Easy

Polynomial Feature Expansion

Easy

~20 min

code completion

Polynomial Feature Expansion

Degree-2 polynomial features let a linear model learn non-linear relationships by explicitly adding squared and interaction terms. For a sample $[x_{1}, x_{2}]$ , the degree-2 expansion adds:

[x_{1}, x_{2}, x_{1}^{2}, x_{1} x_{2}, x_{2}^{2}]

Generally for d original features the degree-2 expansion contains:

The d original features

(2 d + 1)

terms:

x_{i}^{2}

for each

i

, plus

x_{i} x_{j}

for each

i \leq j

In this problem, produce the sorted expansion: original features first, then squared terms in column order, then cross-terms with $i < j$ in lexicographic column order.

Example: X = [[1, 2]]

output = [[1, 2, 1, 2, 4]]

Original:

[1, 2]

Squared:

[1^{2}, 2^{2}] = [1, 4]

Cross:

[1 \times 2] = [2]

Your task:

Implement poly_features(X) that returns an array with original + degree-2 terms.

Example Tests

2-feature row: 5 output columns

Input: {"X":[[1,2]]}

Expected: [1,5]

First row of expansion: original then squares then cross-term

Input: {"X":[[1,2]]}

Expected: [1,2,1,4,2]

1-feature input: only original and squared columns, no cross terms

Input: {"X":[[3]]}

Expected: [[3,9]]

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