BiocNeighbors 1.22.0
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$index)## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 4507 1085 500 227 478 9802 1730 5746 1100 628
## [2,] 2589 4533 9240 524 7720 8177 8831 6667 8700 441
## [3,] 5109 430 6499 4465 6993 7202 2372 3516 1789 9239
## [4,] 3904 2818 128 7977 4060 9920 2256 7755 624 5406
## [5,] 7731 3973 8541 1184 964 5974 8372 6989 1335 4491
## [6,] 7888 3784 9091 2303 9660 2874 7292 745 7267 3494head(fout$distance)## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.9767670 0.9841882 1.0020700 1.0033059 1.0287915 1.0390664 1.0491234
## [2,] 0.6838043 0.8183776 0.9562435 0.9594600 0.9716077 0.9759345 0.9841573
## [3,] 0.8404967 0.8683284 0.8735712 0.9223438 0.9257924 0.9333166 0.9440326
## [4,] 0.9675290 0.9999831 1.0056546 1.0235907 1.0333157 1.0700736 1.0824257
## [5,] 0.8031319 0.9724362 1.0108992 1.0159501 1.0278135 1.1077578 1.1172013
## [6,] 0.8002232 0.8482672 0.9253086 0.9382818 0.9492094 0.9533863 0.9706040
## [,8] [,9] [,10]
## [1,] 1.0506659 1.0521176 1.0873076
## [2,] 0.9917927 0.9940748 1.0001611
## [3,] 0.9573487 0.9593465 0.9674145
## [4,] 1.0904314 1.0919558 1.0949146
## [5,] 1.1246821 1.1466751 1.1578654
## [6,] 0.9899207 0.9917975 1.0146288Each 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$index[3,]## [1] 5109 430 6499 4465 6993 7202 2372 3516 1789 9239… with the following distances to those neighbors:
fout$distance[3,]## [1] 0.8404967 0.8683284 0.8735712 0.9223438 0.9257924 0.9333166 0.9440326
## [8] 0.9573487 0.9593465 0.9674145Note 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$index)## [,1] [,2] [,3] [,4] [,5]
## [1,] 4421 3516 4885 9301 5776
## [2,] 1962 5017 1251 2981 2270
## [3,] 4421 1730 1001 6351 5218
## [4,] 8877 8182 4092 2033 3259
## [5,] 1085 3952 8868 5961 6264
## [6,] 7374 7138 4528 7894 18head(qout$distance)## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.9262715 0.9584064 0.9716758 0.9747832 0.9791279
## [2,] 0.8242135 0.9540551 0.9812614 0.9922348 1.0075502
## [3,] 0.8064825 0.8364945 0.8414388 0.8616491 0.9092441
## [4,] 0.8058215 0.8446077 0.8871687 0.8954431 0.9501778
## [5,] 0.9360906 0.9521199 0.9624938 0.9758149 0.9890881
## [6,] 0.9591010 0.9849566 1.0226872 1.0360835 1.0381943Each 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$index[3,]## [1] 4421 1730 1001 6351 5218… with the following distances to those neighbors:
qout$distance[3,]## [1] 0.8064825 0.8364945 0.8414388 0.8616491 0.9092441Again, 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,] 5109 430 6499 4465 6993
## [2,] 3904 2818 128 7977 4060
## [3,] 7731 3973 8541 1184 964
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.8404967 0.8683284 0.8735712 0.9223438 0.9257924
## [2,] 0.9675290 0.9999831 1.0056546 1.0235907 1.0333157
## [3,] 0.8031319 0.9724362 1.0108992 1.0159501 1.0278135If 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 4.4.0 beta (2024-04-15 r86425)
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## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
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## [1] BiocParallel_1.38.0 BiocNeighbors_1.22.0 knitr_1.46
## [4] BiocStyle_2.32.0
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## loaded via a namespace (and not attached):
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## [25] bslib_0.7.0 Matrix_1.7-0 tools_4.4.0
## [28] BiocGenerics_0.50.0 cachem_1.0.8Wang, 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.