Calculate Correlation Matrix

Calculate Correlation Matrix

Write a Python function to calculate the correlation matrix for a given dataset. The function should take in a 2D numpy array X and an optional 2D numpy array Y. If Y is not provided, the function should calculate the correlation matrix of X with itself. It should return the correlation matrix as a 2D numpy array.

Example:

Input:

X = np.array([[1, 2],
                  [3, 4],
                  [5, 6]])
    output = calculate_correlation_matrix(X)
    print(output)

Output:

# [[1. 1.]
    #  [1. 1.]]

Reasoning:

The function calculates the correlation matrix for the dataset X. In this example, the correlation between the two features is 1, indicating a perfect linear relationship.

import numpy as np

def calculate_correlation_matrix(X, Y=None):
	# Your code here
	if Y is None:
		Y = X
	
	row,col = X.shape
	correlation_matrix = np.zeros((col,col))
	for i in range(col):
		for j in range(col):
			mean_X = np.mean(X[:,i])
			mean_Y = np.mean(Y[:,j])
			covariance = np.sum((X[:,i] - mean_X) * (Y[:,j] - mean_Y))
			std_X = np.sqrt(np.sum((X[:,i] - mean_X) ** 2))
			std_Y = np.sqrt(np.sum((X[:,j] - mean_Y) ** 2))
			correlation_matrix[i,j] = covariance / (std_X * std_Y)
	
	return np.array(correlation_matrix,dtype=float)

Test Case Results

2 of 3 tests passed 

查找原因中

官方题解

import numpy as np

def calculate_correlation_matrix(X, Y=None):
    # Helper function to calculate standard deviation
    def calculate_std_dev(A):
        return np.sqrt(np.mean((A - A.mean(0))**2, axis=0))
    
    if Y is None:
        Y = X
    n_samples = np.shape(X)[0]
    # Calculate the covariance matrix
    covariance = (1 / n_samples) * (X - X.mean(0)).T.dot(Y - Y.mean(0))
    # Calculate the standard deviations
    std_dev_X = np.expand_dims(calculate_std_dev(X), 1)
    std_dev_y = np.expand_dims(calculate_std_dev(Y), 1)
    # Calculate the correlation matrix
    correlation_matrix = np.divide(covariance, std_dev_X.dot(std_dev_y.T))

    return np.array(correlation_matrix, dtype=float)