Methodology and Statistics Unit
Institute of Psychology
Faculty of Social and Behavioural Sciences, Leiden University

On December 21st 2021Beibei Yuan has defended her thesis The δ-machine: Classification based on dissimilarities towards prototypes at the Leiden University.

Summary
This thesis describes a dissimilarity-based classification tool, the δ-machine, which gives an alternative way of statistical modeling compared to the conventional ones that directly use predictor variables. We use the symbol δ, because it is commonly used as a symbol for dissimilarities in multidimensional scaling.
In this thesis, we discuss the properties of the δ-machine, and extend the δ-machine from handling continuous predictor variables only to handle different types of predictor variables, including continuous, ordinal, nominal, and binary predictor variables via the two tailored dissimilarity functions. Furthermore, we study the classification performance of the δ-machine in high dimensional data. We propose a Majorization-Minimization algorithm to interpolate new data points coherently into previously constructed classical multidimensional scaling (CMDS) configurations, and use the proposed algorithm in the δ-machine in high dimensional data scenario, where CMDS is applied to reduce the original high dimensional predictor variables. In order to make predictions for new data points, therefore, needs to interpolate them into the constructed CMDS.
The δ-machine shows promising predictive performance in general and is able to find informative exemplars/prototypes, which bring extra insights of data. The informative (typical) exemplars could be used in the further study.

Supervisors
Prof. M. de Rooij & Prof. W.J. Heiser

Financed by
NWO

Period
1 October 2015 – 21 December 2021