# Preventing Dominance of One Cluster

# 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.