Preventing Dominance of One Cluster

Overview

• Conscience Factor: To prevent one cluster unit (prototype vector) from dominating as the winning cluster unit, a conscience factor is used to penalise.
• Activation Value Calculation: $o_{k, p} = 1$ if certain conditions are met, otherwise $o_{k, p} = 0$.
• Conscience Factor Update: The conscience factor $b_k(t)$ is updated based on the winning history of the output unit.
• penalize output units that win too frequently, preventing one output unit from dominating.

Formula

Activation Value

$o_{k, p} = \begin{cases}1 & \text{for } \min \left\{d_{k, p} - b_k(t)\right\} \\ 0 & \text{otherwise}\end{cases}$   where $d_{k, p}$ is the Euclidean distance, and $b_k(t)$ is the conscience factor.

Conscience factor

Conscience Factor Components:

• $b_k(t) = \gamma\left(\frac{1}{l} - g_k(t)\right)$
• $g_k(t) = g_k(t-1) + \beta\left(o_{k, p} - g_k(t-1)\right)$

Initialization:

• $g_k(0) = 0$
• $b_k(0) = \frac{1}{l}$

Explanation:

• As more winning occurs ($o_{k, p} = 1$), $g_k(t)$ becomes larger, and $b_k(t)$ becomes a larger negative value.
• This negative value ($\left|b_k(t)\right|$) is then added to the Euclidean distance $d_{k, p}$.

Effect:

• More frequent winning by an output unit results in a larger $g_k(t),$ leading to a larger negative $b_k(t)$.
• The larger $\left|b_k(t)\right|$ is added to $d_{k, p}$, effectively penalizing the winning output unit and making it less likely to win frequently.