BiocNeighbors 1.16.0
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$index)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 717 5496 3565 8997 7322 866 4694 2917 3343 6072
## [2,] 1853 3527 5796 790 9964 8919 4410 7172 7672 8837
## [3,] 4700 8828 3653 4087 4599 7992 3385 7156 4363 4785
## [4,] 6406 8363 1675 9586 1425 4676 5775 9240 9710 5488
## [5,] 5739 6973 1454 6377 5065 5883 3622 2642 1627 6345
## [6,] 9150 432 7032 4270 5856 291 6420 2732 2673 1429head(fout$distance)## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 1.0786411 1.0935873 1.1091675 1.1110469 1.1135933 1.1282774 1.1372475
## [2,] 0.9813525 1.0827709 1.0910177 1.1131309 1.1348132 1.1391874 1.1529560
## [3,] 0.8852510 0.9270202 0.9349374 0.9863894 0.9865515 0.9885502 1.0247215
## [4,] 0.8541885 0.9425756 0.9639482 0.9666795 0.9863081 1.0008632 1.0195524
## [5,] 0.7791659 0.8932182 0.9575628 0.9940821 1.0036101 1.0358600 1.0452221
## [6,] 0.8065253 0.8381450 0.8574622 0.8711766 0.8881060 0.9022264 0.9250125
## [,8] [,9] [,10]
## [1,] 1.1439494 1.1440076 1.1514502
## [2,] 1.1562024 1.1569880 1.1654826
## [3,] 1.0308652 1.0315084 1.0323486
## [4,] 1.0379479 1.0419155 1.0497176
## [5,] 1.0516996 1.0558903 1.0571575
## [6,] 0.9367332 0.9618553 0.9633797Each 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$index[3,]## [1] 4700 8828 3653 4087 4599 7992 3385 7156 4363 4785… with the following distances to those neighbors:
fout$distance[3,]## [1] 0.8852510 0.9270202 0.9349374 0.9863894 0.9865515 0.9885502 1.0247215
## [8] 1.0308652 1.0315084 1.0323486Note 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$index)## [,1] [,2] [,3] [,4] [,5]
## [1,] 7459 4411 8165 5320 2984
## [2,] 39 1469 772 5990 5448
## [3,] 7979 4022 7683 1120 6510
## [4,] 2554 9370 8031 9103 1448
## [5,] 9713 6659 3394 7012 499
## [6,] 8299 7001 241 9121 2402head(qout$distance)## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.9477588 0.9632012 1.0194776 1.0381358 1.062561
## [2,] 0.9175062 0.9570939 0.9703075 0.9707472 1.014997
## [3,] 0.9670374 0.9827063 0.9945135 1.0007530 1.019716
## [4,] 0.9760775 0.9784902 1.0200073 1.0330013 1.046844
## [5,] 0.8773103 0.9597151 1.0116841 1.0118393 1.036191
## [6,] 0.9351569 0.9700087 1.0046291 1.0344532 1.049225Each 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$index[3,]## [1] 7979 4022 7683 1120 6510… with the following distances to those neighbors:
qout$distance[3,]## [1] 0.9670374 0.9827063 0.9945135 1.0007530 1.0197165Again, 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,] 4700 8828 3653 4087 4599
## [2,] 6406 8363 1675 9586 1425
## [3,] 5739 6973 1454 6377 5065
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.8852510 0.9270202 0.9349374 0.9863894 0.9865515
## [2,] 0.8541885 0.9425756 0.9639482 0.9666795 0.9863081
## [3,] 0.7791659 0.8932182 0.9575628 0.9940821 1.0036101If 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 4.2.1 (2022-06-23)
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## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
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## other attached packages:
## [1] BiocParallel_1.32.0 BiocNeighbors_1.16.0 knitr_1.40
## [4] BiocStyle_2.26.0
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## [28] compiler_4.2.1 bslib_0.4.0 stats4_4.2.1
## [31] jsonlite_1.8.3Wang, 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.