Algorithms for binary factor analysis
Aleš Keprt · DSpace VŠB-TUO (VŠB-TUO) · 2006
This doctoral thesis, or dissertation, is devoted to binary data and their factorization, which is a special kind of data analysis. Binary Factor Analysis (BFA) is a nonlinear analysis of binary data, where neither classical linear algebra, nor mathematical (functional) analysis can be used. It is a binary variant of a commonly used statistical method called factor analysis. Classical factor analysis was originally developed and used by psychologists to detect hidden psychic disorders by observation of visible symptoms. Classical factor analysis works with real valued data in normal distribution. Alongside it, Binary Factor Analysis uses the same notation with a different underlying algebra to express the same kind of analysis for binary valued data. In the past, it has been shown that although classical factor analysis often works seamlessly even for data of other kinds of distribution, it is not able to effectively express symptom–factor relations in binary data, which one can see for example in psychology, medicine, or sociology. Presented doctoral thesis aims to cover BFA from several different aspects, and to specialize on problem solving algorithms. It starts from the underlying algebra, and fundamental definitions. This first part of the work is rather mathematical, but only fundamental definitions are made to keep the text understandable. The second and main part is devoted to algorithms. Several original algorithms for BFA are proposed and described, they range from main factorization algorithms through important underlying algorithms to small supporting ones, with most space devoted to main factorization. Because of a large computational complexity of BFA, a considerable effort is also being put to investigation of parallel and distributed algorithms. Third part is devoted to experimental results. The last part is the user’s manual to BiF, a reference implementation of all presented algorithms. The manual contains not only technical description, but also guidelines aimed to be a starting point for an analyst, e.g. a sociologist or a psychologist, trying to check out how he or she can benefit from BFA. Most of presented algorithms are the results of my own work. They are based on a number of different fields of computer science and mathematics, and main benefits of binary factorization is supposed to be seen in human sciences. That’s also making the work truly interdisciplinary, and forced the notation to be unified throughout all chapters, and possibly less common in some particular cases.