BiocNeighbors 1.6.0
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$index)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 8087 9400 1103 4827 789 9043 7093 2546 5489 9048
## [2,] 7038 6879 6487 9297 5524 2617 4995 1168 7587 7743
## [3,] 1231 6550 6701 10 9733 8813 3246 611 583 991
## [4,] 483 5924 361 476 6253 8707 4219 1617 6874 352
## [5,] 5644 7989 8849 7191 9553 5721 9874 7789 8376 9174
## [6,] 8263 3926 6004 7436 8491 5874 7509 4529 2916 9661
head(fout$distance)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8731521 0.9653392 0.9683257 1.0338930 1.0469617 1.0588056 1.0589208
## [2,] 0.8773101 0.9183035 0.9312565 0.9603871 0.9887890 0.9897631 0.9898572
## [3,] 0.9518038 0.9971894 1.0096301 1.0268473 1.0493543 1.0515094 1.0960192
## [4,] 0.9359130 0.9661439 0.9718334 0.9792598 0.9834347 0.9908157 0.9926092
## [5,] 0.8554691 0.9441565 1.0489588 1.0668435 1.0738195 1.0743257 1.0972799
## [6,] 0.9303372 0.9845239 1.0764743 1.0816151 1.0861782 1.1095560 1.1246339
## [,8] [,9] [,10]
## [1,] 1.0624306 1.063123 1.072711
## [2,] 0.9909363 1.002287 1.004458
## [3,] 1.1053905 1.108868 1.109241
## [4,] 1.0250100 1.030065 1.030114
## [5,] 1.1034892 1.112987 1.135207
## [6,] 1.1424204 1.159952 1.162334
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$index[3,]
## [1] 1231 6550 6701 10 9733 8813 3246 611 583 991
… with the following distances to those neighbors:
fout$distance[3,]
## [1] 0.9518038 0.9971894 1.0096301 1.0268473 1.0493543 1.0515094 1.0960192
## [8] 1.1053905 1.1088682 1.1092409
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$index)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 4873 4487 8454 5838 2319
## [2,] 2021 5494 1764 9941 7871
## [3,] 7868 3630 2361 2179 2459
## [4,] 4331 588 2727 1405 1222
## [5,] 8965 3862 6363 5891 4995
## [6,] 2136 7567 47 5842 7333
head(qout$distance)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.9222334 0.9531127 0.9896927 0.9934973 1.0093904
## [2,] 0.9983183 1.0161948 1.0401222 1.0419147 1.1294887
## [3,] 1.0775833 1.0783785 1.1454099 1.1586000 1.1840437
## [4,] 0.8741795 0.9455144 0.9718740 1.0135042 1.0259661
## [5,] 0.8920619 0.9137741 0.9658429 0.9875645 0.9892986
## [6,] 0.8688632 0.9187435 0.9663638 0.9792254 1.0009669
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$index[3,]
## [1] 7868 3630 2361 2179 2459
… with the following distances to those neighbors:
qout$distance[3,]
## [1] 1.077583 1.078378 1.145410 1.158600 1.184044
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,] 1231 6550 6701 10 9733
## [2,] 483 5924 361 476 6253
## [3,] 5644 7989 8849 7191 9553
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.9518038 0.9971894 1.0096301 1.0268473 1.0493543
## [2,] 0.9359130 0.9661439 0.9718334 0.9792598 0.9834347
## [3,] 0.8554691 0.9441565 1.0489588 1.0668435 1.0738195
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 4.0.0 (2020-04-24)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Mojave 10.14.6
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
##
## locale:
## [1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] BiocParallel_1.22.0 BiocNeighbors_1.6.0 knitr_1.28
## [4] BiocStyle_2.16.0
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.4.6 bookdown_0.18 lattice_0.20-41
## [4] digest_0.6.25 grid_4.0.0 stats4_4.0.0
## [7] magrittr_1.5 evaluate_0.14 rlang_0.4.5
## [10] stringi_1.4.6 S4Vectors_0.26.0 Matrix_1.2-18
## [13] rmarkdown_2.1 tools_4.0.0 stringr_1.4.0
## [16] parallel_4.0.0 xfun_0.13 yaml_2.2.1
## [19] compiler_4.0.0 BiocGenerics_0.34.0 BiocManager_1.30.10
## [22] htmltools_0.4.0
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.