# ALOPEX

Updated on
Covid-19

ALOPEX (an acronym from "ALgorithms Of Pattern EXtraction") 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 (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

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

Δ   W i j ( n ) = γ   Δ   W i j ( n 1 ) Δ   R ( n ) + r i ( n )

Where:

• n 0 is the iteration or time-step.
• Δ   W i j ( n ) is the difference between the current and previous value of system variable   W i j at iteration n   .
• Δ   R ( n ) is the difference between the current and previous value of the response function   R , at iteration n   .
• γ   is the learning rate parameter ( γ   < 0 minimizes R ,   and γ   > 0 maximizes R   )
• r i ( n )   N ( 0 , σ   2 )
• ## Discussion

Essentially, ALOPEX changes each system variable W i j ( n ) based on a product of: the previous change in the variable Δ W i j ( n 1 ) , the resulting change in the cost function Δ R ( n ) , and the learning rate parameter γ . Further, to find the absolute minimum (or maximum), the stochastic process r i j ( n ) (Gaussian or other) is added to stochastically "push" the algorithm out of any local minima.

## References

ALOPEX Wikipedia

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