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 $H^{\prime }$ of size $m$ is defined as:

$$d_{\cos }(H,H^{\prime })=\cos \alpha =\frac{H\ast H^{\prime }}{\Vert H\Vert \Vert H^{\prime }\Vert }=\frac{\sum _{m=1}^M{H}_m\ast H_m^{\prime }}{\sqrt{\sum _{m=1}^M{H}_m^2}\ast \sqrt{\sum _{m=1}^M{H^{\prime }}_m^2}}$$

Attributes:

• not a metric, a similarity

Attributes for normalized histograms:

• $d(H,H^{\prime })\in [0,1]$

• $d(H,H)=1$

• $d(H,H^{\prime })=d(H^{\prime },H)$

Attributes for not-normalized histograms:

• $d(H,H^{\prime })\in [-1,1]$

• $d(H,H)=1$

• $d(H,H^{\prime })=d(H^{\prime },H)$

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.