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Visible to Intel only — GUID: GUID-E0C451CB-4928-4429-BB90-EF0AE6E86E1E
Covariance
In statistics, covariance and correlation are two of the most fundamental measures of linear dependence between two random variables. The covariance and the correlation represent the joint variability of any two features. The correlation is dimensionless, while the covariance is measured in units obtained by multiplying the units of the two features. Another important distinction is that covariance can be affected by the higher variance of one feature, while correlation removes the effect of the variances by normalizing the covariance of two features by their square-root of variances. Their usage is application-dependent. The covariance algorithm computes the following:
Means
Covariance (sample and estimated by maximum likelihood method)
Correlation
Operation |
Computational methods |
Programming Interface |
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Mathematical formulation
Computing
Given a dataset with n feature vectors of dimension p, the means is a matrix, the covariance and the correlation matrices are square matrices. The means, the covariance, and the correlation are computed with the following formulas:
Statistic |
Definition |
---|---|
Means |
, where |
Covariance matrix (sample) |
, where , , |
Covariance matrix (maximum likelihood) |
, where , , |
Correlation matrix |
, where , , |
Partial Computing
Given a block of a dataset with n feature vectors of p dimension, the sums is a matrix, the cross product is square matrices. The sums and cross product are computed with the following formulas:
Statistic |
Definition |
---|---|
Sums |
, where |
Cross product matrix |
, , |
Finalize Computing
Given a partial result with partial products, the means is a matrix, the covariance and correlation matrices are square matrices. The means, the covariance, and the correlation are computed with the following formulas:
Statistic |
Definition |
---|---|
Means |
, where |
Covariance matrix (sample) |
, where , , |
Covariance matrix (maximum likelihood) |
, where , , |
Correlation matrix |
, where , , |
Computation method: dense
The method computes means, variance-covariance, or correlation matrix for the dense data. This is the default and the only method supported.
Programming Interface
Refer to API Reference: Covariance.
Online mode
The algorithm supports online mode.
Distributed mode
The algorithm supports distributed execution in SPMD mode (only on GPU).