ML CodingmediumNumpy~15m

Z-Score Standardization

Problem

You are preprocessing a feature matrix for a machine learning model. Raw features have different scales — age ranges from 0-100, salary from 0-200000. Before training, you must standardize each feature column to have mean=0 and standard deviation=1 using z-score normalization.

Given a 2D matrix where each row is a sample and each column is a feature, standardize each column using z = (x - mean) / std. Use population standard deviation (divide by N, not N-1). If a column has std=0 (all values identical), set its output to 0.0. Round each value to 6 decimal places. Return as a list of lists.

Examples

Example 1

Input: [[10, -5], [10, 5]]

Output: [[0.0, -1.0], [0.0, 1.0]]

Column 0 has std=0 (all 10s) → output 0.0. Column 1: mean=0, std=5, z-scores: -5/5=-1.0, 5/5=1.0.

Example 2

Input: [[10], [20], [30]]

Output: [[-1.224745], [0.0], [1.224745]]

Mean=20, std≈8.165. z(10)=(10-20)/8.165=-1.224745, z(20)=0.0, z(30)=1.224745.

Example 3

Input: [[-100], [-200]]

Output: [[1.0], [-1.0]]

Mean=-150, std=50. z(-100)=(-100-(-150))/50=1.0. More negative value gets negative z-score.

Constraints

›2 <= rows <= 100
›1 <= cols <= 100
›-1000 <= matrix[i][j] <= 1000

Reference solution

Reference solution available after you attempt the question.

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