1 Introduction

The BiocNeighbors package implements a few algorithms for exact nearest neighbor searching:

• The k-means for k-nearest neighbors (KMKNN) algorithm (Wang 2012) uses k-means clustering to create an index. Within each cluster, the distance of each of that cluster’s points to the cluster center are computed and used to sort all points. Given a query point, the distance to each cluster center is determined and the triangle inequality is applied to determine which points in each cluster warrant a full distance calculation.
• The vantage point (VP) tree algorithm (Yianilos 1993) involves constructing a tree where each node is located at a data point and is associated with a subset of neighboring points. Each node progressively partitions points into two subsets that are either closer or further to the node than a given threshold. Given a query point, the triangle inequality is applied at each node in the tree to determine if the child nodes warrant searching.

Both methods involve a component of randomness during index construction, though the k-nearest neighbors result is fully deterministic11 Except in the presence of ties, see ?findKNN for details..

2 Identifying k-nearest neighbors

The most obvious application is to perform a k-nearest neighbors search. We’ll mock up an example here with a hypercube of points, for which we want to identify the 10 nearest neighbors for each point.

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

The findKNN() method expects a numeric matrix as input with data points as the rows and variables/dimensions as the columns. We indicate that we want to use the KMKNN algorithm by setting BNPARAM=KmknnParam() (which is also the default, so this is not strictly necessary here). We could use a VP tree instead by setting BNPARAM=VptreeParam().

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

##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,] 6709 9627 8683 8907 4811 8728 9935 5093 1868   121
## [2,] 7593 9203 6652  961 2856 8711 4412 8907 4666  2811
## [3,] 8361 2534 7096 1443 8355 5135  730 9233 5057  3333
## [4,] 6116 9935 8994 4613 7533 7671 4938  587 9627  6673
## [5,] 4363 7309 3126 6247 4800 2470 1907  285 7956  3990
## [6,] 8871 5867 7618 1557 1016 7067  473  187  271  1517

head(fout$distance)

##           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
## [1,] 0.9134994 0.9279878 0.9321199 0.9432648 0.9759880 0.9883781 0.9904984
## [2,] 0.8612897 0.9499456 0.9703708 0.9782614 1.0085772 1.0099281 1.0102099
## [3,] 1.0378627 1.0478542 1.0709121 1.0858699 1.0869769 1.0923892 1.0965950
## [4,] 0.9568614 1.0717803 1.0742441 1.0990840 1.1128575 1.1139495 1.1360398
## [5,] 0.8285719 0.8375260 0.8930268 0.9053241 0.9169200 0.9226835 0.9358931
## [6,] 0.7955337 0.9129179 0.9275191 0.9435631 0.9749024 0.9931279 0.9980455
##           [,8]      [,9]     [,10]
## [1,] 0.9966502 1.0032015 1.0052059
## [2,] 1.0129669 1.0177056 1.0362768
## [3,] 1.1051209 1.1088504 1.1158236
## [4,] 1.1429454 1.1429834 1.1538995
## [5,] 0.9490294 0.9546187 0.9621188
## [6,] 0.9994188 1.0027133 1.0101063

Each row of the index matrix corresponds to a point in data and contains the row indices in data that are its nearest neighbors. For example, the 3rd point in data has the following nearest neighbors:

fout$index[3,]

##  [1] 8361 2534 7096 1443 8355 5135  730 9233 5057 3333

… with the following distances to those neighbors:

fout$distance[3,]

##  [1] 1.037863 1.047854 1.070912 1.085870 1.086977 1.092389 1.096595 1.105121
##  [9] 1.108850 1.115824

Note that the reported neighbors are sorted by distance.

3 Querying k-nearest neighbors

Another application is to identify the k-nearest neighbors in one dataset based on query points in another dataset. Again, we mock up a small data set:

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

We then use the queryKNN() function to identify the 5 nearest neighbors in data for each point in query.

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

##      [,1] [,2] [,3] [,4] [,5]
## [1,] 4271 6336 1896   66 5255
## [2,]  577 2631 4942 8018 9216
## [3,] 1282 7391 6915 9507 6113
## [4,] 8115 5553 2903 1729 1585
## [5,] 9979 5919 7712 1312 6032
## [6,] 7124 1550 5867 4266 1743

head(qout$distance)

##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 0.8255378 0.9534278 0.9662206 0.9895064 0.9973368
## [2,] 0.9082208 0.9134062 0.9218634 0.9518809 0.9672650
## [3,] 0.9416898 0.9466910 0.9773505 0.9956400 0.9989399
## [4,] 1.0114986 1.0219494 1.0297100 1.0405589 1.0559577
## [5,] 0.8845057 0.8972909 0.8973070 0.9025898 0.9055773
## [6,] 1.0793351 1.0811115 1.1228046 1.1345023 1.1360885

Each row of the index matrix contains the row indices in data that are the nearest neighbors of a point in query. For example, the 3rd point in query has the following nearest neighbors in data:

qout$index[3,]

## [1] 1282 7391 6915 9507 6113

… with the following distances to those neighbors:

qout$distance[3,]

## [1] 0.9416898 0.9466910 0.9773505 0.9956400 0.9989399

Again, the reported neighbors are sorted by distance.

4 Further options

Users can perform the search for a subset of query points using the subset= argument. This yields the same result as but is more efficient than performing the search for all points and subsetting the output.

findKNN(data, k=5, subset=3:5)

## $index
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 8361 2534 7096 1443 8355
## [2,] 6116 9935 8994 4613 7533
## [3,] 4363 7309 3126 6247 4800
## 
## $distance
##           [,1]     [,2]      [,3]      [,4]     [,5]
## [1,] 1.0378627 1.047854 1.0709121 1.0858699 1.086977
## [2,] 0.9568614 1.071780 1.0742441 1.0990840 1.112857
## [3,] 0.8285719 0.837526 0.8930268 0.9053241 0.916920

If only the indices are of interest, users can set get.distance=FALSE to avoid returning the matrix of distances. This will save some time and memory.

names(findKNN(data, k=2, get.distance=FALSE))

## [1] "index"

It is also simple to speed up functions by parallelizing the calculations with the BiocParallel framework.

library(BiocParallel)
out <- findKNN(data, k=10, BPPARAM=MulticoreParam(3))

For multiple queries to a constant data, the pre-clustering can be performed in a separate step with buildIndex(). The result can then be passed to multiple calls, avoiding the overhead of repeated clustering22 The algorithm type is automatically determined when BNINDEX is specified, so there is no need to also specify BNPARAM in the later functions..

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

Advanced users may also be interested in the raw.index= argument, which returns indices directly to the precomputed object rather than to data. This may be useful inside package functions where it may be more convenient to work on a common precomputed object.

5 Session information

sessionInfo()

## R version 3.6.0 (2019-04-26)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.2 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.9-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.9-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                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=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] BiocParallel_1.18.0 BiocNeighbors_1.2.0 knitr_1.22         
## [4] 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] tools_3.6.0         stringr_1.4.0       parallel_3.6.0     
## [13] xfun_0.6            yaml_2.2.0          compiler_3.6.0     
## [16] BiocGenerics_0.30.0 BiocManager_1.30.4  htmltools_0.3.6