1 Identifying all neighbors within range

Another application of the KMKNN or VP tree algorithms is to identify all neighboring points within a certain distance1 The default here is Euclidean, but again, we can set distance="Manhattan" in the BNPARAM object if so desired. 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$index)
## [[1]]
##  [1] 6307    1 2704 2708 5004 4868 1933 2679 2631 9372
## 
## [[2]]
## [1] 1378 7679    2 4665
## 
## [[3]]
## [1]    3 3934
## 
## [[4]]
## [1] 4844    4 3743
## 
## [[5]]
## [1] 2509 5745 1877    5 5752 8222  429 1835 2485
## 
## [[6]]
##  [1] 2287 1303  387 8873 2209 6979 1787 9550    6 7421 4287
head(fout$distance)
## [[1]]
##  [1] 0.9867971 0.0000000 0.9198131 0.9814426 0.8810862 0.9461322 0.9109379
##  [8] 0.9860806 0.9790864 0.9599674
## 
## [[2]]
## [1] 0.7816283 0.9656471 0.0000000 0.9769939
## 
## [[3]]
## [1] 0.0000000 0.9691575
## 
## [[4]]
## [1] 0.9355751 0.0000000 0.9820630
## 
## [[5]]
## [1] 0.9219408 0.9931680 0.9607401 0.0000000 0.9734772 0.9923300 0.9623091
## [8] 0.9112840 0.9473762
## 
## [[6]]
##  [1] 0.9866593 0.9993977 0.9640843 0.9935514 0.9826977 0.9543303 0.9753682
##  [8] 0.9867198 0.0000000 0.9751370 0.9052411

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]    3 3934

… with the following distances to those neighbors:

fout$distance[[3]]
## [1] 0.0000000 0.9691575

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 4.4.0 alpha (2024-03-27 r86216)
## Platform: aarch64-apple-darwin20
## Running under: macOS Ventura 13.6.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
## 
## locale:
## [1] en_US.UTF-8/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_1.38.0  BiocNeighbors_1.22.0 knitr_1.45          
## [4] BiocStyle_2.32.0    
## 
## loaded via a namespace (and not attached):
##  [1] cli_3.6.2           rlang_1.1.3         xfun_0.43          
##  [4] jsonlite_1.8.8      S4Vectors_0.42.0    htmltools_0.5.8    
##  [7] stats4_4.4.0        sass_0.4.9          rmarkdown_2.26     
## [10] grid_4.4.0          evaluate_0.23       jquerylib_0.1.4    
## [13] fastmap_1.1.1       yaml_2.3.8          lifecycle_1.0.4    
## [16] bookdown_0.38       BiocManager_1.30.22 compiler_4.4.0     
## [19] codetools_0.2-19    Rcpp_1.0.12         lattice_0.22-6     
## [22] digest_0.6.35       R6_2.5.1            parallel_4.4.0     
## [25] bslib_0.6.2         Matrix_1.7-0        tools_4.4.0        
## [28] BiocGenerics_0.50.0 cachem_1.0.8