# Detecting approximate nearest neighbors

Aaron Lun1

1Cancer Research UK Cambridge Institute, Cambridge, United Kingdom

#### Revised: 2 December 2018

#### Package

BiocNeighbors 1.2.0

# 1 Introduction

The BiocNeighbors package provides several algorithms for approximate neighbor searches:

- The Annoy (Approximate Nearest Neighbors Oh Yeah) method uses C++ code in the RcppAnnoy package. It works by building a tree where a random hyperplane partitions points into two child groups at each internal node. This is repeated to construct a forest of trees where the number of trees determines the accuracy of the search. Given a query data point, we identify all points in the same leaf node for each tree. We then take the union of leaf node sets across trees and search them exactly for the nearest neighbors.
- The HNSW (Hierarchical Navigable Small Worlds) method uses C++ code in the RcppHNSW package. It works by building a series of nagivable small world graphs containing links between points across the entire data set. The algorithm walks through the graphs where each step is chosen to get closer to a given query point. Different graphs contain links of different lengths, yielding a hierarchy where earlier steps are large and later steps are small. The accuracy of the search is determined by the connectivity of the graphs and the size of the intermediate list of potential neighbors.

These methods complement the exact algorithms described previously. Again, it is straightforward to switch from one algorithm to another by simply changing the `BNPARAM` argument in `findKNN` and `queryKNN`.

# 2 Identifying nearest neighbors

We perform the k-nearest neighbors search with the Annoy algorithm by specifying `BNPARAM=AnnoyParam()`.

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

    fout <- findKNN(data, k=10, BNPARAM=AnnoyParam())
    head(fout$index)

    ##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
    ## [1,] 2518  960 4651 3041 4593 9968 8204  148 9109  5322
    ## [2,] 7182 7627  480  167 2686 9737 7865 8253 4963  6519
    ## [3,]   96 8041  737 3280 6599 9222 2716 6781 2631  5531
    ## [4,] 1110 3395 6911 4060 6786 9344 5618 6930 6946  8445
    ## [5,] 6667 6231 5911 5863  333 9098   97 6999 7902   108
    ## [6,] 8000 3855 7572 1638 3080 9730 4500 9249 1871  7343

    head(fout$distance)

    ##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
    ## [1,] 0.9886118 1.0789745 1.1011719 1.1072190 1.1282983 1.1313829 1.1483887
    ## [2,] 0.9678174 0.9989009 1.0001528 1.0149844 1.0430777 1.0773309 1.0787989
    ## [3,] 0.8530040 0.8537472 0.8600176 0.9204907 0.9455487 0.9627153 0.9936166
    ## [4,] 0.9085732 0.9782447 1.0332650 1.0345398 1.0529071 1.0630660 1.1026986
    ## [5,] 0.8995217 0.9690334 1.0282756 1.0286645 1.0287858 1.0454463 1.0488964
    ## [6,] 0.9976661 1.0789716 1.0794306 1.1559469 1.1651425 1.1816528 1.1842009
    ##          [,8]     [,9]    [,10]
    ## [1,] 1.153453 1.160346 1.161580
    ## [2,] 1.093732 1.102553 1.103060
    ## [3,] 1.010614 1.025963 1.028584
    ## [4,] 1.135454 1.137568 1.138443
    ## [5,] 1.053010 1.055878 1.069182
    ## [6,] 1.184640 1.189335 1.194872

We can also identify the k-nearest neighbors in one dataset based on query points in another dataset.

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

    qout <- queryKNN(data, query, k=5, BNPARAM=AnnoyParam())
    head(qout$index)

    ##      [,1] [,2] [,3] [,4] [,5]
    ## [1,] 6388 1238 8748 4223 7113
    ## [2,] 3568  713 3653 9873 7198
    ## [3,] 6606 5190 8826 8325  168
    ## [4,] 2999 7547 1646 7016  667
    ## [5,] 3825 6983 7762 6548 8791
    ## [6,]   76  673 6958 5864 1673

    head(qout$distance)

    ##           [,1]      [,2]      [,3]      [,4]      [,5]
    ## [1,] 0.8677352 0.8680670 0.8719941 0.9507282 0.9643818
    ## [2,] 0.9030752 0.9831578 1.0177069 1.0188230 1.0511543
    ## [3,] 0.8654836 0.9786622 0.9809887 0.9890227 1.0002736
    ## [4,] 0.9947681 1.0191822 1.0230621 1.0469787 1.0477513
    ## [5,] 0.7239743 1.0286745 1.0508665 1.0740196 1.0862203
    ## [6,] 0.9796220 1.0947175 1.1007018 1.1038973 1.1076198

It is similarly easy to use the HNSW algorithm by setting `BNPARAM=HnswParam()`.

# 3 Further options

Most of the options described for the KMKNN algorithm 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.
- `BNINDEX` to build the forest once for a given data set and re-use it across calls.

The use of a pre-built `BNINDEX` is illustrated below:

    pre <- buildIndex(data, BNPARAM=AnnoyParam())
    out1 <- findKNN(BNINDEX=pre, k=5)
    out2 <- queryKNN(BNINDEX=pre, query=query, k=2)

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

# 4 Saving the index files

The forest of trees form an indexing structure that is saved to file. By default, this file is located in `tempdir()`11 On HPC file systems, you can change `TEMPDIR` to a location that is more amenable to parallelized access. and will be removed when the session finishes.

    AnnoyIndex_path(pre)

    ## [1] "C:\\Users\\biocbuild\\bbs-3.9-bioc\\tmpdir\\Rtmp2njyY7\\file1d8061e27de7.idx"

If the index is to persist across sessions, the path of the index file can be directly specified in `buildIndex`. However, this means that it becomes the responsibility of the user to clean up any temporary indexing files after calculations are complete.

# 5 Session information

    sessionInfo()

    ## R version 3.6.0 (2019-04-26)
    ## 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_1.2.0 knitr_1.22          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] BiocParallel_1.18.0 tools_3.6.0         stringr_1.4.0
    ## [13] parallel_3.6.0      xfun_0.6            yaml_2.2.0
    ## [16] compiler_3.6.0      BiocGenerics_0.30.0 BiocManager_1.30.4
    ## [19] htmltools_0.3.6