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| '''ALOPEX''' (an acronym from "'''''AL'''gorithms '''O'''f '''P'''attern '''EX'''traction''") is a correlation based machine learning algorithm first proposed by [[Evangelia Micheli-Tzanakou|Tzanakou]] and Harth in 1974.
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| ==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.
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| ==Method==
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| ALOPEX, in its simplest form is defined by an updating equation:
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| <math>\Delta\ W_{ij}(n) = \gamma\ \Delta\ W_{ij}(n-1) \Delta\ R(n) + r_i(n) </math>
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| Where:
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| *<math>n \geq 0</math> is the iteration or time-step.
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| *<math>\Delta\ W_{ij}(n)</math> is the difference between the current and previous value of system variable <math>\ W_{ij}</math> at iteration <math>n \ </math>.
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| *<math>\Delta\ R(n)</math> is the difference between the current and previous value of the response function <math>\ R,</math> at iteration <math>n \ </math>.
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| *<math>\gamma\ </math> is the learning rate parameter <math>(\gamma\ < 0 </math> minimizes <math>R, \ </math> and <math>\gamma\ > 0 </math> maximizes <math>R \ )</math>
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| *<math>r_i(n) \sim\ N(0,\sigma\ ^2)</math>
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| ==Discussion==
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| Essentially, ALOPEX changes each system variable <math>W_{ij}(n)</math> based on a product of: the previous change in the variable <math>\Delta</math><math>W_{ij}(n-1)</math>, the resulting change in the cost function <math>\Delta</math><math>R(n)</math>, and the learning rate parameter <math>\gamma</math>. Further, to find the absolute minimum (or maximum), the stochastic process <math>r_{ij}(n)</math> (Gaussian or other) is added to stochastically "push" the algorithm out of any local minima.
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| ==References==
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| *Harth, E., & Tzanakou, E. (1974) Alopex: A stochastic method for determining visual receptive fields. Vision Research, '''14''':1475-1482. [http://dx.doi.org/10.1016/0042-6989(74)90024-8 Abstract from ScienceDirect]
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| [[Category:Classification algorithms]]
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| [[Category:Neural networks]]
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| {{compu-AI-stub}}
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