BiocNeighbors 1.5.1

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,] 1619 7201 7573 321 5921 863 312 3310 806 6225
## [2,] 75 7736 8735 3998 9001 7778 9996 5822 8719 4553
## [3,] 2075 8658 3029 5653 7567 6783 1383 4555 116 133
## [4,] 9536 8526 1625 7032 3053 9921 6167 7549 2690 7690
## [5,] 3092 3215 4245 484 6144 5606 6472 9528 7258 11
## [6,] 5278 5015 1460 8038 937 3264 558 4971 4883 7317
```

`head(fout$distance)`

```
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 0.9016699 0.9318565 0.9772659 0.9949794 1.038618 1.041176 1.056427
## [2,] 0.9917201 1.0245719 1.0259660 1.0266167 1.032166 1.050191 1.051409
## [3,] 0.8278054 0.9012230 1.0060742 1.0214293 1.037359 1.044597 1.057421
## [4,] 0.9249825 0.9271723 0.9663386 1.0077784 1.012115 1.019327 1.024750
## [5,] 0.9582251 0.9789901 1.0099590 1.0323164 1.036857 1.038603 1.041321
## [6,] 0.8968374 0.9329467 0.9414597 0.9798813 1.006685 1.022083 1.034494
## [,8] [,9] [,10]
## [1,] 1.067170 1.075106 1.085567
## [2,] 1.062184 1.071266 1.080524
## [3,] 1.066949 1.077623 1.078929
## [4,] 1.035183 1.036362 1.041160
## [5,] 1.047111 1.056788 1.058003
## [6,] 1.042925 1.048861 1.051233
```

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] 2075 8658 3029 5653 7567 6783 1383 4555 116 133`

… with the following distances to those neighbors:

`fout$distance[3,]`

```
## [1] 0.8278054 0.9012230 1.0060742 1.0214293 1.0373587 1.0445967 1.0574210
## [8] 1.0669490 1.0776234 1.0789287
```

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,] 7754 1432 5154 28 5659
## [2,] 4348 5057 6525 7569 9199
## [3,] 6429 7208 6693 9606 9287
## [4,] 4724 5517 6041 7145 1191
## [5,] 8891 5995 7069 4476 9397
## [6,] 5515 1 6353 312 8961
```

`head(qout$distance)`

```
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.9348642 0.9971274 1.0126300 1.0286586 1.0439788
## [2,] 0.9829474 1.0067578 1.0132464 1.0210246 1.0326293
## [3,] 0.8734023 0.8888589 0.8934396 0.9151888 0.9376425
## [4,] 0.8847359 0.8986644 0.9009389 0.9144456 0.9303230
## [5,] 0.9086042 0.9771849 0.9873951 1.0039442 1.0154987
## [6,] 0.6845494 1.0223525 1.0900201 1.0973710 1.0997798
```

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] 6429 7208 6693 9606 9287`

… with the following distances to those neighbors:

`qout$distance[3,]`

`## [1] 0.8734023 0.8888589 0.8934396 0.9151888 0.9376425`

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,] 2075 8658 3029 5653 7567
## [2,] 9536 8526 1625 7032 3053
## [3,] 3092 3215 4245 484 6144
##
## $distance
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.8278054 0.9012230 1.0060742 1.021429 1.037359
## [2,] 0.9249825 0.9271723 0.9663386 1.007778 1.012115
## [3,] 0.9582251 0.9789901 1.0099590 1.032316 1.036857
```

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 Under development (unstable) (2019-10-24 r77329)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.3 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.11-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.11-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_1.21.0 BiocNeighbors_1.5.1 knitr_1.25
## [4] BiocStyle_2.15.0
##
## loaded via a namespace (and not attached):
## [1] Rcpp_1.0.2 bookdown_0.14 lattice_0.20-38
## [4] digest_0.6.22 grid_4.0.0 stats4_4.0.0
## [7] magrittr_1.5 evaluate_0.14 rlang_0.4.1
## [10] stringi_1.4.3 S4Vectors_0.25.0 Matrix_1.2-17
## [13] rmarkdown_1.16 tools_4.0.0 stringr_1.4.0
## [16] parallel_4.0.0 xfun_0.10 yaml_2.2.0
## [19] compiler_4.0.0 BiocGenerics_0.33.0 BiocManager_1.30.9
## [22] htmltools_0.4.0
```

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.