Selecting a Distance Function

Lloyd's algorithm converges for the class of distance functions called Bregman Divergences. We provide a number of Bregman Divergences. When selecting a distance function, consider the domain of the input data. For example, frequency data is integral. Similarity of frequencies or distributions are best performed using the Kullback-Leibler divergence.

Name	Divergence
BregmanDivergence.EUCLIDEAN	Squared Euclidean
BregmanDivergence.RELATIVE_ENTROPY	Kullback-Leibler
BregmanDivergence.DISCRETE_KL	Kullback-Leibler
BregmanDivergence.DISCRETE_SMOOTHED_KL	Kullback-Leibler
BregmanDivergence.SPARSE_SMOOTHED_KL	Kullback-Leibler
BregmanDivergence.LOGISTIC_LOSS	Logistic Loss
BregmanDivergence.GENERALIZED_I	Generalized I
BregmanDivergence.ITAKURA_SAITO	Itakura-Saito

You may construct instances of BregmanDivergence using the BregmanDivergencecompanion object.

package com.massivedatascience.divergence

object BregmanDivergence {
  def apply(name: String): BregmanDivergence = ???
}

From this, one may construct a distance function using the BregmanPointOps companion function.

From your BregmanDivergence, you may create an instance of the distance function by using the apply method of the BregmanPointOps companion object.

package com.massivedatascience.clusterer

object BregmanPointOps {
  def apply(d: BregmanDivergence): BregmanPointOps = ???
}