Problems

1 / 1

Compute Pearson Correlation Matrix

Data ProcessingLinear Algebra

Medium

Compute the Pearson correlation matrix without using np.corrcoef. Begin with the sample covariance matrix $\Sigma$ and the feature standard deviations $\sigma_i$ :

R_{ij} = \frac{\Sigma_{ij}}{\sigma_i\sigma_j}

Here, $R_{ij}$ is the correlation between features $i$ and $j$ . If either feature has zero variance, the corresponding correlation is NaN, including its diagonal entry. Return the full matrix as a NumPy array.

Loading visualization...

Examples

Input: X = [[1, 2], [2, 3], [3, 5]]

Output: [[1.0, 0.981981], [0.981981, 1.0]]

Explanation: Both features increase together, but their relationship is not perfectly proportional.

Input: X = [[1, 2], [2, 4], [3, 6]]

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

Input: X = [[1, 6], [2, 4], [3, 2]]

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

Hint 1

Compute covariance from centered data with centered.T @ centered / (N - 1).

Hint 2

Use np.sqrt(np.diag(covariance)) and np.outer() to build the denominator.

Requirements

Compute sample covariance without np.corrcoef
Normalize covariance by the outer product of feature standard deviations
Return NaN where a feature has zero variance
Return a NumPy array of shape $(D,D)$

Constraints

X is a rectangular numeric list with shape $(N,D)$
$2 \le N \le 10{,}000$
Use NumPy only

Try Similar Problems

Covariance Matrix Matrix Normalization Sample Var Std Linear Regression Closed Form Bootstrap Mean

Prev Next