Normalization

Z-Score Normalization: standardisation to zero mean and unit standard deviation

Hellwig, Z. · 1968

Overview

Normalization (standardisation, Z-score). Output typically normalized_matrix (higher value = preferred).

Strengths

•Method-specific: Normalization (standardisation, Z-score)

Method assistant

Grounded explanations: it explains the method, it does not compute.

Edge cases

•See F.steps and D.parameters for Z-SCORE-NORMALIZATION-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

•Bkz. Z-SCORE-NORMALIZATION F.steps citation_anchor'lar ve P.verification_status.

Worked example

1.Adım 1 (F1): Compute column mean x̄_j and population standard deviation σ_j = √(Σ_i(x_ij − x̄_j)²/m). Benefit: z_ij = (x_ij − x̄_j)/σ_j. Cost: z_ij = (x̄_j − x_ij)/σ_j (direction flip so higher is better). Formül: z_{ij} = \begin{cases} (x_{ij}-\bar{x}_j)/\sigma_j & j\in J^{+} \\ (\bar{x}_j-x_{ij})/\sigma_j & j\in J^{-} \end{cases},\quad \sigma_j = \sqrt{\frac{1}{m}\sum_i(x_{ij}-\bar{x}_j)^2} Anchor: Hellwig 1968, p.310 (standardisation formula; pending PDF page verification)

How to cite

Hellwig, Z. (1968). Zastosowanie metody taksonomicznej do typologicznego podzialu krajow ze wzgledu na poziom ich rozwoju oraz zasoby i strukture wykwalifikowanych kadr technicznych. Przeglad Statystyczny.

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Worked example

1.Adım 1 (F1): Compute column mean x̄_j and population standard deviation σ_j = √(Σ_i(x_ij − x̄_j)²/m). Benefit: z_ij = (x_ij − x̄_j)/σ_j. Cost: z_ij = (x̄_j − x_ij)/σ_j (direction flip so higher is better). Formül: z_{ij} = \begin{cases} (x_{ij}-\bar{x}_j)/\sigma_j & j\in J^{+} \\ (\bar{x}_j-x_{ij})/\sigma_j & j\in J^{-} \end{cases},\quad \sigma_j = \sqrt{\frac{1}{m}\sum_i(x_{ij}-\bar{x}_j)^2} Anchor: Hellwig 1968, p.310 (standardisation formula; pending PDF page verification)