OLS Menu

Different options are available if a FIS file is available or not. The OLS algorithm [2,3,11] transforms each data file example into a fuzzy rule, and selects the most important rules with the least squares criterion, by linear regression and Gram-Schmidt orthogonalization. After the selection step, a second passage is done to optimize the selected rule conclusions.

As for all FisPro learning procedures, two steps must be distinguished: generating the partitions if necessary, and inducing rules.

Our implementation is motivated and described in detail in [5].

Generate partitions

If there is no current FIS, the first step is the partition generation from data. Two options are available. We advise to use standard fuzzy partitions (as in the FIS menu Generate a FIS without rules, section 1.6).

We also propose the original OLS algorithm, which consists of generating a Gaussian MF for each data point variable value. These MFs are then clustered to limit their number to MAX_MF (999) . Note that, in that case, the partitions are not standard fuzzy partitions.

If there is a current FIS file, the input fuzzy partitions are kept.

Generate rules

The second step consists of two stage: the rule selection étape and the rule conclusion optimization. The algorithm uses one output (default=first output, or last column in data file). Two criteria are used together to select the rules in the first stage:

• Part of output inertia not explained by the rules (Default=0.1).

• Number of rules (Default=100).

The prodedure stops as soon as one criterion is satisfied. With the default values, the inertia one is usually the first to be fulfilled.

The stage 2 uses a least squares optimization to set the selected rule conclusion values. If there is a current FIS, an option allows to keep the existing rules, which means that only the rule conclusions are changed.

The optimization, which does not change the partitions nor the rule premise, but only the rule conclusions, is also available in the Generate conclusions option of the FIS menu (section 1.8).

Reduce the output vocabulary

The rule conclusions generated by OLS are all distinct from each other, so it can be interesting to reduce the number of distinct conclusions.

This is done by a clustering operation, for which two options are available: start from the rule conclusions, or start from the output data values in the data file.

The number of distinct conclusions, or the tolerated performance loss, can be set. Indeed the voabulary reduction usually goes together with an accuracy loss

With that option, the output can be fuzzified, meaning that a standard output fuzzy partition is built using the new conclusions as MF centers. “fuzzifier” la sortie, c'est à dire construire une partition floue

The Reduce the output vocabulary option is also available in the FIS menu “Generate Conclusions” option.