# distmc: Distance Matrix Computation with multi-threads In Rlof: R Parallel Implementation of Local Outlier Factor(LOF)

## Description

This function is similar to `dist()` in stats, with additional support of multi-threading.

## Usage

 `1` ```distmc(x, method = "euclidean", diag = FALSE, upper = FALSE, p = 2) ```

## Arguments

 `x` a numeric matrix, data frame or `"dist"` object. `method` the distance measure to be used. This must be one of `"euclidean"`, `"maximum"`, `"manhattan"`, `"canberra"`, `"binary"` or `"minkowski"`. Any unambiguous substring can be given. `diag` logical value indicating whether the diagonal of the distance matrix should be printed by `print.dist`. `upper` logical value indicating whether the upper triangle of the distance matrix should be printed by `print.dist`. `p` The power of the Minkowski distance.

## Details

Available distance measures are (written for two vectors x and y):

`euclidean`:

Usual square distance between the two vectors (2 norm).

`maximum`:

Maximum distance between two components of x and y (supremum norm)

`manhattan`:

Absolute distance between the two vectors (1 norm).

`canberra`:

sum(|x_i - y_i| / |x_i + y_i|). Terms with zero numerator and denominator are omitted from the sum and treated as if the values were missing.

This is intended for non-negative values (e.g. counts): taking the absolute value of the denominator is a 1998 R modification to avoid negative distances.

`binary`:

(aka asymmetric binary): The vectors are regarded as binary bits, so non-zero elements are ‘on’ and zero elements are ‘off’. The distance is the proportion of bits in which only one is on amongst those in which at least one is on.

`minkowski`:

The p norm, the pth root of the sum of the pth powers of the differences of the components.

Missing values are allowed, and are excluded from all computations involving the rows within which they occur. Further, when `Inf` values are involved, all pairs of values are excluded when their contribution to the distance gave `NaN` or `NA`.
If some columns are excluded in calculating a Euclidean, Manhattan, Canberra or Minkowski distance, the sum is scaled up proportionally to the number of columns used. If all pairs are excluded when calculating a particular distance, the value is `NA`.

The `"distmc"` method of `as.matrix()` and `as.dist()` can be used for conversion between objects of class `"dist"` and conventional distance matrices.

`as.dist()` is a generic function. Its default method handles objects inheriting from class `"dist"`, or coercible to matrices using `as.matrix()`. Support for classes representing distances (also known as dissimilarities) can be added by providing an `as.matrix()` or, more directly, an `as.dist` method for such a class.

## Value

`distmc` returns an object of class `"dist"`.

The lower triangle of the distance matrix stored by columns in a vector, say `do`. If `n` is the number of observations, i.e., `n <- attr(do, "Size")`, then for i < j ≤ n, the dissimilarity between (row) i and j is `do[n*(i-1) - i*(i-1)/2 + j-i]`. The length of the vector is n*(n-1)/2, i.e., of order n^2.

The object has the following attributes (besides `"class"` equal to `"dist"`):

 `Size` integer, the number of observations in the dataset. `Labels` optionally, contains the labels, if any, of the observations of the dataset. `Diag, Upper` logic, corresponding to the arguments `diag` and `upper` above, specifying how the object should be printed. `call` optional, the `call` used to create the object. `method` optional, the distance measure used; resulting from `distmc()`, the (`match.arg()`ed) `method` argument.

## References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979) Multivariate Analysis. Academic Press.

Borg, I. and Groenen, P. (1997) Modern Multidimensional Scaling. Theory and Applications. Springer.

`dist()` in the stats package
 ```1 2 3``` ```data(iris) df<-iris[-5] dist.data<-distmc(df,'manhattan') ```