# Detecting all neighbors within range

Aaron Lun1

1Cancer Research UK Cambridge Institute, Cambridge, United Kingdom

#### Revised: 28 September 2018

#### Package

BiocNeighbors 1.10.0

# 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 1 1 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] 1
    ##
    ## [[2]]
    ## [1] 8590 7680 7011 2032 4387    2 8714
    ##
    ## [[3]]
    ## [1] 5720   37    3 1718 7418 1383 1735
    ##
    ## [[4]]
    ##  [1]    4  936 4186 6117 8777 4572  580 8218 5449 1043 8709 8334 1074 3703 8663
    ##
    ## [[5]]
    ## [1]    5 4862 6994
    ##
    ## [[6]]
    ## [1] 3791 6649    6 2611

    head(fout$distance)

    ## [[1]]
    ## [1] 0
    ##
    ## [[2]]
    ## [1] 0.9797965 0.9654207 0.8971848 0.9617076 0.9352298 0.0000000 0.8493332
    ##
    ## [[3]]
    ## [1] 0.9803434 0.9667961 0.0000000 0.9705440 0.9895502 0.9865487 0.9303542
    ##
    ## [[4]]
    ##  [1] 0.0000000 0.9721815 0.7464181 0.9984760 0.9626595 0.9352461 0.9854087
    ##  [8] 0.9147710 0.7629608 0.9298186 0.8944313 0.9532620 0.8190642 0.9233504
    ## [15] 0.9655886
    ##
    ## [[5]]
    ## [1] 0.0000000 0.9897847 0.9676718
    ##
    ## [[6]]
    ## [1] 0.9787186 0.9679821 0.0000000 0.9441925

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] 5720   37    3 1718 7418 1383 1735

… with the following distances to those neighbors:

    fout$distance[[3]]

    ## [1] 0.9803434 0.9667961 0.0000000 0.9705440 0.9895502 0.9865487 0.9303542

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 4.1.0 RC (2021-05-10 r80283)
    ## Platform: x86_64-w64-mingw32/x64 (64-bit)
    ## Running under: Windows Server x64 (build 17763)
    ##
    ## Matrix products: default
    ##
    ## locale:
    ## [1] LC_COLLATE=C
    ## [2] LC_CTYPE=English_United States.1252
    ## [3] LC_MONETARY=English_United States.1252
    ## [4] LC_NUMERIC=C
    ## [5] LC_TIME=English_United States.1252
    ##
    ## attached base packages:
    ## [1] stats     graphics  grDevices utils     datasets  methods   base
    ##
    ## other attached packages:
    ## [1] BiocParallel_1.26.0  BiocNeighbors_1.10.0 knitr_1.33
    ## [4] BiocStyle_2.20.0
    ##
    ## loaded via a namespace (and not attached):
    ##  [1] Rcpp_1.0.6          magrittr_2.0.1      BiocGenerics_0.38.0
    ##  [4] lattice_0.20-44     R6_2.5.0            rlang_0.4.11
    ##  [7] stringr_1.4.0       tools_4.1.0         parallel_4.1.0
    ## [10] grid_4.1.0          xfun_0.23           jquerylib_0.1.4
    ## [13] htmltools_0.5.1.1   yaml_2.2.1          digest_0.6.27
    ## [16] bookdown_0.22       Matrix_1.3-3        BiocManager_1.30.15
    ## [19] S4Vectors_0.30.0    sass_0.4.0          evaluate_0.14
    ## [22] rmarkdown_2.8       stringi_1.6.2       compiler_4.1.0
    ## [25] bslib_0.2.5.1       stats4_4.1.0        jsonlite_1.7.2