Determining the Dimensionality of Multidimensional Scaling Representations for Cognitive Modeling

Area of Science:

• Cognitive Science
• Psychology
• Computational Neuroscience

Background:

• Multidimensional scaling (MDS) models are foundational in cognitive modeling, representing stimuli in a coordinate space.
• The selection of dimensionality in MDS significantly impacts cognitive model accuracy but often relies on suboptimal heuristics.
• Accurate dimensionality determination is essential for reliable cognitive representations.

Purpose of the Study:

• To develop a Bayesian approach for determining the dimensionality of multidimensional scaling (MDS) models.
• To address the limitations of heuristic-based dimensionality selection in cognitive modeling.
• To formalize the balance between data fit and model complexity in MDS.

Main Methods:

• A probabilistic formulation of multidimensional scaling was employed.
• The Bayesian Information Criterion (BIC) was adapted for dimensionality determination within the Bayesian framework.
• Monte Carlo simulations were utilized to assess the accuracy of the proposed method.

Main Results:

• The Bayesian Information Criterion (BIC) approach effectively balances data fit and model complexity.
• The determined dimensionality is accurate when a substantial number of stimuli are analyzed or when data precision is known.
• The method was successfully demonstrated on a dataset of geometric stimulus similarities.

Conclusions:

• The developed Bayesian approach provides a robust method for dimensionality determination in multidimensional scaling.
• This approach enhances the reliability of cognitive models by improving the accuracy of stimulus representations.
• Incorporating data precision information further strengthens the accuracy of dimensionality estimation.