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$index)
##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 6670 5842 4500 3393 8541 7131 9803 9499 1765  7784
## [2,]   41 8166 2239 9779 9915 9942 2601  306 7626  5323
## [3,] 8682  807 2703 2960 9354 6073  978 8852 6997  2741
## [4,] 7672 4103 2564 4031 6400 3554 4607 4557 7800  3620
## [5,] 7464 2283  158 6981 4752 8833 2908 3936 8379  3841
## [6,] 8952 5883 9564  130 4482 3590 4024 9142 5892   238
head(fout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
## [1,] 0.7185587 0.8849660 0.8990269 0.9272472 0.9426381 0.9509270 0.9781944
## [2,] 0.9375380 1.0224338 1.0480847 1.0677400 1.0908558 1.1178118 1.1202444
## [3,] 0.9684885 0.9710075 0.9873037 0.9948838 1.0341672 1.0428770 1.0463076
## [4,] 0.9653872 1.0137937 1.0161486 1.0230589 1.0237193 1.0367494 1.0368437
## [5,] 0.8731992 0.8765553 0.8851078 0.8890289 0.9425309 0.9523616 0.9726140
## [6,] 0.9558727 1.0701734 1.0881078 1.1048518 1.1080862 1.1132088 1.1334031
##          [,8]     [,9]    [,10]
## [1,] 1.014034 1.016446 1.024055
## [2,] 1.123012 1.124689 1.128097
## [3,] 1.069681 1.081369 1.088220
## [4,] 1.039266 1.041562 1.047012
## [5,] 0.979152 1.008427 1.011603
## [6,] 1.134022 1.140072 1.154267

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$index)
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1162  391 4447 2610 5932
## [2,] 9325 8106  264 9919 6426
## [3,] 4514 6004 2082 7320 5387
## [4,] 7159 1214 7660 2820 8678
## [5,] 5989 8563 4765 2050  738
## [6,] 3098 9614 1291  901 8368
head(qout$distance)
##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 0.8793623 0.8979356 0.9143692 0.9378607 1.0349739
## [2,] 0.9202604 0.9274356 0.9511770 0.9615410 0.9667929
## [3,] 0.8071835 0.9572333 0.9834715 1.0442172 1.0469409
## [4,] 0.9567441 1.1421938 1.1536205 1.1682745 1.1762619
## [5,] 0.7843636 0.9174890 0.9415302 0.9419450 0.9560050
## [6,] 0.8676425 0.9382980 0.9920224 1.0139333 1.0571074

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 and will be removed when the session finishes.

AnnoyIndex_path(pre)
## [1] "C:\\Users\\biocbuild\\bbs-3.11-bioc\\tmpdir\\Rtmpe0W1Zo\\file15e4172e18da.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 Under development (unstable) (2020-01-27 r77730)
## 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_1.5.2 knitr_1.28          BiocStyle_2.15.6   
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.3          bookdown_0.18       lattice_0.20-40    
##  [4] digest_0.6.25       grid_4.0.0          stats4_4.0.0       
##  [7] magrittr_1.5        evaluate_0.14       rlang_0.4.5        
## [10] stringi_1.4.6       S4Vectors_0.25.12   Matrix_1.2-18      
## [13] rmarkdown_2.1       BiocParallel_1.21.2 tools_4.0.0        
## [16] stringr_1.4.0       parallel_4.0.0      xfun_0.12          
## [19] yaml_2.2.1          compiler_4.0.0      BiocGenerics_0.33.0
## [22] BiocManager_1.30.10 htmltools_0.4.0