Dictionary - Definition of Alopex

Definition: Alopex


Part of Speech	Definition
Noun	1. Arctic foxes.[Wordnet].
Source: WordNet 3.0 Copyright © 2006 by Princeton University. All rights reserved.		Top

Date "Alopex" was first used in popular English literature: sometime before 1914. (references)

Common Expressions: Alopex

Expressions	Definition
Alopex lagopus	Thickly-furred fox of Arctic regions; brownish in summer and white in winter. Source: Wordnet 3.0 Copyright © 2006 by Princeton University. All rights reserved.
Genus Alopex	Arctic foxes. Source: Wordnet 3.0 Copyright © 2006 by Princeton University. All rights reserved.
Source: compiled by the editor from various references; see credits.		Top

Extended Definition: Alopex

ALOPEX

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:

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

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

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

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

Source: adapted by the editor from Wikipedia, the free encyclopedia; from the article "ALOPEX". Image Credit.
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Topics by Level of Interest: Alopex
Topics sorted by level of Interest	Level (1=low, 600=high)	Topics sorted Alphabetically	Level (1=low, 600=high)
Alopex	6	Alopex	6
Source: the editor, created by/for EVE to gauge likely levels of human interest in linguistically triggered topics (compiled across various sources, such as Wikipedia and specialty expression glosses).