# 1 Introduction

The BiocNeighbors package provides several algorithms for approximate neighbor searches:

• The Annoy (Approximate Nearest Neighbors Oh Yeah) method uses C++ code from the RcppAnnoy package. It works by building a tree where a random hyperplane partitions a group of 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 from 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 move 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$index) ## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] ## [1,] 3330 453 5202 1713 84 1954 6101 5370 6996 255 ## [2,] 4316 4108 8339 2349 8027 4012 7406 4294 9085 2981 ## [3,] 1488 2739 4203 7265 2415 9604 1684 4807 1929 368 ## [4,] 503 3776 3251 223 8246 154 7273 4974 8659 4734 ## [5,] 263 2254 4146 7821 8135 6604 5996 1620 8644 2938 ## [6,] 9232 5844 9273 2854 29 6970 6750 3720 8387 6651 head(fout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]     [,7]
## [1,] 0.9549388 0.9730841 0.9882953 0.9905818 0.9938405 0.9974384 1.000726
## [2,] 1.0250026 1.0309801 1.0598124 1.1316205 1.1389508 1.1660076 1.177922
## [3,] 0.8048801 0.9330851 0.9579151 0.9606285 0.9664934 1.0006901 1.012451
## [4,] 0.8739503 0.9477754 0.9998853 1.0192013 1.0375460 1.0391052 1.041700
## [5,] 0.9000127 0.9015812 0.9615081 0.9739660 0.9995403 1.0007290 1.025438
## [6,] 0.9290770 1.0146314 1.0224247 1.0559702 1.0629684 1.0785404 1.093382
##          [,8]     [,9]    [,10]
## [1,] 1.002664 1.007617 1.019291
## [2,] 1.178585 1.190359 1.196825
## [3,] 1.012911 1.023324 1.029479
## [4,] 1.052582 1.058496 1.059432
## [5,] 1.058356 1.063869 1.067919
## [6,] 1.100609 1.100866 1.105177

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$index) ## [,1] [,2] [,3] [,4] [,5] ## [1,] 9728 4016 4777 1961 3795 ## [2,] 8444 2423 9186 7961 4366 ## [3,] 5585 8332 6774 3664 6207 ## [4,] 1247 2838 748 5210 8646 ## [5,] 25 8704 419 589 6180 ## [6,] 2465 864 5663 6221 4024 head(qout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 0.9035632 0.9583917 0.9695784 0.9708687 0.9732593
## [2,] 0.7779893 0.9002860 0.9738870 0.9785135 0.9811455
## [3,] 0.7432720 0.9567128 0.9840043 1.0007811 1.0292883
## [4,] 0.9533122 0.9736031 0.9905141 1.0444406 1.0453193
## [5,] 0.8218890 0.8650465 0.9208409 0.9362080 0.9643939
## [6,] 0.9163575 0.9436435 1.0057408 1.0197005 1.0507250

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

# 3 Further options

Most of the options described for the exact methods 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)

Both Annoy and HNSW perform searches based on the Euclidean distance by default. Searching by Manhattan distance is done by simply setting distance="Manhattan" in AnnoyParam() or HnswParam().

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

# 4 Saving the index files

Both Annoy and HNSW generate indexing structures - a forest of trees and series of graphs, respectively - that are saved to file when calling buildIndex(). By default, this file is located in tempdir()1 On HPC file systems, you can change TEMPDIR to a location that is more amenable to concurrent access. and will be removed when the session finishes.

AnnoyIndex_path(pre)
## [1] "/tmp/RtmpFLnDHO/file7bd9127d33df.idx"

If the index is to persist across sessions, the path of the index file can be directly specified in buildIndex. This can be used to construct an index object directly using the relevant constructors, e.g., AnnoyIndex(), HnswIndex(). However, it becomes the responsibility of the user to clean up any temporary indexing files after calculations are complete.

# 5 Session information

sessionInfo()
## R version 3.6.2 (2019-12-12)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.3 LTS
##
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.10-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.10-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] BiocNeighbors_1.4.2 knitr_1.28          BiocStyle_2.14.4
##
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.3          bookdown_0.17       lattice_0.20-40
##  [4] digest_0.6.25       grid_3.6.2          stats4_3.6.2
##  [7] magrittr_1.5        evaluate_0.14       rlang_0.4.4
## [10] stringi_1.4.6       S4Vectors_0.24.3    Matrix_1.2-18
## [13] rmarkdown_2.1       BiocParallel_1.20.1 tools_3.6.2
## [16] stringr_1.4.0       parallel_3.6.2      xfun_0.12
## [19] yaml_2.2.1          compiler_3.6.2      BiocGenerics_0.32.0
## [22] BiocManager_1.30.10 htmltools_0.4.0