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$index)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 6295 4952 1090 1828 1118 3005 7483 8335 5016 4974
## [2,] 593 4223 9895 1005 8169 8085 3289 7681 9791 3429
## [3,] 8599 6332 2204 3155 4281 5885 131 4218 5120 3655
## [4,] 6114 3358 2674 9434 5635 861 3999 2065 532 25
## [5,] 5045 7114 7362 1603 6834 5890 8249 4851 8645 7582
## [6,] 7679 1538 4627 9115 4510 3678 3596 2076 2472 2674
head(fout$distance)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.8681479 0.8897752 0.9127894 0.9348734 0.9461919 0.9735984 0.9839596
## [2,] 0.9571206 0.9589984 0.9771774 1.0156536 1.0161441 1.0239847 1.0274582
## [3,] 0.8818880 0.9236179 0.9334733 1.0055367 1.0401387 1.0464910 1.0729269
## [4,] 0.8700128 1.0540885 1.0715972 1.0922847 1.0970133 1.1099301 1.1137744
## [5,] 0.8718934 0.8776878 0.9640895 0.9744083 0.9932702 0.9986655 1.0063359
## [6,] 0.7529839 0.9099724 1.0097919 1.0444033 1.0565020 1.0635699 1.0994820
## [,8] [,9] [,10]
## [1,] 0.9850137 0.992611 1.005767
## [2,] 1.0376677 1.049334 1.063692
## [3,] 1.0793518 1.103488 1.117661
## [4,] 1.1190147 1.127653 1.130532
## [5,] 1.0487871 1.054724 1.056918
## [6,] 1.1012567 1.124284 1.125254
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$index[3,]
## [1] 8599 6332 2204 3155 4281 5885 131 4218 5120 3655
… with the following distances to those neighbors:
fout$distance[3,]
## [1] 0.8818880 0.9236179 0.9334733 1.0055367 1.0401387 1.0464910 1.0729269
## [8] 1.0793518 1.1034884 1.1176614
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$index)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 2041 5949 8717 6163 6573
## [2,] 1280 6397 3815 4852 1571
## [3,] 8008 4922 5053 3575 8831
## [4,] 7311 3384 7207 2337 8812
## [5,] 2219 6322 8332 6718 4064
## [6,] 570 2483 6753 2806 2125
head(qout$distance)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.0366429 1.0565809 1.0691140 1.0708496 1.0752425
## [2,] 0.9454142 1.0606813 1.0691869 1.1141864 1.1199522
## [3,] 0.8896047 0.9690943 0.9718616 0.9880406 0.9886149
## [4,] 0.7650812 0.8937650 0.9142046 0.9336479 0.9483447
## [5,] 0.8883523 0.9312492 0.9392397 0.9452236 0.9647510
## [6,] 0.8526225 0.8776879 0.8951662 0.9584557 0.9758564
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$index[3,]
## [1] 8008 4922 5053 3575 8831
… with the following distances to those neighbors:
qout$distance[3,]
## [1] 0.8896047 0.9690943 0.9718616 0.9880406 0.9886149
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,] 8599 6332 2204 3155 4281
## [2,] 6114 3358 2674 9434 5635
## [3,] 5045 7114 7362 1603 6834
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.8818880 0.9236179 0.9334733 1.0055367 1.0401387
## [2,] 0.8700128 1.0540885 1.0715972 1.0922847 1.0970133
## [3,] 0.8718934 0.8776878 0.9640895 0.9744083 0.9932702
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-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_1.26.0 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.