• Source: Alopex

Alopex may refer to:

Alopex lagopus, a taxonomic synonym for the Arctic fox, Vulpes lagopus
ALOPEX a correlation-based machine learning algorithm
Alopex (Teenage Mutant Ninja Turtles), a character in the Teenage Mutant Ninja Turtles franchise
Alopex (Ancient Greek: ἀλώπηξ) ancient Greek for fox

• Source: ALOPEX

ALOPEX (an abbreviation of "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
)


{\displaystyle \Delta \ W_{ij}(n)=\gamma \ \Delta \ W_{ij}(n-1)\Delta \ R(n)+r_{i}(n)}


where:




n
≥
0


{\displaystyle n\geq 0}

is the iteration or time-step.




Δ


W

i
j


(
n
)


{\displaystyle \Delta \ W_{ij}(n)}

is the difference between the current and previous value of system variable





W

i
j




{\displaystyle \ W_{ij}}

at iteration



n


{\displaystyle n}

.




Δ

R
(
n
)


{\displaystyle \Delta \ R(n)}

is the difference between the current and previous value of the response function




R
,


{\displaystyle \ R,}

at iteration



n


{\displaystyle n}

.




γ


{\displaystyle \gamma }

is the learning rate parameter



(
γ

<
0


{\displaystyle (\gamma \ <0}

minimizes



R
,


{\displaystyle R,}

and



γ

>
0


{\displaystyle \gamma \ >0}

maximizes



R

)


{\displaystyle R\ )}






r

i


(
n
)
∼

N
(
0
,
σ



2


)


{\displaystyle r_{i}(n)\sim \ N(0,\sigma \ ^{2})}





Discussion


Essentially, ALOPEX changes each system variable




W

i
j


(
n
)


{\displaystyle W_{ij}(n)}

based on a product of: the previous change in the variable



Δ


{\displaystyle \Delta }






W

i
j


(
n
−
1
)


{\displaystyle W_{ij}(n-1)}

, the resulting change in the cost function



Δ


{\displaystyle \Delta }





R
(
n
)


{\displaystyle R(n)}

, and the learning rate parameter



γ


{\displaystyle \gamma }

. Further, to find the absolute minimum (or maximum), the stochastic process




r

i
j


(
n
)


{\displaystyle r_{ij}(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

Kata Kunci Pencarian:

• Pingai-laut
• Rubah Teumessos
• Mamalia
• Rubah arktik
• Canidae
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• Vulpes
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• Daftar pangram
• Alopex
• ALOPEX
• Arctic fox
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• Brachypalpus alopex
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