R: Lp distances.

LPDistance {TSdist} | R Documentation

## Lp distances.

### Description

Computes the distance based on the chosen Lp norm between a pair of numeric vectors.

### Usage

    LPDistance(x, y, method="euclidean", ...)

### Arguments

`x` | Numeric vector containing the first time series.
`y` | Numeric vector containing the second time series.
`method` | A value in "euclidean", "manhattan", "infnorm", "minkowski".
`...` | If method="minkowski" a positive integer value must be specified for `p`.

### Details

The distances based on Lp norms are computed between two numeric vectors using the following formulas:

Euclidean distance: √{(x_i-y_i)^2)}

Manhattan distance: ∑{|x_i-y_i|}

Infinite norm distance: \max{|x_i-y_i|}

Minkowski distance: √[p]{(x_i-y_i)^p)}

The two series must have the same length. Furthermore, in the case of the Minkowski distance, `p` must be specified as a positive integer value.

### Value

`d` | The computed distance between the pair of series.

### Author(s)

Usue Mori, Alexander Mendiburu, Jose A. Lozano.

### See Also

These distances are also implemeted in separate functions. For more information see `EuclideanDistance`, `ManhattanDistance`, `MinkowskiDistance` and `InfNormDistance`

To calculate this distance measure using `ts`, `zoo` or `xts` objects see `TSDistances`. To calculate distance matrices of time series databases using this measure see `TSDatabaseDistances`.

### Examples

    # The objects example.series1 and example.series2 are two
    # numeric series of length 100 contained in the TSdist package.

    data(example.series1)
    data(example.series2)

    # For information on their generation and shape see help
    # page of example.series.

    help(example.series)

    # Compute the different Lp distances

    # Euclidean distance

    LPDistance(example.series1, example.series2, method="euclidean")

    # Manhattan distance

    LPDistance(example.series1, example.series2, method="manhattan")

    # Infinite norm distance

    LPDistance(example.series1, example.series2, method="infnorm")

    # Minkowski distance with p=3.

    LPDistance(example.series1, example.series2, method="minkowski", p=3)

[Package TSdist version 3.6 Index]