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# medpy.metric.histogram.cosine¶

medpy.metric.histogram.cosine(h1, h2)[source]

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: h1 : sequence The first histogram. h2 : sequence The second histogram, same bins as h1. cosine : float 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.