ALOPEX

From Wikipedia, the free encyclopedia

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

Contents 1 Principle 2 Method 3 Discussion 4 References

[edit] Principle

In machine learning, the goal is to train a system to minimize a cost function or (refering 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.

[edit] 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
• 

[edit] Discussion

Essentially, ALOPEX changes each system variable W_ij(n) based on a product of: the previous change in the variable ΔW_ij(n − 1), the resulting change in the cost function ΔR(n), and the learning rate parameter γ. 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.

[edit] References

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