Location-Scale Matching for Approximate Quasi-Order Sampling.

Area of Science:

• Mathematics
• Computer Science
• Data Mining
• Statistics

Background:

• Quasi-orders, reflexive and transitive binary relations, have applications in psychological testing and data mining.
• Current data mining techniques rely on simulations with randomly generated quasi-orders, which may not be representative.
• There is a need for methods to generate approximately representative samples of quasi-orders for more reliable simulations.

Purpose of the Study:

• To develop techniques for approximately representative sampling of quasi-orders.
• To enable the construction of quasi-order samples suitable for large-scale data mining simulations.
• To improve the validity of simulation studies in data mining by using representative quasi-order samples.

Main Methods:

• Polynomial regression curves were fitted to the mean and standard deviation of quasi-order size versus item number.
• Extrapolated regression values informed two sampling techniques: a discrete method and a continuous method using normal distribution.
• Quasi-orders were constructed using a biased randomized doubly inductive method and then resampled to match discrete and continuous distributions.

Main Results:

• Regression analysis revealed quadratic and linear relationships for mean and standard deviation, respectively.
• The proposed discrete and continuous sampling methods successfully generated approximately representative quasi-order samples.
• The location-scale matching approach proved effective for very large item sets, constructing samples up to n=400.

Conclusions:

• The developed sampling techniques provide a robust method for generating representative quasi-orders for simulation studies.
• These methods address the limitations of purely random quasi-order generation, enhancing simulation accuracy.
• The approach is scalable and effective for large item sets, advancing data mining simulation capabilities.