Mathematical Approaches to User Modeling

Abstract

The first edition of the book “Mathematical Approaches to User Modeling” is developed from the PhD dissertation “A User Modeling for Adaptive Learning”. It was accepted on 4th January 2015 by Scientific Research Publishing (SCIRP) and finished on 13rd July 2016 but it is not published yet. Following is the abstract of the book.User model is description of user's information and characteristics in abstract level. User model is very important to adaptive software which aims to support user as much as possible. The process to construct user model is called user modeling. As the title suggests, the book focuses on mathematical approaches to user modeling. The book includes seven main chapters. Chapter I is a survey of user model, user modeling, and adaptive learning. Chapter II introduces the general architecture of the proposed user modeling system Zebra and Triangular Learner Model (TLM). Chapter III, IV, V describes three sub-models of TLM such as knowledge sub-model, learning style sub-model, and learning history sub-model in full of mathematical formulas and fundamental methods. These are the most important chapters. Chapter VI gives some approaches to evaluate TLM and Zebra. Chapter VII summarizes the research and discusses future trend of Zebra.The whole book is available at http://mum.locnguyen.net. In general, the first difference of the book is to introduce my innovative works in mathematics, probability, user modeling, machine learning, data mining, and adaptive learning. The second difference is that the user modeling system Zebra is implemented as computer software associated to the book, available at http://zebra.locnguyen.net. Moreover, examples, mathematical formulas, and mathematical models inside the book are implemented separately and integrated into another computer software.

Tutorial on artificial neural network

“…for hidden unit 𝑗 Backpropagation algorithm (backward propagation algorithm) is described here along with an example of document classification (Nguyen, 2022), which is implementation of propagation rule, weight update rule, and bias update rule. Suppose a sample consists of many data rows and each row has many attributes.…”

“…330-333) is also a famous supervised learning algorithm for classification, besides learning feedforward NN. Therefore, backpropagation algorithm here is applied to classify the corpus as an example of supervised learning by NN (Nguyen, 2022). It processes iteratively data rows in training corpus and compares network's prediction for each row to actual class of the row.…”