BiocNeighbors 1.18.0
The BiocNeighbors package implements a few algorithms for exact nearest neighbor searching:
Both KMKNN and VP-trees involve a component of randomness during index construction, though the k-nearest neighbors result is fully deterministic1 Except in the presence of ties, see ?"BiocNeighbors-ties"
for details..
The most obvious application is to perform a k-nearest neighbors search. We’ll mock up an example here with a hypercube of points, for which we want to identify the 10 nearest neighbors for each point.
nobs <- 10000
ndim <- 20
data <- matrix(runif(nobs*ndim), ncol=ndim)
The findKNN()
method expects a numeric matrix as input with data points as the rows and variables/dimensions as the columns.
We indicate that we want to use the KMKNN algorithm by setting BNPARAM=KmknnParam()
(which is also the default, so this is not strictly necessary here).
We could use a VP tree instead by setting BNPARAM=VptreeParam()
.
fout <- findKNN(data, k=10, BNPARAM=KmknnParam())
head(fout$index)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 1475 3924 6398 1397 3803 6226 1092 1775 2695 3033
## [2,] 1431 8407 9210 9827 2004 4755 3055 2425 9199 5591
## [3,] 6260 7596 967 1345 8065 4257 3837 5540 7794 7771
## [4,] 6506 5140 6063 9410 3777 5683 1085 8505 7022 6758
## [5,] 8441 5030 5374 7217 6286 913 8360 7175 940 2197
## [6,] 9020 4120 3344 6359 1046 5928 5920 6907 2418 4224
head(fout$distance)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8608422 0.8641390 0.8916383 0.9634926 0.9858023 0.9863873 0.9895430
## [2,] 1.0696593 1.0755356 1.1319923 1.1392915 1.1428294 1.1497810 1.1649679
## [3,] 0.7505679 0.7655474 0.8155142 0.8735982 0.8831654 0.8992442 0.9017388
## [4,] 0.8032986 0.9396509 0.9482572 0.9535497 0.9631937 0.9645796 0.9766409
## [5,] 0.8779930 0.9590474 0.9826428 0.9922442 0.9938853 1.0051482 1.0140008
## [6,] 0.8733323 0.8964203 0.9325068 0.9486481 0.9787784 0.9808929 0.9817277
## [,8] [,9] [,10]
## [1,] 0.9896291 0.9977157 1.0028539
## [2,] 1.1699543 1.1931662 1.2049512
## [3,] 0.9085771 0.9095112 0.9160579
## [4,] 1.0147802 1.0227495 1.0240145
## [5,] 1.0261465 1.0336971 1.0481576
## [6,] 0.9904496 0.9927003 1.0028325
Each row of the index
matrix corresponds to a point in data
and contains the row indices in data
that are its nearest neighbors.
For example, the 3rd point in data
has the following nearest neighbors:
fout$index[3,]
## [1] 6260 7596 967 1345 8065 4257 3837 5540 7794 7771
… with the following distances to those neighbors:
fout$distance[3,]
## [1] 0.7505679 0.7655474 0.8155142 0.8735982 0.8831654 0.8992442 0.9017388
## [8] 0.9085771 0.9095112 0.9160579
Note that the reported neighbors are sorted by distance.
Another application is to identify the k-nearest neighbors in one dataset based on query points in another dataset. Again, we mock up a small data set:
nquery <- 1000
ndim <- 20
query <- matrix(runif(nquery*ndim), ncol=ndim)
We then use the queryKNN()
function to identify the 5 nearest neighbors in data
for each point in query
.
qout <- queryKNN(data, query, k=5, BNPARAM=KmknnParam())
head(qout$index)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 4742 3996 9038 6194 4911
## [2,] 4925 2585 1224 1741 8216
## [3,] 8294 9668 8002 75 5677
## [4,] 5214 1799 3507 19 3465
## [5,] 2308 1638 1433 7871 3097
## [6,] 1934 7571 4126 7883 8290
head(qout$distance)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.0606358 1.0856064 1.0872369 1.1049552 1.1120492
## [2,] 0.8582900 0.9097412 0.9594431 0.9804437 0.9907725
## [3,] 0.9986486 1.0459272 1.1040033 1.1123857 1.1137113
## [4,] 0.8744265 0.9634130 1.0127840 1.0206271 1.0275663
## [5,] 0.8834043 0.9047219 0.9589461 0.9621767 1.0220830
## [6,] 0.8552389 0.8994096 0.9060309 0.9180037 0.9400187
Each row of the index
matrix contains the row indices in data
that are the nearest neighbors of a point in query
.
For example, the 3rd point in query
has the following nearest neighbors in data
:
qout$index[3,]
## [1] 8294 9668 8002 75 5677
… with the following distances to those neighbors:
qout$distance[3,]
## [1] 0.9986486 1.0459272 1.1040033 1.1123857 1.1137113
Again, the reported neighbors are sorted by distance.
Users can perform the search for a subset of query points using the subset=
argument.
This yields the same result as but is more efficient than performing the search for all points and subsetting the output.
findKNN(data, k=5, subset=3:5)
## $index
## [,1] [,2] [,3] [,4] [,5]
## [1,] 6260 7596 967 1345 8065
## [2,] 6506 5140 6063 9410 3777
## [3,] 8441 5030 5374 7217 6286
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.7505679 0.7655474 0.8155142 0.8735982 0.8831654
## [2,] 0.8032986 0.9396509 0.9482572 0.9535497 0.9631937
## [3,] 0.8779930 0.9590474 0.9826428 0.9922442 0.9938853
If only the indices are of interest, users can set get.distance=FALSE
to avoid returning the matrix of distances.
This will save some time and memory.
names(findKNN(data, k=2, get.distance=FALSE))
## [1] "index"
It is also simple to speed up functions by parallelizing the calculations with the BiocParallel framework.
library(BiocParallel)
out <- findKNN(data, k=10, BPPARAM=MulticoreParam(3))
For multiple queries to a constant data
, the pre-clustering can be performed in a separate step with buildIndex()
.
The result can then be passed to multiple calls, avoiding the overhead of repeated clustering2 The algorithm type is automatically determined when BNINDEX
is specified, so there is no need to also specify BNPARAM
in the later functions..
pre <- buildIndex(data, BNPARAM=KmknnParam())
out1 <- findKNN(BNINDEX=pre, k=5)
out2 <- queryKNN(BNINDEX=pre, query=query, k=2)
The default setting is to search on the Euclidean distance.
Alternatively, we can use the Manhattan distance by setting distance="Manhattan"
in the BiocNeighborParam
object.
out.m <- findKNN(data, k=5, BNPARAM=KmknnParam(distance="Manhattan"))
Advanced users may also be interested in the raw.index=
argument, which returns indices directly to the precomputed object rather than to data
.
This may be useful inside package functions where it may be more convenient to work on a common precomputed object.
sessionInfo()
## R version 4.3.0 RC (2023-04-13 r84269 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows Server 2022 x64 (build 20348)
##
## Matrix products: default
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## locale:
## [1] LC_COLLATE=C
## [2] LC_CTYPE=English_United States.utf8
## [3] LC_MONETARY=English_United States.utf8
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.utf8
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## time zone: America/New_York
## tzcode source: internal
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## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] BiocParallel_1.34.0 BiocNeighbors_1.18.0 knitr_1.42
## [4] BiocStyle_2.28.0
##
## loaded via a namespace (and not attached):
## [1] cli_3.6.1 rlang_1.1.0 xfun_0.39
## [4] jsonlite_1.8.4 S4Vectors_0.38.0 htmltools_0.5.5
## [7] stats4_4.3.0 sass_0.4.5 rmarkdown_2.21
## [10] grid_4.3.0 evaluate_0.20 jquerylib_0.1.4
## [13] fastmap_1.1.1 yaml_2.3.7 bookdown_0.33
## [16] BiocManager_1.30.20 compiler_4.3.0 codetools_0.2-19
## [19] Rcpp_1.0.10 lattice_0.21-8 digest_0.6.31
## [22] R6_2.5.1 parallel_4.3.0 bslib_0.4.2
## [25] Matrix_1.5-4 tools_4.3.0 BiocGenerics_0.46.0
## [28] cachem_1.0.7
Wang, X. 2012. “A Fast Exact k-Nearest Neighbors Algorithm for High Dimensional Search Using k-Means Clustering and Triangle Inequality.” Proc Int Jt Conf Neural Netw 43 (6): 2351–8.
Yianilos, P. N. 1993. “Data Structures and Algorithms for Nearest Neighbor Search in General Metric Spaces.” In SODA, 93:311–21. 194.