Streaming Min-Max Normalization

Feature EngineeringData Processing

Medium

Normalize a sequence of batches while maintaining running per-feature extrema. Initialize each running minimum to $+\infty$ and each running maximum to $-\infty$ . For every incoming batch, update both arrays before normalizing that batch:

x'_{ij} = \frac{x_{ij}-m_j}{\max(M_j-m_j,\varepsilon)}

Here, $m_j$ and $M_j$ are the updated running minimum and maximum for feature $j$ , and $\varepsilon$ is eps. Return normalized_batches as a list of NumPy arrays and the final min and max arrays in a dictionary.

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Examples

Input: D = 2, batches = [[[1, 3], [2, 1]]]

Output: {"normalized_batches": [[[0.0, 1.0], [1.0, 0.0]]], "min": [1.0, 1.0], "max": [2.0, 3.0]}

Explanation: The first batch establishes both feature ranges before it is normalized.

Input: D = 1, batches = [[[5], [3]]]

Output: {"normalized_batches": [[[1.0], [0.0]]], "min": [3.0], "max": [5.0]}

Hint 1

Update state with np.minimum, np.maximum, np.min, and np.max.

Hint 2

Use np.maximum(running_max - running_min, eps) as the denominator.

Requirements

Initialize running minima and maxima with positive and negative infinity
Update running state before normalizing each batch
Protect constant feature ranges with eps
Return exactly normalized_batches, min, and max in a dictionary with NumPy array values

Constraints

D is a positive integer
batches is a nonempty list of nonempty two-dimensional arrays with D columns
eps is positive
Use NumPy only

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