Unsupervised Classification of Surface Defects in Wire Rod Production Obtained by Eddy Current Sensors

. 2015 Apr 29;15(5):10100–10117. doi: 10.3390/s150510100

Algorithm 3. Evolving self-organizing map.

Start with k = 0, Inline graphic

= ∅,

= ∅.

Choose a new x ∈ Σ and compute:

V_{m} (x) = {y \in V : Δ (x, y) < ϵ}

(16)

_m(x) = ∅ go to 4.

Update:

V^{'} = V \cup {x}

(17)

E^{'} = E \cup {(x, y_{1}), (x, y_{2})}

(18)

where:

Δ (x, y_{1}) = min {y : y \in V}

(19)

Δ (x, y_{2}) = min {y : y \neq y_{1}, y \in V}

(20)

and go to 5.

Let y* be such that:

Δ (x, y^{*}) = min {Δ (x, y) : y \in V_{m}}

(21)

and

(y*) = {y : (y,y*) ∈ Inline graphic

}. Update:

V^{'} = {ϕ (y) : y \in V}

(22)

Where:

ϕ (y) = {\begin{array}{l} (1 - α) y + α x & y \in {y^{*} \cup N (y^{*})} \\ y & otherwise \end{array}

(23)

and:

α = γ e^{- {| Δ (z, x) |}^{2} / 2 σ^{2}}

(24)

Update the connection strengths as follows:

s (y_{i}, y_{j}) = ϵ / Δ (y_{i}, y_{j})

(25)

for any (y_i, y_j) ∈ Inline graphic

′ ×

′ and i ≠ j.

Do k′ = k + 1; if mod (k′, τ) = 0, remove the weakest connection.

Do k = k′, Inline graphic

and

, and go to 2.