# Correlation Matrix To Pairs

The Correlation Matrix to Pairs node is designed to take an Input Correlation Matrix and convert it into an equivalent list of Correlation Pairs.

The Correlation Matrix represents the degree of Horizontal Differentiation between Features, Benefits, Attributes, Levels, and Products. The Correlation Matrix may be used by a downstream node (such as the Matrix Distributions node or the Feature Generation node) to generate a set of Customer Distributions comprising the Willingness To Pay (WTP) of individual Virtual Customers.

For example, the Input Correlation Matrix may be a 3×3 matrix of correlation values (doubles between -1.0 and +1.0) with row names and column names of ‘A’, ‘B’, and ‘C’. The matrix describes all the correlations between Customer Distribution A, Customer Distribution B, and Customer Distribution C. The Output Correlation Pairs would then individually list the same correlations between A:B, A:C, and B:C.

The Input Correlation Matrix will first be converted into a clean and symmetrical Correlation Matrix. That means: (a) the diagonal A:A, B:B, C:C correlations will be set to 1.0; (b) correlation values will be limit-ranged to between -1.0 and +1.0; (c) missing correlations will be set to 0.0; and (d) the correlation for A:B will be set the same as the correlation for B:A (hence lower-left-triangle and upper-right-triangle correlation matrices can be input).

The purpose of this node is to provide the user with flexibility when setting and managing the Horizontal Differentiation (correlations) between Customer Distributions. A downstream Feature Generation node or a downstream Matrix Distribution node both requires an Input Correlation Matrix to generate a set of Customer Distributions. With this node, the user could edit the Correlation Pairs list, scale the Correlation Pairs list so that each Customer Distribution was more-or-less correlated with other Customer Distributions, or concatenate the Correlation Pairs list with another set of correlations developed elsewhere. Working with a list can be easier than working with a matrix.

This Community Node documentation assumes you have already downloaded the open-source KNIME analytics platform and installed the free Market Simulation (Community Edition) plugin. If not, start by returning to Getting Started.

# #1 Simple Conversion

The Input Correlation Matrix is converted to a list of Output Correlation Pairs.

## Inputs

#### Correlation Matrix

The Input Correlation Matrix can be generated by a ‘Table Creator’ node or any other upstream node that can generate a square matrix of correlation values. The node assumes the correlations are related to Customer Distributions, but any correlation matrix can be used.

A triangular matrix of correlation values can also be used, regardless of whether it is an upper-right-triangular matrix or lower-left-triangular matrix.

## Node

#### Configuration

The ‘Correlation Matrix To Pairs’ node does not need to be configured. It simply converts a matrix of correlation values into a list.

## Outputs

#### Output List

Correlation values are listed in pairs of ‘From Distribution’ and ‘To Distribution’. If multiple correlations are provided for A:B or B:A then the highest-non-zero correlation will be used.