Correlation Matrix

Shipping

array_correlation

Pearson correlation matrix of a data matrix whose columns are variables

Signature

Inputs

aMatrixrequired— A 2-D matrix; each COLUMN is a variable, each ROW an observation. Non-2-D input is rejected.

Outputs

correlationMatrix— Symmetric $k\times k$ Pearson correlation matrix ($k$ = number of columns); unit diagonal.

Description

Correlation Matrix takes a 2-D matrix whose columns are variables and rows are observations, and returns the symmetric $k \times k$ Pearson correlation matrix $R$ , where $R_{ij}$ is the linear correlation coefficient between column $i$ and column $j$ . The diagonal is all ones (each variable perfectly correlates with itself) and entries lie in $[- 1, 1]$ .

Correlation is the covariance normalized by the product of standard deviations, so it is dimensionless and scale-invariant — multiplying a column by a constant leaves its correlations unchanged. This makes $R$ ideal for spotting linear dependence across heterogeneous variables (different units, different magnitudes). The node requires a rank-2 input and rejects vectors or tensors with a clear error. It is stateless.

Mathematics

R_{ij} = \frac{cov ( X _{i} , X _{j} )}{σ _{X_{i}} σ _{X_{j}}}, R_{ii} = 1, R_{ij} \in [- 1, 1]

Examples

Two perfectly correlated columns

A matrix with columns $[1, 2, 3]^{⊤}$ and $[2, 4, 6]^{⊤}$ (the second is twice the first) yields $R = [1111]$ — the off-diagonal $+ 1$ signals exact positive linear dependence regardless of the scale factor.

Applications

Feature-correlation heatmaps for screening redundant variables before modelling.
Detecting linearly-coupled sensor channels in a DAQ matrix.
Sanity-checking that variables assumed independent are in fact uncorrelated.

Neat

Because correlation normalizes out scale, a column in volts and a column in millivolts of the same signal correlate at exactly $+1$ — the matrix is immune to unit choice.

The columns-are-variables convention matches pandas/NumPy `corrcoef(rowvar=False)`, so a matrix exported from a DataFrame drops straight in.