ALOPEX

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ALOPEX (an acronym from "ALgorithms Of Pattern EXtraction") is a correlation based machine learning algorithm first proposed by Tzanakou and Harth in 1974.

Principle[edit]

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[edit]

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

\Delta\ W_{ij}(n) = \gamma\ \Delta\ W_{ij}(n-1) \Delta\ R(n) + r_i(n)

Where:

  • n \geq 0 is the iteration or time-step.
  • \Delta\ W_{ij}(n) is the difference between the current and previous value of system variable \ W_{ij} at iteration n \ .
  • \Delta\ R(n) is the difference between the current and previous value of the response function \ R, at iteration n \ .
  • \gamma\ is the learning rate parameter (\gamma\ < 0 minimizes R, \ and \gamma\ > 0 maximizes R \ )
  • r_i(n) \sim\ N(0,\sigma\ ^2)

Discussion[edit]

Essentially, ALOPEX changes each system variable W_{ij}(n) based on a product of: the previous change in the variable \DeltaW_{ij}(n-1), the resulting change in the cost function \DeltaR(n), and the learning rate parameter \gamma. Further, to find the absolute minimum (or maximum), the stochastic process r_{ij}(n) (Gaussian or other) is added to stochastically "push" the algorithm out of any local minima.

References[edit]

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