BiocNeighbors 1.3.5

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 deterministic1 Except in the presence of ties, see `?findKNN`

for details..

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,] 8643 8050 7556 1791 4870 8307 8629 8019 9312 5341
## [2,] 5039 9249 243 1143 6499 3085 7503 161 5712 3050
## [3,] 7506 5840 2518 6 1088 4421 6208 7573 990 9407
## [4,] 1027 662 5137 1460 6846 4309 9395 9133 180 4288
## [5,] 2707 3685 8865 495 8993 3949 4583 2054 385 1070
## [6,] 3548 7151 1351 2059 6314 4411 7116 7499 9969 5867
```

`head(fout$distance)`

```
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.9928941 1.0142308 1.0616408 1.0736943 1.0908586 1.0942658 1.1019943
## [2,] 0.8132958 0.8967493 0.9023984 0.9345345 0.9748746 0.9812595 0.9867675
## [3,] 1.0829746 1.1423671 1.1580350 1.2010582 1.2023029 1.2079923 1.2112802
## [4,] 0.8652383 0.9778326 0.9925514 1.0043222 1.0069838 1.0101185 1.0245297
## [5,] 0.9143798 0.9690342 0.9991463 1.0304064 1.0421800 1.0571152 1.0595250
## [6,] 0.8284996 0.8471161 0.8522459 0.9318427 0.9468924 0.9524671 0.9531929
## [,8] [,9] [,10]
## [1,] 1.1232429 1.1268754 1.1422908
## [2,] 1.0037871 1.0047605 1.0213207
## [3,] 1.2203126 1.2238721 1.2275924
## [4,] 1.0260313 1.0264183 1.0329192
## [5,] 1.0604566 1.0632011 1.0674584
## [6,] 0.9537012 0.9603866 0.9661172
```

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] 7506 5840 2518 6 1088 4421 6208 7573 990 9407`

… with the following distances to those neighbors:

`fout$distance[3,]`

```
## [1] 1.082975 1.142367 1.158035 1.201058 1.202303 1.207992 1.211280 1.220313
## [9] 1.223872 1.227592
```

Note that the reported neighbors are sorted by distance.

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,] 8811 6071 2838 1342 5033
## [2,] 5408 2380 7810 7902 7808
## [3,] 3144 2212 7847 8559 709
## [4,] 8183 5403 7618 5460 8569
## [5,] 8384 3346 4215 5805 3038
## [6,] 597 2503 604 868 2022
```

`head(qout$distance)`

```
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.7731231 0.7849397 0.8591461 0.9307955 0.9320467
## [2,] 0.8230939 0.8432400 0.9054017 0.9205062 0.9359921
## [3,] 0.9397287 1.0152623 1.0362824 1.0418488 1.0609618
## [4,] 0.9595535 0.9883123 1.0193167 1.0199952 1.0249624
## [5,] 0.9146208 0.9792278 0.9972007 1.0036989 1.0083684
## [6,] 1.0225860 1.0238219 1.0238623 1.0642002 1.0661172
```

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] 3144 2212 7847 8559 709`

… with the following distances to those neighbors:

`qout$distance[3,]`

`## [1] 0.9397287 1.0152623 1.0362824 1.0418488 1.0609618`

Again, the reported neighbors are sorted by distance.

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,] 7506 5840 2518 6 1088
## [2,] 1027 662 5137 1460 6846
## [3,] 2707 3685 8865 495 8993
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.0829746 1.1423671 1.1580350 1.201058 1.202303
## [2,] 0.8652383 0.9778326 0.9925514 1.004322 1.006984
## [3,] 0.9143798 0.9690342 0.9991463 1.030406 1.042180
```

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 clustering2 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)
```

The default setting is to search on the Euclidean distance.
Alternatively, we can use the Manhattan distance by setting `distance="Manhattan"`

in the `BiocNeighborParam`

object.

`out.m <- findKNN(data, k=5, BNPARAM=KmknnParam(distance="Manhattan"))`

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.

`sessionInfo()`

```
## R version 3.6.1 (2019-07-05)
## 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
## [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_1.19.2 BiocNeighbors_1.3.5 knitr_1.24
## [4] BiocStyle_2.13.2
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.2 bookdown_0.13 lattice_0.20-38
## [4] digest_0.6.20 grid_3.6.1 stats4_3.6.1
## [7] magrittr_1.5 evaluate_0.14 stringi_1.4.3
## [10] S4Vectors_0.23.23 Matrix_1.2-17 rmarkdown_1.15
## [13] tools_3.6.1 stringr_1.4.0 parallel_3.6.1
## [16] xfun_0.9 yaml_2.2.0 compiler_3.6.1
## [19] BiocGenerics_0.31.5 BiocManager_1.30.4 htmltools_0.3.6
```

Wang, X. 2012. “A Fast Exact k-Nearest Neighbors Algorithm for High Dimensional Search Using k-Means Clustering and Triangle Inequality.” *Proc Int Jt Conf Neural Netw* 43 (6):2351–8.

Yianilos, P. N. 1993. “Data Structures and Algorithms for Nearest Neighbor Search in General Metric Spaces.” In *SODA*, 93:311–21. 194.