# 1 Identifying all neighbors within range

Another application of the KMKNN or VP tree algorithms is to identify all neighboring points within a certain (Euclidean) distance of the current point. We first mock up some data:

nobs <- 10000
ndim <- 20
data <- matrix(runif(nobs*ndim), ncol=ndim)

We apply the findNeighbors() function to data:

fout <- findNeighbors(data, threshold=1)
head(fout$index) ## [[1]] ## [1] 1756 1 9355 ## ## [[2]] ## [1] 9194 9848 2 2040 4586 ## ## [[3]] ## [1] 6913 5574 3 1850 ## ## [[4]] ## [1] 5445 244 6441 4 3412 8251 6973 6063 1305 ## ## [[5]] ## [1] 6756 5950 2678 9138 7053 1863 7470 5 9421 1422 8176 8881 ## ## [[6]] ## [1] 6 head(fout$distance)
## [[1]]
## [1] 0.9096893 0.0000000 0.9021399
##
## [[2]]
## [1] 0.9583510 0.9663208 0.0000000 0.9486633 0.9698446
##
## [[3]]
## [1] 0.9689200 0.7661127 0.0000000 0.6021658
##
## [[4]]
## [1] 0.9454924 0.9360769 0.9739233 0.0000000 0.9362015 0.8937635 0.9912348
## [8] 0.9894622 0.9926280
##
## [[5]]
##  [1] 0.9987764 0.9558512 0.8611543 0.9918701 0.9771978 0.9277783 0.9781327
##  [8] 0.0000000 0.9867415 0.9620960 0.8994385 0.9159305
##
## [[6]]
## [1] 0

Each entry of the index list corresponds to a point in data and contains the row indices in data that are within threshold. For example, the 3rd point in data has the following neighbors:

fout$index[[3]] ## [1] 6913 5574 3 1850 … with the following distances to those neighbors: fout$distance[[3]]
## [1] 0.9689200 0.7661127 0.0000000 0.6021658

Note that, for this function, the reported neighbors are not sorted by distance. The order of the output is completely arbitrary and will vary depending on the random seed. However, the identity of the neighbors is fully deterministic.

# 2 Querying another data set for neighbors

The queryNeighbors() function is also provided for identifying all points within a certain distance of a query point. Given a query data set:

nquery <- 1000
ndim <- 20
query <- matrix(runif(nquery*ndim), ncol=ndim)

… we apply the queryNeighbors() function:

qout <- queryNeighbors(data, query, threshold=1)
length(qout$index) ## [1] 1000 … where each entry of qout$index corresponds to a row of query and contains its neighbors in data. Again, the order of the output is arbitrary but the identity of the neighbors is deterministic.

# 3 Further options

Most of the options described for findKNN() are also applicable here. For example:

• subset to identify neighbors for a subset of points.
• get.distance to avoid retrieving distances when unnecessary.
• BPPARAM to parallelize the calculations across multiple workers.
• raw.index to return the raw indices from a precomputed index.

Note that the argument for a precomputed index is precomputed:

pre <- buildIndex(data, BNPARAM=KmknnParam())
fout.pre <- findNeighbors(BNINDEX=pre, threshold=1)
qout.pre <- queryNeighbors(BNINDEX=pre, query=query, threshold=1)

Users are referred to the documentation of each function for specific details.

# 4 Session information

sessionInfo()
## R version 3.6.0 (2019-04-26)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.2 LTS
##
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.9-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.9-bioc/R/lib/libRlapack.so
##
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=C
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base
##
## other attached packages:
## [1] BiocParallel_1.18.0 BiocNeighbors_1.2.0 knitr_1.22
## [4] BiocStyle_2.12.0
##
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.1          bookdown_0.9        digest_0.6.18
##  [4] stats4_3.6.0        magrittr_1.5        evaluate_0.13
##  [7] stringi_1.4.3       S4Vectors_0.22.0    rmarkdown_1.12
## [10] tools_3.6.0         stringr_1.4.0       parallel_3.6.0
## [13] xfun_0.6            yaml_2.2.0          compiler_3.6.0
## [16] BiocGenerics_0.30.0 BiocManager_1.30.4  htmltools_0.3.6