BiocNeighbors 1.4.2
The BiocNeighbors package implements a few algorithms for exact nearest neighbor searching:
Both methods involve a component of randomness during index construction, though the k-nearest neighbors result is fully deterministic1 Except in the presence of ties, see ?findKNN
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$index)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 1881 8278 3628 5229 6391 9639 6161 7671 5375 5037
## [2,] 3432 6646 4652 782 7068 5634 4408 5663 2795 751
## [3,] 9029 8006 4575 7 3232 774 1207 1112 8270 7643
## [4,] 135 2543 613 2054 5954 797 7852 1271 5963 5719
## [5,] 521 752 8056 4628 1134 5878 8624 7083 6162 9431
## [6,] 6003 4150 574 8355 5948 6947 4176 3989 5718 5707
head(fout$distance)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8053135 0.8344659 0.8597889 0.8675684 0.8903521 0.9510813 0.9541194
## [2,] 0.9231167 0.9317375 0.9677469 0.9691288 0.9693556 0.9707015 0.9762002
## [3,] 0.9674346 1.0275486 1.0556525 1.0923730 1.1129987 1.1219975 1.1402440
## [4,] 1.0107910 1.0346099 1.0550829 1.0576011 1.0749991 1.0769960 1.0805129
## [5,] 0.9196937 0.9447228 0.9824839 0.9871147 0.9942311 1.0174962 1.0189802
## [6,] 0.9658588 0.9816334 0.9958824 1.0291708 1.0416947 1.0525788 1.0570698
## [,8] [,9] [,10]
## [1,] 0.9567863 0.9773559 0.9800960
## [2,] 0.9766540 0.9814470 0.9872668
## [3,] 1.1422397 1.1547846 1.1638458
## [4,] 1.0839071 1.0840470 1.0903321
## [5,] 1.0193400 1.0205089 1.0397422
## [6,] 1.0711706 1.0814136 1.0856588
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$index[3,]
## [1] 9029 8006 4575 7 3232 774 1207 1112 8270 7643
… with the following distances to those neighbors:
fout$distance[3,]
## [1] 0.9674346 1.0275486 1.0556525 1.0923730 1.1129987 1.1219975 1.1402440
## [8] 1.1422397 1.1547846 1.1638458
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$index)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 3116 1922 7629 104 77
## [2,] 4330 8770 5493 8495 6613
## [3,] 96 2671 2717 5074 3563
## [4,] 6919 5293 7579 6739 8893
## [5,] 5898 1706 532 9060 1513
## [6,] 4944 3700 987 8835 9258
head(qout$distance)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.8477125 0.9520432 0.9528356 0.9533169 0.9873199
## [2,] 1.0110129 1.0158369 1.0206459 1.0561397 1.0701870
## [3,] 0.9009902 0.9609223 0.9808124 0.9998865 1.0299645
## [4,] 0.9132506 0.9161617 0.9163441 0.9603837 0.9647815
## [5,] 0.9640249 0.9984658 1.0019975 1.0360102 1.0717339
## [6,] 0.8440024 0.8859069 0.8912034 0.9447737 0.9465425
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$index[3,]
## [1] 96 2671 2717 5074 3563
… with the following distances to those neighbors:
qout$distance[3,]
## [1] 0.9009902 0.9609223 0.9808124 0.9998865 1.0299645
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,] 9029 8006 4575 7 3232
## [2,] 135 2543 613 2054 5954
## [3,] 521 752 8056 4628 1134
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.9674346 1.0275486 1.0556525 1.0923730 1.1129987
## [2,] 1.0107910 1.0346099 1.0550829 1.0576011 1.0749991
## [3,] 0.9196937 0.9447228 0.9824839 0.9871147 0.9942311
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 3.6.2 (2019-12-12)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: OS X El Capitan 10.11.6
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/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_1.20.1 BiocNeighbors_1.4.2 knitr_1.28
## [4] BiocStyle_2.14.4
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.3 bookdown_0.17 lattice_0.20-40
## [4] digest_0.6.25 grid_3.6.2 stats4_3.6.2
## [7] magrittr_1.5 evaluate_0.14 rlang_0.4.4
## [10] stringi_1.4.6 S4Vectors_0.24.3 Matrix_1.2-18
## [13] rmarkdown_2.1 tools_3.6.2 stringr_1.4.0
## [16] parallel_3.6.2 xfun_0.12 yaml_2.2.1
## [19] compiler_3.6.2 BiocGenerics_0.32.0 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.