**ALOPEX** (an acronym from "**AL**gorithms **O**f **P**attern **EX**traction") is a correlation based machine learning algorithm first proposed by Tzanakou and Harth in 1974.

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.

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
)
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.