Predicting Product Choice with Symbolic Regression and Classification 209
Ta b l e 3 Market shares from direct choice task and a decision tree search
8 A Non-Linear Discriminant Analysis (NLDA) Search
The next evolutionary search involved Linear Discriminant Analysis (LDA). Since
this search was conducted at a node-depth of two (see below) this was technically
Non-Linear Discriminant Analysis (NLDA). The ‘net’ code-expression generator
for LDS searches takes the following form:
net(node-depth, inputs, outputs, x |v, n |h |s)The penultimate parameter was introduced to handle extremely large numbers of
input variables. Its two values have the following meanings:
- ‘x’ signifies concrete features (when there are fewer than 250 independent
variables) - ‘v’ signifies abstract variables (when there are more than 250 independent
variables)
The final parameter allows the user to constrain the output to be in one of three
forms:
- ‘n’ signifies ‘no operator’ (results unconstrained)
- ‘h’ signifies hyperbolic tangent (results in the range 1 toC 1 )
- ‘s’ signifies sigmoid (results in the range 0 to 1)
The specific goal for the product search was:
select(net(2,18,8,x,n))
Two represented the node-depth. The 18 utility scores were the inputs, and the
eight outputs corresponded to the eight product choices. The ‘x’ parameter implies
concrete features rather than abstract variables. The final parameter indicates the
output values were unconstrained but since the select command was wrapped around
the goal specification, the outputs were constrained to be in the range of 1–8. After
24,000 well-formed formulas, the NLDA search produced a champion on the testing
data with a CEP error of 92 % (Table4).