BiocNeighbors 1.10.0
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$index)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 7099 6200 6485 6893 9566 1376 7958 549 1537 1004
## [2,] 6936 4179 6137 6017 7734 9695 230 3106 6858 8956
## [3,] 248 2387 3544 2209 5215 4001 6934 6721 7898 3241
## [4,] 6424 641 3170 5808 2430 2729 8751 3399 3651 2834
## [5,] 5668 9722 337 4637 1921 8452 8644 5026 5484 9431
## [6,] 6059 678 2246 1047 791 2869 8134 2848 2706 6974
head(fout$distance)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8879002 0.9122381 0.9154213 0.9255397 0.9335748 0.9506347 0.9537064
## [2,] 0.9010761 0.9980604 1.0274427 1.0387540 1.0417325 1.0446863 1.0620324
## [3,] 0.8776323 0.9098536 0.9763203 0.9881648 1.0064094 1.0116512 1.0148250
## [4,] 0.7958431 0.9037620 0.9277526 0.9330558 0.9330847 0.9353315 0.9427484
## [5,] 0.9621558 0.9621896 0.9777817 0.9847706 1.0280363 1.0352073 1.0369808
## [6,] 0.9077439 0.9254729 0.9847225 0.9933598 1.0003513 1.0053419 1.0331628
## [,8] [,9] [,10]
## [1,] 0.9611631 0.9704880 0.9842655
## [2,] 1.0623869 1.0641231 1.0647031
## [3,] 1.0288918 1.0377311 1.0486898
## [4,] 0.9465238 0.9575306 0.9593012
## [5,] 1.0377079 1.0451699 1.0767352
## [6,] 1.0441608 1.0489526 1.0640462
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$index[3,]
## [1] 248 2387 3544 2209 5215 4001 6934 6721 7898 3241
… with the following distances to those neighbors:
fout$distance[3,]
## [1] 0.8776323 0.9098536 0.9763203 0.9881648 1.0064094 1.0116512 1.0148250
## [8] 1.0288918 1.0377311 1.0486898
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$index)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 3931 5577 5677 9840 1850
## [2,] 5515 2337 4938 8714 7807
## [3,] 174 7374 715 5501 7084
## [4,] 5597 3619 3950 4720 9437
## [5,] 1578 6238 6819 2180 7274
## [6,] 6742 2874 9497 5657 6536
head(qout$distance)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.0199987 1.0376850 1.0826383 1.1128773 1.1222347
## [2,] 0.8533508 0.8911792 0.9712616 0.9755471 1.0036667
## [3,] 0.9105697 0.9430303 0.9549132 0.9844046 0.9863771
## [4,] 0.9818129 0.9857438 1.0347501 1.0629480 1.0629703
## [5,] 0.8306203 0.9305679 0.9624847 0.9669547 1.0193001
## [6,] 0.8811809 0.9762420 0.9881336 0.9966026 0.9966967
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$index[3,]
## [1] 174 7374 715 5501 7084
… with the following distances to those neighbors:
qout$distance[3,]
## [1] 0.9105697 0.9430303 0.9549132 0.9844046 0.9863771
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,] 248 2387 3544 2209 5215
## [2,] 6424 641 3170 5808 2430
## [3,] 5668 9722 337 4637 1921
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.8776323 0.9098536 0.9763203 0.9881648 1.0064094
## [2,] 0.7958431 0.9037620 0.9277526 0.9330558 0.9330847
## [3,] 0.9621558 0.9621896 0.9777817 0.9847706 1.0280363
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 4.1.0 RC (2021-05-10 r80283)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Mojave 10.14.6
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.1/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_1.26.0 BiocNeighbors_1.10.0 knitr_1.33
## [4] BiocStyle_2.20.0
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.6 magrittr_2.0.1 BiocGenerics_0.38.0
## [4] lattice_0.20-44 R6_2.5.0 rlang_0.4.11
## [7] stringr_1.4.0 tools_4.1.0 parallel_4.1.0
## [10] grid_4.1.0 xfun_0.23 jquerylib_0.1.4
## [13] htmltools_0.5.1.1 yaml_2.2.1 digest_0.6.27
## [16] bookdown_0.22 Matrix_1.3-3 BiocManager_1.30.15
## [19] S4Vectors_0.30.0 sass_0.4.0 evaluate_0.14
## [22] rmarkdown_2.8 stringi_1.6.2 compiler_4.1.0
## [25] bslib_0.2.5.1 stats4_4.1.0 jsonlite_1.7.2
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.