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*
Python* with DPC++ support
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.
Optimization Notice |
|---|
Intel’s compilers may or may not optimize to the same degree for
non-Intel microprocessors for optimizations that are not unique to
Intel microprocessors. These optimizations include SSE2, SSE3, and
SSSE3 instruction sets and other optimizations. Intel does not
guarantee the availability, functionality, or effectiveness of any
optimization on microprocessors not manufactured by Intel.
Microprocessor-dependent optimizations in this product are intended
for use with Intel microprocessors. Certain optimizations not
specific to Intel microarchitecture are reserved for Intel
microprocessors. Please refer to the applicable product User and
Reference Guides for more information regarding the specific
instruction sets covered by this notice. Notice revision #20110804 |