Data Normalization Techniques: Z-Score and Min-Max Scaling

Feature scaling is a critical preprocessing step in machine learning that transforms numerical features to a common scale without distorting differences in the ranges of values. Raw features often have vastly different magnitudes—for instance, age might range from 0-100 while income ranges from 0-1,000,000. This discrepancy can cause significant problems for many machine learning algorithms.

This problem focuses on implementing two of the most widely-used normalization techniques:

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1. Standardization (Z-Score Normalization)

Standardization transforms each feature to have a mean of 0 and a standard deviation of 1. For each value in a feature column, the transformation is computed as:

$$z = \frac{x - \mu}{\sigma}$$

Where:

• x is the original value
• μ (mu) is the mean of the feature column
• σ (sigma) is the standard deviation of the feature column

This technique is particularly useful when:

• Your data follows a Gaussian distribution (or close to it)
• You're using algorithms that assume normally distributed data
• You need to handle outliers while preserving their information

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2. Min-Max Normalization

Min-max normalization rescales each feature to a fixed range of [0, 1], where the minimum value maps to 0 and the maximum value maps to 1. The formula is:

$$x_{scaled} = \frac{x - x_{min}}{x_{max} - x_{min}}$$

Where:

• x is the original value
• x_min is the minimum value in the feature column
• x_max is the maximum value in the feature column

This technique is preferred when:

• You need bounded values within a specific range
• Your algorithm is sensitive to the magnitude of values (e.g., neural networks with sigmoid activation)
• The feature distribution is not necessarily Gaussian

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Your Task

Write a Python function that takes a 2D NumPy array representing a dataset (where each row is a data sample and each column represents a feature). Apply both scaling techniques column-wise and return the results as two separate 2D arrays. All values should be rounded to 4 decimal places.

Important: Apply scaling independently to each feature column, computing statistics (mean, std, min, max) for each column separately.

data = [[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]

[[[-1.2247, -1.2247], [0.0, 0.0], [1.2247, 1.2247]], [[0.0, 0.0], [0.5, 0.5], [1.0, 1.0]]]

data = [[1.0, 2.0, 3.0], [4.0, 5.0, 6.0], [7.0, 8.0, 9.0]]

[[[-1.2247, -1.2247, -1.2247], [0.0, 0.0, 0.0], [1.2247, 1.2247, 1.2247]], [[0.0, 0.0, 0.0], [0.5, 0.5, 0.5], [1.0, 1.0, 1.0]]]

data = [[-1.0, 0.0, 1.0], [2.0, 3.0, 4.0]]

[[[-1.0, -1.0, -1.0], [1.0, 1.0, 1.0]], [[0.0, 0.0, 0.0], [1.0, 1.0, 1.0]]]