Independent Feature Scaling

data-analysis

Definition

Independent Feature Scaling

Independent feature scaling is the principle that statistical scaling operations must be applied individually to each feature dimension of a dataset. Formally, for a dataset $D=\{{\mathbf{x}}^{(i)}{\}}_{i=1}^m$ with ${\mathbf{x}}^{(i)}\in {\mathbb{R}}^d$, the scaling parameters ${\theta }_j$ (e.g., ${\min }_j,{\mu }_j$) are computed for each dimension $j\in \{1,\dots ,d\}$ independently:

${\theta }_j=f(\{x_j^{(i)}{\}}_{i=1}^m)$

Rationale

This approach prevents features with larger numerical ranges from disproportionately influencing the learning process, particularly for distance-based methods. It ensures that the relative variance within each feature is preserved without inter-feature interference or numerical dominance.