# Detecting all neighbors within range

Aaron Lun1

1Cancer Research UK Cambridge Institute, Cambridge, United Kingdom

#### Revised: 28 September 2018

#### Package

BiocNeighbors 1.0.0

# 1 Identifying all neighbors within range

Another application of the KMKNN algorithm 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] 9683    1
    ##
    ## [[2]]
    ## [1] 5081    2
    ##
    ## [[3]]
    ## [1] 6654 5761    3
    ##
    ## [[4]]
    ## [1] 1297    4
    ##
    ## [[5]]
    ## [1] 6016  851    5 2987 3824
    ##
    ## [[6]]
    ##  [1] 2798 2768 7733 8357 5223 6087 1123 5628  901  242    6 5366

    head(fout$distance)

    ## [[1]]
    ## [1] 0.9581993 0.0000000
    ##
    ## [[2]]
    ## [1] 0.9711536 0.0000000
    ##
    ## [[3]]
    ## [1] 0.9069003 0.9263137 0.0000000
    ##
    ## [[4]]
    ## [1] 0.9829846 0.0000000
    ##
    ## [[5]]
    ## [1] 0.9738536 0.9320095 0.0000000 0.9778623 0.9370519
    ##
    ## [[6]]
    ##  [1] 0.8952555 0.9503344 0.8737941 0.9848975 0.9932740 0.9187211 0.9914165
    ##  [8] 0.9677364 0.9921727 0.9791581 0.0000000 0.9180528

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] 6654 5761    3

… with the following distances to those neighbors:

    fout$distance[[3]]

    ## [1] 0.9069003 0.9263137 0.0000000

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

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

# 4 Session information

    sessionInfo()

    ## R version 3.5.1 Patched (2018-07-24 r75008)
    ## Platform: x86_64-w64-mingw32/x64 (64-bit)
    ## Running under: Windows Server 2012 R2 x64 (build 9600)
    ##
    ## 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] BiocNeighbors_1.0.0 BiocParallel_1.16.0 knitr_1.20
    ## [4] BiocStyle_2.10.0
    ##
    ## loaded via a namespace (and not attached):
    ##  [1] Rcpp_0.12.19        bookdown_0.7        digest_0.6.18
    ##  [4] rprojroot_1.3-2     backports_1.1.2     stats4_3.5.1
    ##  [7] magrittr_1.5        evaluate_0.12       stringi_1.2.4
    ## [10] S4Vectors_0.20.0    rmarkdown_1.10      tools_3.5.1
    ## [13] stringr_1.3.1       parallel_3.5.1      xfun_0.4
    ## [16] yaml_2.2.0          compiler_3.5.1      BiocGenerics_0.28.0
    ## [19] BiocManager_1.30.3  htmltools_0.3.6