BiocNeighbors 1.20.2
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$index)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 3990 1256 2678 8189 1786 5729 5726 1542 5000 1416
## [2,] 5723 7206 162 508 7157 2557 6072 645 3507 3219
## [3,] 3150 2092 8001 2389 3315 3017 416 7905 1343 2104
## [4,] 6592 8313 2598 4078 9490 3143 1649 5658 6134 7544
## [5,] 747 5797 5847 6325 6183 8674 1091 1408 712 616
## [6,] 2706 5154 5955 1131 9008 8692 8837 146 9084 149
head(fout$distance)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 1.0192533 1.0247568 1.0281821 1.0488706 1.0500594 1.0512640 1.0619946
## [2,] 0.8311384 0.8937575 0.9153321 0.9483128 0.9789319 1.0855162 1.0865905
## [3,] 1.0448792 1.1124269 1.1202775 1.1307786 1.1824509 1.1908090 1.2053786
## [4,] 0.7515965 0.8451115 0.8463285 0.8773696 0.8788666 0.8837025 0.8980226
## [5,] 0.8458863 0.9264530 0.9888018 1.0014175 1.0027488 1.0098700 1.0128590
## [6,] 0.9340589 1.0078800 1.0261086 1.0402877 1.0534461 1.0604241 1.1142859
## [,8] [,9] [,10]
## [1,] 1.0730520 1.0745016 1.0760593
## [2,] 1.0958460 1.1005297 1.1071504
## [3,] 1.2099943 1.2122591 1.2151444
## [4,] 0.9053535 0.9185046 0.9222714
## [5,] 1.0157803 1.0190847 1.0253924
## [6,] 1.1289262 1.1301519 1.1528408
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$index[3,]
## [1] 3150 2092 8001 2389 3315 3017 416 7905 1343 2104
… with the following distances to those neighbors:
fout$distance[3,]
## [1] 1.044879 1.112427 1.120277 1.130779 1.182451 1.190809 1.205379 1.209994
## [9] 1.212259 1.215144
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$index)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 6401 1014 5776 9858 6161
## [2,] 2902 7581 1169 1316 4376
## [3,] 3652 170 7005 9353 7201
## [4,] 2215 9568 5005 5033 2814
## [5,] 5743 5242 2632 4851 4115
## [6,] 1809 9397 8548 5473 5132
head(qout$distance)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.8050374 0.8462342 0.8506457 0.9750981 0.9802985
## [2,] 0.8913882 0.9587463 0.9702392 0.9975312 1.0062795
## [3,] 0.9320308 0.9775122 0.9929154 1.0210373 1.0808122
## [4,] 0.9226920 0.9374076 0.9919162 1.0283241 1.0378355
## [5,] 0.8773009 0.8788105 0.8913275 0.9005823 0.9056954
## [6,] 0.8453398 0.8590331 0.8916978 0.9019537 0.9646821
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$index[3,]
## [1] 3652 170 7005 9353 7201
… with the following distances to those neighbors:
qout$distance[3,]
## [1] 0.9320308 0.9775122 0.9929154 1.0210373 1.0808122
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,] 3150 2092 8001 2389 3315
## [2,] 6592 8313 2598 4078 9490
## [3,] 747 5797 5847 6325 6183
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.0448792 1.1124269 1.1202775 1.1307786 1.1824509
## [2,] 0.7515965 0.8451115 0.8463285 0.8773696 0.8788666
## [3,] 0.8458863 0.9264530 0.9888018 1.0014175 1.0027488
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 4.3.2 Patched (2023-11-01 r85457)
## Platform: x86_64-apple-darwin20 (64-bit)
## Running under: macOS Monterey 12.7.1
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
##
## locale:
## [1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: America/New_York
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] BiocParallel_1.36.0 BiocNeighbors_1.20.2 knitr_1.45
## [4] BiocStyle_2.30.0
##
## loaded via a namespace (and not attached):
## [1] cli_3.6.2 rlang_1.1.2 xfun_0.41
## [4] jsonlite_1.8.8 S4Vectors_0.40.2 htmltools_0.5.7
## [7] stats4_4.3.2 sass_0.4.8 rmarkdown_2.25
## [10] grid_4.3.2 evaluate_0.23 jquerylib_0.1.4
## [13] fastmap_1.1.1 yaml_2.3.8 lifecycle_1.0.4
## [16] bookdown_0.37 BiocManager_1.30.22 compiler_4.3.2
## [19] codetools_0.2-19 Rcpp_1.0.11 lattice_0.22-5
## [22] digest_0.6.33 R6_2.5.1 parallel_4.3.2
## [25] bslib_0.6.1 Matrix_1.6-4 tools_4.3.2
## [28] BiocGenerics_0.48.1 cachem_1.0.8
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.