Bregman Centroid Asymmetry
Find different centroids by reversing the arguments of a convex divergence.
Free theory articleFind different centroids by reversing the arguments of a convex divergence.
Concept & interpretation
Bregman divergences are generalized distance-like measures generated by convex functions. Unlike standard metrics, they are generally not symmetric. This means that the left and right centroids of a dataset can be different.
Experiment
Explore how different divergences affect the left centroid.
- Open the module at Bregman Centroid Asymmetry.
- Set Data to "Spread".
- Set Divergence to "Generalized KL". Observe the Left dual centroid is 2.0.
- Change Divergence to "Squared". Observe that the Left dual centroid is now equal to the right arithmetic centroid, 2.3333333333333335, since squared distance is symmetric.
- Change Divergence to "Itakura Saito". Observe the Left dual centroid becomes 1.7142857142857142, which is the harmonic mean.