## Developer Guide and Reference

• 2021.6
• 04/11/2022
• 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 of feature vectors of dimension , the problem is to compute the sample means and variance-covariance matrix or correlation matrix:
Correlation and Variance-Covariance Matrices
Statistic
Definition
Means , where Variance-covariance matrix , where , , Correlation matrix , where , , ## Computation

The following computation modes are available:

## Examples

C++ (CPU)
Batch Processing:
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.