ALOPEX (an abbreviation of "algorithms of pattern extraction") is a correlation based machine learning algorithm first proposed by Tzanakou and Harth in 1974.

Principle

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In machine learning, the goal is to train a system to minimize a cost function or (referring to ALOPEX) 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 (or maximum) of the response function.

Method

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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

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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 (or maximum), the stochastic process   (Gaussian or other) is added to stochastically "push" the algorithm out of any local minima.

References

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  • Harth, E., & Tzanakou, E. (1974) Alopex: A stochastic method for determining visual receptive fields. Vision Research, 14:1475-1482. Abstract from ScienceDirect