Implement Column-Wise Z-Score Standardization

MediumPython

Problem

Smartsheet machine learning pipelines may contain features with very different numeric ranges. Implement a function that transforms a feature matrix using either min-max normalization or population z-score standardization.

Formal Specification

Given X, a non-empty rectangular matrix represented as a list of rows, where each row is one sample and each column is one feature, and a string method:

For method = "minmax", scale each column to the range [0, 1] using (x - minimum) / (maximum - minimum).
For method = "standard", transform each column using (x - mean) / standard_deviation, where the mean and standard deviation are computed across all rows. Use population standard deviation, dividing variance by the number of rows.
If a column has no variation, output 0.0 for every value in that column.
Return a new matrix. Do not modify X.

Constraints

1 <= len(X) <= 10^4
1 <= len(X[0]) <= 100
X is rectangular
Every feature value is a finite number
method is either "minmax" or "standard"

Function Signature

def scale_features(X, method):

Formal Specification

Given X, a non-empty rectangular matrix represented as a list of rows, where each row is one sample and each column is one feature, and a string method:

For method = "minmax", scale each column to the range [0, 1] using (x - minimum) / (maximum - minimum).
For method = "standard", transform each column using (x - mean) / standard_deviation, where the mean and standard deviation are computed across all rows. Use population standard deviation, dividing variance by the number of rows.
If a column has no variation, output 0.0 for every value in that column.
Return a new matrix. Do not modify X.