Differentiation Horizontal

Input Ports

Input Related Features: The collection of related Feature names. These may be ordinal Features related by the fact that they can be ranked. For example, the Feature List may be '5-star', '4-star', '3-star', and '2-star'. Or these may be categorical Features that are not ranked but are nevertheless related. For example, the Features 'Japanese', 'Korean', and 'German' will be correlated (Customers generally perceive the two Asian Products as being more similar to each other than to the European Products). Unrelated Features, having no Correlation, should be generated using several of these Differentiation Horizontal nodes. Note that an input table having just a single Feature is quite normal and, in fact, desirable. It is mathematically possible to select a set of orthogonal (uncorrelated) Features that describe the Products in a Market (see "Rotations in Factor Analysis"). In this case, each orthogonal Feature should be created using different 'Differentiation Horizontal' nodes, with perhaps simple Variations generated for each Product. The Input Related Features should include the following columns:

1. Feature (string): The name of all the related Features that will appear within the Output Correlation Matrix. The Horizontal Differentiation, along with the Vertical Differentiation, of the Feature needs to be described to generate a Customer Distribution and build a Product Willingness To Pay (WTP) Matrix.

Input Feature Variations: (optional) A Variation of a Feature may be associated with a Brand, Product, Channel, Demographic, or Technology. A Variation may also be an Attribute from Conjoint Analysis, such that: Variation = Attribute, and Feature = Level. If the Variation is the name of a Brand, then all Products having the same Brand will exhibit the same Variation on the Feature. For example, 'Sony', 'Samsung', 'Canon', and 'Apple' may all offer their own Variations of the Features listed. The Brands 'Sony', 'Samsung', and 'Canon' may all have a Conformity = 0.95 (they all offer a normal Feature with only a little distinction), whereas 'Apple' may have a Conformity = 0.20 because Apple's Variation is highly distinctive. Note that these values do not describe whether 'Sony' is better or worse than 'Apple'. Horizontal Differentiation describes only whether Customers view the Features and Variations as similar or different. Vertical Differentiation is also required to determine which is 'better'. The Input Feature Variations should include the following columns:

1. Variation (string): The Variation name to give to each of the related Features. For example, if a Feature is 'Horse Power' then the Variations might be 'Diesel Engine', 'Gasoline Engine', and 'Electric Engine'.
2. Feature (string): (optional) If a Feature is specified in the Input Feature Variations list, then only the specified Features will have the Variation. If the Feature column is missing, or if the Feature cell is blank, then all Features will have this Variation.
3. Conformity (double): (optional) The degree of Conformity the Variation has from a Feature norm (range limited to between +1.0 and 0.0). Conformity = 1.0 (default) means that the Variation precisely offers what is expected from the normal Feature. Conformity = 0.0 means that the Variation is vastly different and unpredictable from the norm. Conformity = 0.95 is typical, and would be used to generate a range of Features that all offer small Variations around what is accepted as a Feature norm. In this example, 'Diesel Engine' and 'Gasoline Engine' might both have a Variation = 0.9 while 'Electric Engine' might have a Variation = 0.3.

Output Ports

Output Correlation Matrix: The output set of correlations that define the relationship between Feature Variations and downstream Customer Distributions. The Correlation Matrix will be symmetrical such that the number of data rows match the number of columns. Each row [Feature].[Variation] name will be unique and correspond to a column of the same name. The Output Correlation Matrix will contain these columns:

1. Distribution: The row name of the [Feature].[Variation] within the Output Correlation Matrix.
2. Order: The Order of each unique Feature if Features are Ranked (Ordinal).
3. Correlated Distributions: The column name of the [Feature].[Variation] within the Output Correlation Matrix, along with the degree of correlation to the row [Feature].[Variation]. Output correlations will be symmetrical and range-limited to -1.0 and +1.0.

Output Correlation Repaired Matrix: The repaired output set of correlations that define the relationship between Feature Variations and downstream Customer Distributions. Repairing is required when the correlations are unrealistic. For example, if A is highly correlated to B (for example, A:B = +0.99) and if A is highly correlated with C (for example, A:C = +0.99) then B must be highly correlated with C (that is, B:C >> 0.0). More precisely, the Correlation Matrix must have all positive definite Eigenvalues. Note that it is not necessary for downstream nodes that generate Customer Distributions (such as the Matrix Distributions node or the Feature Generation node) to use this Correlation Repaired Matrix as these downstream nodes will always first self-repair the Input Correlation Matrix. The Output Correlation Repaired Matrix will contain the same columns as the Output Correlation Matrix:

1. Distribution: The row name of the [Feature].[Variation] within the Output Correlation Repaired Matrix.
2. Order: The Order of each unique Feature if Features are Ranked (Ordinal).
3. Correlated Distributions: The column name of the [Feature].[Variation] within the Output Correlation Matrix, along with the repaired degree of correlation to the row [Feature].[Variation]. Output correlations will be symmetrical and range-limited to -1.0 and +1.0.

Output Correlation Error Matrix: The difference between the Output Correlation Matrix and the Output Correlation Repaired Matrix. This is a convenience output to show how the Correlation Matrix needs to be repaired before Customer Distributions for the Feature Variations can be generated. The Output Correlation Error Matrix will contain the same columns as the Output Correlation Matrix:

1. Distribution: The row name of the [Feature].[Variation] within the Output Correlation Error Matrix.
2. Order: The Order of each unique Feature if Features are Ranked (Ordinal).
3. Correlated Distributions: The column name of the [Feature].[Variation] within the Output Correlation Matrix, along with the difference between the output correlation and the repaired correlation.

Popular Predecessors

• Table Creator38 %
• Differentiation Vertical25 %
• Column Rename13 %
• k-Means13 %
• Demand Curve13 %

Popular Successors

• Matrix Distributions86 %
• Scatter Plot (legacy)14 %