ward_Hierarchical_1963,li_studies_2002}{SampleCore}. |
275 | 291 | #' |
276 | 292 | #' The dendrogram is built by agglomerative hierarchical clustering using the |
277 | 293 | #' linkage criterion specified by \code{\link[stats]{hclust}}. For |
|
288 | 304 | #' \subsection{Cluster-Based Sampling via Hierarchical Clustering with Medoid |
289 | 305 | #' Selection}{Partitions accessions into \mjseqn{n} clusters by cutting a |
290 | 306 | #' hierarchical clustering dendrogram at height \mjseqn{k = n}, then selects |
291 | | -#' the within-cluster medoid as the representative of each cluster. |
| 307 | +#' the within-cluster medoid as the representative of each cluster |
| 308 | +#' \insertCite{kaufman_clustering_1987,ward_Hierarchical_1963}{SampleCore}. |
292 | 309 | #' |
293 | 310 | #' For each cluster \mjseqn{C_k}, the medoid is the accession minimising |
294 | 311 | #' total within-cluster distance: |
|
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