# distancematrix: functions to compute pair wise distances between vectors In hopach: Hierarchical Ordered Partitioning and Collapsing Hybrid (HOPACH)

## Description

The function `distancematrix` is applied to a matrix of data to compute the pair wise distances between all rows of the matrix. In hopach versions >= 2.0.0 these distance functions are calculated in C, rather than R, to improve run time performance. function `distancevector` is applied to a matrix and a vector to compute the pair wise distances between each row of the matrix and the vector. Both functions allow different choices of distance metric. The functions `dissmatrix` and `dissvector` allow one to convert between a distance matrix and a vector of the upper triangle. The function `vectmatrix` is used internally.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```distancematrix(X, d, na.rm=TRUE) distancevector(X, y, d, na.rm=TRUE) dissmatrix(v) dissvector(M) vectmatrix(index, p) ```

## Arguments

 `X` a numeric matrix. Missing values will be ignored if na.rm=TRUE. `y` a numeric vector, possibly a row of X. Missing values will be ignoredif na.rm=TRUE. `na.rm` an indicator of whether or not to remove missing values. If na.rm=TRUE (default), then distances are computed over all pairwise non-missing values. Else missing values are propagated through the distance computation. `d` character string specifying the metric to be used for calculating dissimilarities between vectors. The currently available options are "cosangle" (cosine angle or uncentered correlation distance), "abscosangle" (absolute cosine angle or absolute uncentered correlation distance), "euclid" (Euclidean distance), "abseuclid" (absolute Euclidean distance), "cor" (correlation distance), and "abscor" (absolute correlation distance). Advanced users can write their own distance functions and add these. `M` a symmetric matrix of pair wise distances. `v` a vector of pair wise distances corresponding to the upper triangle of a distance matrix, stored by rows. `index` index in a distance vector, like that returned by `dissvector`. `p` number of elements, e.g. the number of rows in a distance matrix.

## Details

In hopach versions <2.0.0, these functions returned the square root of the usual distance for `d="cosangle"`, `d="abscosangle"`, `d="cor"`, and `d="abscor"`. Typically, this transformation makes the dissimilarity correspond more closely with the norm. In order to agree with the `dist` function, the square root is no longer used in versions >=2.0.0.

## Value

For versions >= 2.0.0 `distancematrix`, a `hdist` object of of all pair wise distances between the rows of the data matrix 'X', i.e. the value of `hdist[i,j]` is the distance between rows 'i' and 'j' of 'X', as defined by 'd'. A `hdist` object is an S4 class containing four slots:

 `Data` representing the lower triangle of the symmetric distance matrix. `Size` the number of objects (i.e. rows of the data matrix). `Labels` labels for the objects, usually the numbers 1 to Size. `Call` the distance used in the call to `distancematrix`.

A hdist object and can be converted to a matrix using `as.matrix(hdist)`. (See `hdist` for more details.)

For `distancevector`, a vector of all pair wise distances between rows of 'X' and the vector 'y'. Entry 'j' is the distance between row 'j' of 'X' and the vector 'y'.

For `distancevector`, a vector of all pair wise distances between rows of 'X' and the vector 'y'. Entry 'j' is the distance between row 'j' of 'X' and the vector 'y'.

For `dissmatrix`, the corresponding distance vector. For `dissvector`, the corresponding distance matrix. If 'M' has 'p' rows (and columns), then 'v' is length 'p*(p-1)/2'.

For `vectmatrix`, the indices of the row and column of a distance matrix corresponding to entry `index` in the corresponding distance vector.

## Warning

The correlation and absolute correlation distance functions call the `cor` function, and will therefore fail if there are missing values in the data and na.rm!=TRUE.

## Author(s)

Katherine S. Pollard <[email protected]> and Mark J. van der Laan <[email protected]>, with Greg Walll

## References

van der Laan, M.J. and Pollard, K.S. A new algorithm for hybrid hierarchical clustering with visualization and the bootstrap. Journal of Statistical Planning and Inference, 2003, 117, pp. 275-303.

## See Also

`hopach`, `correlationordering`, `disscosangle`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```mydata<-matrix(rnorm(50),nrow=10) deuclid<-distancematrix(mydata,d="euclid") # old method vdeuclid<-dissvector(deuclid) vdeuclid<-deuclid@Data ddaisy<-daisy(mydata) vdeuclid ddaisy/sqrt(length(mydata[1,])) d1<-distancematrix(mydata,d="abscosangle") d2<-distancevector(mydata,mydata[1,],d="abscosangle") d1[1,] d2 #equal to d1[1,] # old method d3<-dissvector(d1) d3<-d1@Data pair<-vectmatrix(5,10) d1[pair[1],pair[2]] d3[5] ```

hopach documentation built on Nov. 17, 2017, 11:09 a.m.