BiocNeighbors 1.8.0
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$index)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 6103 8528 1292 4561 2182 4378 7264 3345 7483 5964
## [2,] 8948 9335 2489 5325 9012 5484 9399 8309 1802 6803
## [3,] 4828 1437 2609 6206 4510 6989 9060 522 9075 2880
## [4,] 9733 8882 4534 3851 197 9159 8178 6415 8256 3700
## [5,] 9465 5011 7034 4398 7857 6325 578 1150 106 1050
## [6,] 2774 6292 2180 8667 7961 1130 3085 8737 2654 4246
head(fout$distance)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.9103647 0.9361689 0.9717628 1.0335159 1.0337317 1.0425594 1.0441994
## [2,] 0.9042676 0.9223158 0.9576286 0.9702274 0.9753036 0.9953621 0.9986536
## [3,] 1.0031695 1.0207397 1.0856244 1.0941237 1.1359445 1.1422915 1.1590551
## [4,] 0.8973770 1.0187309 1.0491946 1.0502620 1.0554495 1.0647645 1.0762483
## [5,] 0.8625907 1.0215347 1.0470398 1.0554959 1.0633966 1.0772213 1.0844264
## [6,] 0.9662761 1.0399201 1.0611860 1.0676490 1.0718437 1.0753005 1.0813390
## [,8] [,9] [,10]
## [1,] 1.068581 1.073286 1.075732
## [2,] 1.048339 1.067277 1.070248
## [3,] 1.167019 1.167830 1.171124
## [4,] 1.090760 1.106904 1.120498
## [5,] 1.086713 1.090671 1.091018
## [6,] 1.103183 1.120599 1.139403
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$index[3,]
## [1] 4828 1437 2609 6206 4510 6989 9060 522 9075 2880
… with the following distances to those neighbors:
fout$distance[3,]
## [1] 1.003169 1.020740 1.085624 1.094124 1.135945 1.142292 1.159055 1.167019
## [9] 1.167830 1.171124
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$index)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 6176 2579 7200 7223 123
## [2,] 7703 8315 9326 5659 9505
## [3,] 5223 4139 2730 9920 6128
## [4,] 8050 854 9675 3098 8118
## [5,] 3889 4415 8681 9538 7336
## [6,] 131 8508 1293 7311 2702
head(qout$distance)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.9035172 0.9806076 0.9854816 0.9856075 0.9860263
## [2,] 0.8729239 0.9232282 0.9727012 0.9807652 1.0050498
## [3,] 0.8312204 0.8583152 0.8664711 0.8821679 0.9074463
## [4,] 0.8642877 0.9144968 0.9202820 0.9598606 1.0009541
## [5,] 0.9147538 0.9496725 0.9685844 0.9952473 0.9985577
## [6,] 0.9354603 0.9666705 0.9865788 1.0121686 1.0179415
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$index[3,]
## [1] 5223 4139 2730 9920 6128
… with the following distances to those neighbors:
qout$distance[3,]
## [1] 0.8312204 0.8583152 0.8664711 0.8821679 0.9074463
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,] 4828 1437 2609 6206 4510
## [2,] 9733 8882 4534 3851 197
## [3,] 9465 5011 7034 4398 7857
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.0031695 1.020740 1.085624 1.094124 1.135945
## [2,] 0.8973770 1.018731 1.049195 1.050262 1.055450
## [3,] 0.8625907 1.021535 1.047040 1.055496 1.063397
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-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.5 LTS
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## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.12-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.12-bioc/R/lib/libRlapack.so
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## locale:
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## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
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## other attached packages:
## [1] BiocParallel_1.24.0 BiocNeighbors_1.8.0 knitr_1.30
## [4] BiocStyle_2.18.0
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## 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_1.5 evaluate_0.14 rlang_0.4.8
## [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_0.18 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.