medpy.metric.histogram.cosine

medpy.metric.histogram.cosine(h1, h2)

Cosine simmilarity.

Compute the angle between the two histograms in vector space irrespective of their length. The cosine similarity between two histograms \(H\) and \(H'\) of size \(m\) is defined as:

\[d_{\cos}(H, H') = \cos\alpha = \frac{H * H'}{\|H\| \|H'\|} = \frac{\sum_{m=1}^M H_m*H'_m}{\sqrt{\sum_{m=1}^M H_m^2} * \sqrt{\sum_{m=1}^M {H'}_m^2}}\]

Attributes:

• not a metric, a similarity

Attributes for normalized histograms:

• \(d(H, H')\in[0, 1]\)

• \(d(H, H) = 1\)

• \(d(H, H') = d(H', H)\)

Attributes for not-normalized histograms:

• \(d(H, H')\in[-1, 1]\)

• \(d(H, H) = 1\)

• \(d(H, H') = d(H', H)\)

Attributes for not-equal histograms:

• not applicable

Parameters:

h1sequence

The first histogram.

h2sequence

The second histogram, same bins as h1.

Returns:

cosinefloat

Cosine simmilarity.

Notes

The resulting similarity ranges from -1 meaning exactly opposite, to 1 meaning exactly the same, with 0 usually indicating independence, and in-between values indicating intermediate similarity or dissimilarity.