Vectorized Euclidean Distance Matrix via Gram Matrixeasy

Vectorized Euclidean Distance Matrix via Gram Matrix

easy NumPy & Data Wrangling 10–15 min

NumPy allowed · plain Python earns 10 bonus points

A vector transforms

Matrix multiplication is the first computation behind every model.

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01vector

02matrix

03transform

04result

[2, −1] × [[1, 2], [−.5, 1]] = [0, −2]

Computed matrix × vector transformation

Compute the complete pairwise Euclidean distance matrix between two feature sets.

Task

Implement pairwise_euclidean_distance(x, y): given matrices x (N x D) and y (M x D), compute the (N, M) matrix of L2 Euclidean distances sqrt(sum((x_i - y_j)**2)). Round each float to 4 decimal places.

Function Signature

pairwise_euclidean_distance(x: list[list[float]], y: list[list[float]]) -> list[list[float]]

Examples

Example 1: 3-4-5 right triangle points
Input: x = [[0, 0]]
y = [[3, 4]]
Output: [[5]]

Example 2: Identical points zero distance
Input: x = [[1, 2]]
y = [[1, 2], [4, 6]]
Output: [[0, 5]]

Constraints

x has shape N x D, y has shape M x D
D >= 1

Python3Saved ✓

import math

def pairwise_euclidean_distance(x: list[list[float]], y: list[list[float]]) -> list[list[float]]:

"""Compute N x M Euclidean distance matrix between vectors in x and y.

Round each float to 4 decimal places.

"""

pass

Case 1: 3-4-5 right triangle points

Input: x = [[0, 0]]
y = [[3, 4]]

Expected: [[5]]

Case 2: Identical points zero distance

Input: x = [[1, 2]]
y = [[1, 2], [4, 6]]

Expected: [[0, 5]]