BiocNeighbors 1.8.2
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$index)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 796 7834 6121 3287 9002 1815 4170 8305 2287 6691
## [2,] 3822 5446 9054 6891 848 2467 3615 8133 3132 2495
## [3,] 7856 7483 7296 9218 4491 7785 398 3007 579 2745
## [4,] 5235 5749 4483 4635 7416 4507 196 6991 5883 9739
## [5,] 8138 4275 7610 4906 1429 8262 9143 5293 4178 82
## [6,] 2290 461 7617 1951 9730 2369 3121 6169 2457 5199
head(fout$distance)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 1.0373046 1.0445765 1.0504868 1.0538269 1.0593303 1.0726551 1.0867841
## [2,] 0.9482220 0.9580152 1.0094369 1.0194683 1.0244142 1.0626751 1.0873970
## [3,] 0.8915155 0.8953327 1.0262271 1.0593928 1.0654726 1.0703312 1.0824578
## [4,] 0.9157547 0.9235197 0.9605796 0.9828723 0.9955004 1.0240653 1.0286297
## [5,] 0.8898300 0.9073856 0.9089087 0.9216727 0.9386429 0.9573680 0.9596880
## [6,] 0.9320882 0.9345899 0.9668153 0.9915265 0.9965271 0.9985906 0.9998187
## [,8] [,9] [,10]
## [1,] 1.1108151 1.119736 1.1386523
## [2,] 1.1002963 1.110678 1.1162099
## [3,] 1.1043576 1.118109 1.1221874
## [4,] 1.0295654 1.031289 1.0413290
## [5,] 0.9667688 0.970039 0.9947082
## [6,] 1.0048222 1.009934 1.0215948
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$index[3,]
## [1] 7856 7483 7296 9218 4491 7785 398 3007 579 2745
… with the following distances to those neighbors:
fout$distance[3,]
## [1] 0.8915155 0.8953327 1.0262271 1.0593928 1.0654726 1.0703312 1.0824578
## [8] 1.1043576 1.1181090 1.1221874
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$index)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 6685 1905 1911 9711 504
## [2,] 4198 8286 8818 1217 2721
## [3,] 5247 5353 1650 7929 484
## [4,] 5075 430 4906 5938 5932
## [5,] 2304 8975 8396 5975 2751
## [6,] 1752 5610 167 6020 3737
head(qout$distance)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.9438838 1.0558772 1.0823055 1.1123618 1.1129085
## [2,] 0.8940407 0.9220172 0.9630316 0.9968341 1.0090347
## [3,] 0.7798383 0.8930779 0.9779041 0.9820498 1.0335135
## [4,] 0.8884584 0.9286552 0.9387557 0.9441704 0.9511641
## [5,] 0.7651731 0.8788716 0.8827387 0.9562141 0.9579960
## [6,] 0.8928920 0.9737507 0.9759432 1.0030895 1.0108924
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$index[3,]
## [1] 5247 5353 1650 7929 484
… with the following distances to those neighbors:
qout$distance[3,]
## [1] 0.7798383 0.8930779 0.9779041 0.9820498 1.0335135
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,] 7856 7483 7296 9218 4491
## [2,] 5235 5749 4483 4635 7416
## [3,] 8138 4275 7610 4906 1429
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.8915155 0.8953327 1.0262271 1.0593928 1.0654726
## [2,] 0.9157547 0.9235197 0.9605796 0.9828723 0.9955004
## [3,] 0.8898300 0.9073856 0.9089087 0.9216727 0.9386429
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 4.0.3 (2020-10-10)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows Server 2012 R2 x64 (build 9600)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=C
## [2] LC_CTYPE=English_United States.1252
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] BiocParallel_1.24.1 BiocNeighbors_1.8.2 knitr_1.30
## [4] BiocStyle_2.18.1
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.5 bookdown_0.21 lattice_0.20-41
## [4] digest_0.6.27 grid_4.0.3 stats4_4.0.3
## [7] magrittr_2.0.1 evaluate_0.14 rlang_0.4.9
## [10] stringi_1.5.3 S4Vectors_0.28.0 Matrix_1.2-18
## [13] rmarkdown_2.5 tools_4.0.3 stringr_1.4.0
## [16] parallel_4.0.3 xfun_0.19 yaml_2.2.1
## [19] compiler_4.0.3 BiocGenerics_0.36.0 BiocManager_1.30.10
## [22] htmltools_0.5.0
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.