distancematrix {hopach} | R Documentation

## functions to compute pair wise distances between vectors

### Description

The function `distancematrix` is applied to a matrix of data to compute the pair wise distances between all rows of the matrix. The 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

    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

For cosine-angle and correlation (and their absolute values) these functions return the square root of the usual distance, for example as computed by the dist() function. Typically, this transformation makes the dissimilarity correspond more closely with the norm. Also, the Euclidean distance is standardized by the sample size, so that the values produced are equal to the values from the dist() function divided by sqrt(n).

### Value

For `distancematrix`, a matrix of all pair wise distances between rows of 'X'. The value in row 'j' and column 'i' is the distance between rows 'i' and 'j'. The matrix is symmetric, and can be converted to a vector containing the upper triangle using the function `dissvector`.
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 <kpollard@soe.ucsc.edu> and Mark J. van der Laan <laan@stat.berkeley.edu>

### 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.

http://www.stat.berkeley.edu/~laan/Research/Research_subpages/Papers/hopach.pdf

### See Also

`hopach`, `correlationordering`, `disscosangle`

### Examples

    mydata<-matrix(rnorm(50),nrow=10)
    deuclid<-distancematrix(mydata,d="euclid")
    vdeuclid<-dissvector(deuclid)
    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,]

    d3<-dissvector(d1)
    pair<-vectmatrix(5,10)
    d1[pair[1],pair[2]]
    d3[5]

[Package hopach version 1.12.0 Index]