Normalize Features (Min-Max Scaling) - Data Preprocessing

Normalize Features (Min-Max Scaling)

What you'll build

A function that rescales a 1-D array linearly so its smallest value becomes 0 and its largest becomes 1.

Background

Distance-based models and gradient descent are sensitive to feature scale: a feature in the thousands swamps one in fractions. Min-max scaling puts every feature on the same [0, 1] range. It is what scikit-learn's MinMaxScaler does for each column.

Formula

x_norm[i] = (x[i] - min(x)) / (max(x) - min(x))

where min(x) and max(x) are taken over the whole array.

Inputs

• arr: 1-D array of shape (n,), 2 <= n <= 1000, finite ints or floats (tests may pass a Python list, so convert with np.asarray(arr, dtype=float))

Expected return format

A float array of shape (n,) with values in [0, 1]: the minimum maps to 0.0 and the maximum to 1.0.

Edge cases and conventions

• Constant input (max == min): the formula would divide by zero. Return an array of zeros instead, like MinMaxScaler.
• The order of the elements is preserved; the input doesn't need to be sorted.

Constraints

• Use NumPy only; no loops are needed.

Follow-up

• How would you scale a 2-D (n_samples, n_features) matrix column by column?
• Why is min-max scaling a poor choice when the data has outliers?

Input: normalize(np.array([1, 2, 3, 4, 5]))
Output: [0.0, 0.25, 0.5, 0.75, 1.0]

Input: normalize(np.array([3.0, -1.0, 7.0, 1.0]))
Output: [0.5, 0.0, 1.0, 0.25]

Input: normalize(np.array([4.0, 4.0, 4.0]))
Output: [0.0, 0.0, 0.0]

import numpy as np

def normalize(arr: np.ndarray) -> np.ndarray:
    """
    Min-max scale a 1-D array to [0, 1].

    Args:
        arr: 1-D array (or list) of finite numbers, shape (n,)

    Returns:
        Float array of shape (n,): (arr - min) / (max - min),
        or all zeros if every value is the same
    """
    # Your code here
    pass