Description Usage Arguments Details Value Author(s) References See Also Examples

This function computes a matrix of distances from each sequence to a subset of 'seed' sequences using the method outlined in Blacksheilds et al (2010).

1 2 |

`x` |
a matrix of aligned sequences or a list of unaligned sequences. Accepted modes are "character" and "raw" (the latter is for "DNAbin" and "AAbin" objects). |

`seeds` |
optional integer vector indicating which sequences should
be used as the seed sequences. If |

`k` |
integer representing the k-mer size to be used for calculating the distance matrix. Defaults to 5. Note that high values of k may be slow to compute and use a lot of memory due to the large numbers of calculations required, particularly when the residue alphabet is also large. |

`residues` |
either NULL (default; emitted residues are automatically detected from the sequences), a case sensitive character vector specifying the residue alphabet, or one of the character strings "RNA", "DNA", "AA", "AMINO". Note that the default option can be slow for large lists of character vectors. Specifying the residue alphabet is therefore recommended unless x is a "DNAbin" or "AAbin" object. |

`gap` |
the character used to represent gaps in the alignment matrix
(if applicable). Ignored for |

`counts` |
logical indicating whether the (usually large) matrix of k-mer counts should be returned as an attribute of the returned object. Defaults to FALSE. |

This function computes a *n* * log(*n*, 2)^2 k-mer distance matrix
(where *n* is the number of sequences), returning an object of class
`"mbed"`

. If the number of sequences is less than or equal to 19, the full
*n* * *n* distance matrix is produced (since the rounded up value of
log(*19*, 2)^2 is 19). Currently the only distance measure supported is
that of Edgar (2004).

For maximum information retention following the embedding process
it is generally desirable to select the seed sequences based on their
uniqueness, rather than simply selecting a random subset
(Blackshields et al. 2010).
Hence if 'seeds' is set to NULL (the default setting) the the 'mbed'
function selects the subset by clustering the sequence set into
*t* groups using the k-means algorithm (*k* = *t*),
and choosing one representative from each group.
Users can alternatively pass an integer vector (as in the above example)
to specify the seeds manually. See Blackshields et al (2010) for other
seed selection options.

DNA and amino acid sequences can be passed to the function
either as a list of non-aligned sequences or as a matrix of aligned sequences,
preferably in the "DNAbin" or "AAbin" raw-byte format
(Paradis et al 2004, 2012; see the `ape`

package
documentation for more information on these S3 classes).
Character sequences are supported; however ambiguity codes may
not be recognized or treated appropriately, since raw ambiguity
codes are counted according to their underlying residue frequencies
(e.g. the 5-mer "ACRGT" would contribute 0.5 to the tally for "ACAGT"
and 0.5 to that of "ACGGT").

To minimize computation time when counting longer k-mers (k > 3), amino acid sequences in the raw "AAbin" format are automatically compressed using the Dayhoff-6 alphabet as detailed in Edgar (2004). Note that amino acid sequences will not be compressed if they are supplied as a list of character vectors rather than an "AAbin" object, in which case the k-mer length should be reduced (k < 4) to avoid excessive memory use and computation time.

Note that agglomerative (bottom-up) tree-building methods
such as neighbor-joining and UPGMA depend on a full
*n* * *n* distance matrix.
See the `kdistance`

function for details on computing
symmetrical distance matrices.

Returns an object of class `"mbed"`

, whose primary object is
an *n* * log(*n*, 2)^2 matrix
(where *n* is the number of sequences). The returned
object contains additional attributes including an
integer vector of seed sequence indices ("seeds"), a logical vector
identifying the duplicated sequences ("duplicates"), an integer vector
giving the matching indices of the non-duplicated sequences ("pointers"),
a character vector of MD5 digests of the sequences ("hashes"),
an integer vector of sequence lengths ("seqlengths"), and if
`counts = TRUE`

, the matrix of k-mer counts ("kcounts";
see `kcount`

for details).

Shaun Wilkinson

Blackshields G, Sievers F, Shi W, Wilm A, Higgins DG (2010) Sequence embedding
for fast construction of guide trees for multiple sequence alignment.
*Algorithms for Molecular Biology*, **5**, 21.

Edgar RC (2004) Local homology recognition and distance measures in
linear time using compressed amino acid alphabets.
*Nucleic Acids Research*, **32**, 380-385.

Paradis E, Claude J, Strimmer K, (2004) APE: analyses of phylogenetics
and evolution in R language. *Bioinformatics* **20**, 289-290.

Paradis E (2012) Analysis of Phylogenetics and Evolution with R (Second Edition). Springer, New York.

`kdistance`

for full *n* * *n* distance
matrix computation.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
## compute an embedded k-mer distance matrix for the woodmouse
## dataset (ape package) using a k-mer size of 5
library(ape)
data(woodmouse)
## randomly select three sequences as seeds
suppressWarnings(RNGversion("3.5.0"))
set.seed(999)
seeds <- sample(1:15, size = 3)
## embed the woodmouse dataset in three dimensions
woodmouse.mbed <- mbed(woodmouse, seeds = seeds, k = 5)
## print the distance matrix (without attributes)
print(woodmouse.mbed[,], digits = 2)
``` |

```
No0909S No0913S No304
No305 0.0300 0.033 0.032
No304 0.0287 0.012 0.000
No306 0.0203 0.012 0.012
No0906S 0.0249 0.021 0.024
No0908S 0.0228 0.022 0.024
No0909S 0.0000 0.029 0.029
No0910S 0.0258 0.017 0.026
No0912S 0.0158 0.024 0.024
No0913S 0.0287 0.000 0.012
No1103S 0.0133 0.022 0.021
No1007S 0.0036 0.029 0.030
No1114S 0.0343 0.035 0.032
No1202S 0.0249 0.016 0.024
No1206S 0.0207 0.021 0.021
No1208S 0.0036 0.031 0.031
```

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