Developer Guide and Reference

  • 2021.2
  • 03/26/2021
  • Public Content
Contents

Correlation and Variance-Covariance Matrices

Variance-covariance and correlation matrices are among the most important quantitative measures of a data set that characterize statistical relationships involving dependence.
Specifically, the covariance measures the extent to which variables “fluctuate together” (that is, co-vary). The correlation is the covariance normalized to be between -1 and +1. A positive correlation indicates the extent to which variables increase or decrease simultaneously. A negative correlation indicates the extent to which one variable increases while the other one decreases. Values close to +1 and -1 indicate a high degree of linear dependence between variables.

Details

Given a set
X
of
n
feature vectors LaTex Math image. of dimension
p
, the problem is to compute the sample means and variance-covariance matrix or correlation matrix:
Statistic
Definition
Means
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Variance-covariance matrix
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Correlation matrix
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Computation

The following computation modes are available:

Examples

C++ (CPU)
Java*
There is no support for Java on GPU.
Batch Processing:
Python* with DPC++ support
Batch Processing:
Online Processing:
Python*
Batch Processing:
Online Processing:
Distributed Processing:

Performance Considerations

To get the best overall performance when computing correlation or variance-covariance matrices:
  • If input data is homogeneous, provide the input data and store results in homogeneous numeric tables of the same type as specified in the algorithmFPType class template parameter.
  • If input data is non-homogeneous, use AOS layout rather than SOA layout.
Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex​.
Notice revision #20201201

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.