ALOPEX

ALOPEX is a correlation based machine learning algorithm first proposed by Tzanakou and Harth in 1974.

Principle

In machine learning, the goal is to train a system to minimize a cost function or a response function. Many training algorithms, such as backpropagation, have an inherent susceptibility to getting "stuck" in local minima or maxima of the response function. ALOPEX uses a cross-correlation of differences and a stochastic process to overcome this in an attempt to reach the absolute minimum of the response function.

Method

ALOPEX, in its simplest form is defined by an updating equation:
where:

is the iteration or time-step.
is the difference between the current and previous value of system variable at iteration.
is the difference between the current and previous value of the response function at iteration.
is the learning rate parameter minimizes and maximizes

Discussion

Essentially, ALOPEX changes each system variable based on a product of: the previous change in the variable, the resulting change in the cost function, and the learning rate parameter. Further, to find the absolute minimum, the stochastic process is added to stochastically "push" the algorithm out of any local minima.