medpy.metric.histogram.minowski¶
-
medpy.metric.histogram.
minowski
(h1, h2, p=2)[source]¶ Minowski distance.
With \(p=2\) equal to the Euclidean distance, with \(p=1\) equal to the Manhattan distance, and the Chebyshev distance implementation represents the case of \(p=\pm inf\).
The Minowksi distance between two histograms \(H\) and \(H'\) of size \(m\) is defined as:
\[d_p(H, H') = \left(\sum_{m=1}^M|H_m - H'_m|^p \right)^{\frac{1}{p}}\]Attributes:
- a real metric
Attributes for normalized histograms:
- \(d(H, H')\in[0, \sqrt[p]{2}]\)
- \(d(H, H) = 0\)
- \(d(H, H') = d(H', H)\)
Attributes for not-normalized histograms:
- \(d(H, H')\in[0, \infty)\)
- \(d(H, H) = 0\)
- \(d(H, H') = d(H', H)\)
Attributes for not-equal histograms:
- not applicable
Parameters: h1 : sequence
The first histogram.
h2 : sequence
The second histogram.
p : float
The \(p\) value in the Minowksi distance formula.
Returns: minowski : float
Minowski distance.
Raises: ValueError
If
p
is zero.