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
dimension
X
of n
feature vectors of
dimension p
, the problem is to compute the sample means and
variance-covariance matrix or correlation matrix: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 |