#### Title

#### Date of Award

Fall 12-16-2019

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy in Analytic and Data Science

#### Department

Statistics and Analytical Sciences

#### Committee Chair

Dr Ying Xie

#### Committee Member

Dr Sherry Ni

#### Committee Member

Dr Gene Ray

#### Committee Member

Dr Babak Moazzez

#### Committee Member

Dr Stefanos Manganaris

#### Abstract

This research presents the development of a new framework for analyzing ordered class data, commonly called “ordinal class” data. The focus of the work is the development of classifiers (predictive models) that predict classes from available data. Ratings scales, medical classification scales, socio-economic scales, meaningful groupings of continuous data, facial emotional intensity and facial age estimation are examples of ordinal data for which data scientists may be asked to develop predictive classifiers. It is possible to treat ordinal classification like any other classification problem that has more than two classes. Specifying a model with this strategy does not fully utilize the ordering information of classes. Alternatively, the researcher may choose to treat the ordered classes as though they are continuous values. This strategy imposes a strong assumption that the real “distance” between two adjacent classes is equal to the distance between two other adjacent classes (e.g., a rating of ‘0’ versus ‘1,’ on an 11-point scale is the same distance as a ‘9’ versus a ‘10’). For Deep Neural Networks (DNNs), the problem of predicting *k* ordinal classes is typically addressed by performing *k-1* binary classifications. These models may be estimated within a single DNN and require an evaluation strategy to determine the class prediction. Another common option is to treat ordinal classes as continuous values for regression and then adjust the cutoff points that represent class boundaries that differentiate one class from another. This research reviews a novel loss function called Ordinal Hyperplane Loss (OHPL) that is particularly designed for data with ordinal classes. OHPLnet has been demonstrated to be a significant advancement in predicting ordinal classes for industry standard structured datasets. The loss function also enables deep learning techniques to be applied to the ordinal classification problem of unstructured data. By minimizing OHPL, a deep neural network learns to map data to an optimal space in which the distance between points and their class centroids are minimized while a nontrivial ordering relationship among classes are maintained. The research reported in this document advances OHPL loss, from a minimally viable loss function, to a more complete deep learning methodology. New analysis strategies were developed and tested that improve model performance as well as algorithm consistency in developing classification models. In the applications chapters, a new algorithm variant is introduced that enables OHPLall to be used when large data records cause a severe limitation on batch size when developing a related Deep Neural Network.

#### Recommended Citation

Vanderheyden, Bob, "Ordinal HyperPlane Loss" (2019). *Analytics and Data Science Dissertations*. 4.

https://digitalcommons.kennesaw.edu/dataphd_etd/4

#### Included in

Artificial Intelligence and Robotics Commons, Numerical Analysis and Scientific Computing Commons, Other Computer Sciences Commons, Other Statistics and Probability Commons, Statistical Models Commons