Correlation

Normalized
Covariance, measures linear correlation

The correlation coefficient, Pearson product-moment correlation coefficient, PPMCC, Bivariate correlation, Pearson's r

Correlation does not imply causation such as spurious correlation.

Since variance is non-negative, correlation bounds to -1 to 1 (

V(\frac{X}{\sigma_X} \pm \frac{Y}{\sigma_Y}) = 2(1\pm\rho)

)

-1 \leq \rho_{XY} = corr(X, Y) = \frac{cov(X, Y)}{\sigma_X\sigma_Y} \leq 1

corr(X,Y) = 1 \leftrightarrow Y = aX + b

Uncorrelated

corr(X, Y) = 0

This means that there is no linear relationship.

Difference with
Convolution is flip

(f \ast g) (x, y) = \int f(i,j) I(x+i, y+j)

Uncorrelated does not imply independence. However, if two random variables X and Y are

Normal distribution uncorrelated, then they are

Pairwise Independence. Since zero correlation makes

Covariance Matrix and thus inverse of covariance matrix become diagonal. The joint PDF simplifies to the product of two independent normal distributions which satisfies

Pairwise Independence.

The correlation between an

Even function and the original variable is zero. (Integral cancels out) Naturally, even powers also exhibit this property.

Correlations

Spearman's rank correlation

Total correlation

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

https://en.wikipedia.org/wiki/Correlation

Pearson correlation coefficient

In statistics, the Pearson correlation coefficient ― also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation, or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1.

https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

Correlation

Normalized Covariance, measures linear correlation

Difference with Convolution is flip

Recommendations

Normalized
Covariance, measures linear correlation

Difference with
Convolution is flip