What “normalized” means

In practice, “normalized” usually means transforming a numeric feature so it no longer carries its original scale (e.g., dollars vs. kilograms vs. milliseconds). The objective is comparability: values land in a consistent range or distribution that your model can learn from more predictably.

Why it matters

• Improves numerical stability and convergence for gradient-based models.
• Prevents “large-unit” features from overpowering smaller ones.
• Helps distance-based methods (kNN, k-means) behave more sensibly.
• Makes regularization (L1/L2) more meaningful across features.

Note: tree-based models are often less sensitive to feature scaling, but scaling still helps in mixed pipelines or when comparing model families.

1) MaxAbs Scaling

Scales each feature by its maximum absolute value so values typically fall in [-1, 1]. Useful when data can be negative and you want to preserve sparsity patterns.

import pandas as pd

df = pd.read_csv("example.csv")

def maxabs_scale(col: pd.Series) -> pd.Series:
    denom = col.abs().max()
    return col / denom if denom != 0 else col

df_scaled = df.apply(maxabs_scale)
df_scaled.head()
        

import pandas as pd
from sklearn.preprocessing import MaxAbsScaler

df = pd.read_csv("example.csv")

scaler = MaxAbsScaler()
df_scaled = pd.DataFrame(scaler.fit_transform(df), columns=df.columns)
df_scaled.head()
        

2) Min–Max Normalization

Rescales a feature into a fixed interval (commonly [0, 1]). Great when you want bounded inputs, but it can be sensitive to outliers because min/max can be pulled by extreme values.

import pandas as pd

df = pd.read_csv("example.csv")

def minmax_scale(col: pd.Series) -> pd.Series:
    rng = col.max() - col.min()
    return (col - col.min()) / rng if rng != 0 else col

df_scaled = df.apply(minmax_scale)
df_scaled.head()
        

import pandas as pd
from sklearn.preprocessing import MinMaxScaler

df = pd.read_csv("example.csv")

scaler = MinMaxScaler(feature_range=(0, 1))
df_scaled = pd.DataFrame(scaler.fit_transform(df), columns=df.columns)
df_scaled.head()
        

3) Z-Score Standardization

Centers a feature at 0 and scales it to unit variance. This is a strong default for many linear models and neural networks because it makes gradients and regularization behave more consistently.

import pandas as pd

df = pd.read_csv("example.csv")

def zscore(col: pd.Series) -> pd.Series:
    std = col.std()
    return (col - col.mean()) / std if std != 0 else col

df_scaled = df.apply(zscore)
df_scaled.head()
        

import pandas as pd
from sklearn.preprocessing import StandardScaler

df = pd.read_csv("example.csv")

scaler = StandardScaler()
df_scaled = pd.DataFrame(scaler.fit_transform(df), columns=df.columns)
df_scaled.head()
        

import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline
from sklearn.impute import SimpleImputer
from sklearn.linear_model import LogisticRegression

df = pd.read_csv("example.csv")

X = df.drop(columns=["target"])
y = df["target"]

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42, stratify=y
)

pipe = Pipeline(steps=[
    ("imputer", SimpleImputer(strategy="median")),
    ("scaler", StandardScaler()),
    ("model", LogisticRegression(max_iter=2000))
])

pipe.fit(X_train, y_train)
pipe.score(X_test, y_test)