BiocNeighbors 1.12.0
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$index)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 1834 8520 6418 8285 1088 8396 5053 3931 2489 6432
## [2,] 7476 4923 2918 9109 6116 2301 3675 2161 9671 6365
## [3,] 4036 5029 5038 5561 9474 3861 7588 1492 9718 7818
## [4,] 503 3535 8856 8716 3422 9037 7334 5337 4024 8401
## [5,] 2706 9857 4184 1820 876 5618 4344 8028 9899 4999
## [6,] 815 2685 1205 3750 6818 3637 9228 1154 4633 8704
head(fout$distance)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.9873224 1.0042547 1.0164828 1.0432194 1.0444058 1.0456076 1.0706495
## [2,] 1.0240366 1.0370456 1.1011682 1.1514759 1.1600620 1.1864552 1.1884515
## [3,] 0.8907877 0.9428800 0.9869554 1.0366111 1.0539570 1.0688997 1.0743881
## [4,] 0.8784366 0.9597062 1.0208576 1.0405754 1.0462169 1.0501523 1.0590181
## [5,] 0.8154634 0.8758563 0.9055711 0.9174330 0.9343276 0.9613431 0.9767778
## [6,] 0.9197168 0.9251531 0.9344843 0.9585882 0.9829316 0.9904147 1.0332483
## [,8] [,9] [,10]
## [1,] 1.0725317 1.0778068 1.0787248
## [2,] 1.1934394 1.1973379 1.2020754
## [3,] 1.0850044 1.0934087 1.0953963
## [4,] 1.0616786 1.0620466 1.0708770
## [5,] 0.9789725 0.9807013 0.9811936
## [6,] 1.0409656 1.0484698 1.0489620
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$index[3,]
## [1] 4036 5029 5038 5561 9474 3861 7588 1492 9718 7818
… with the following distances to those neighbors:
fout$distance[3,]
## [1] 0.8907877 0.9428800 0.9869554 1.0366111 1.0539570 1.0688997 1.0743881
## [8] 1.0850044 1.0934087 1.0953963
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$index)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 5393 8245 5970 4523 4073
## [2,] 4113 3468 289 1372 2273
## [3,] 3437 5191 3275 4174 9877
## [4,] 2019 541 7622 6748 7746
## [5,] 6770 5400 9223 2473 1704
## [6,] 3068 9681 46 3939 5189
head(qout$distance)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.7540807 0.9652551 0.9719752 0.9765699 1.0107931
## [2,] 0.8039612 0.9378730 0.9900544 0.9965463 1.0062733
## [3,] 0.7282259 0.9129151 0.9355368 0.9772487 0.9977412
## [4,] 0.8976409 0.9183535 0.9191570 0.9971014 1.0001932
## [5,] 0.9656236 1.0016202 1.0930467 1.1008310 1.1027531
## [6,] 0.9043726 0.9049974 0.9569925 0.9738977 0.9919256
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$index[3,]
## [1] 3437 5191 3275 4174 9877
… with the following distances to those neighbors:
qout$distance[3,]
## [1] 0.7282259 0.9129151 0.9355368 0.9772487 0.9977412
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,] 4036 5029 5038 5561 9474
## [2,] 503 3535 8856 8716 3422
## [3,] 2706 9857 4184 1820 876
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.8907877 0.9428800 0.9869554 1.036611 1.0539570
## [2,] 0.8784366 0.9597062 1.0208576 1.040575 1.0462169
## [3,] 0.8154634 0.8758563 0.9055711 0.917433 0.9343276
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 4.1.1 (2021-08-10)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows Server x64 (build 17763)
##
## 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_1.28.0 BiocNeighbors_1.12.0 knitr_1.36
## [4] BiocStyle_2.22.0
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.7 magrittr_2.0.1 BiocGenerics_0.40.0
## [4] lattice_0.20-45 R6_2.5.1 rlang_0.4.12
## [7] fastmap_1.1.0 stringr_1.4.0 tools_4.1.1
## [10] parallel_4.1.1 grid_4.1.1 xfun_0.27
## [13] jquerylib_0.1.4 htmltools_0.5.2 yaml_2.2.1
## [16] digest_0.6.28 bookdown_0.24 Matrix_1.3-4
## [19] BiocManager_1.30.16 S4Vectors_0.32.0 sass_0.4.0
## [22] evaluate_0.14 rmarkdown_2.11 stringi_1.7.5
## [25] compiler_4.1.1 bslib_0.3.1 stats4_4.1.1
## [28] 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.