In this paper we present a new idea for the discovery of meaningful clusters from categorical data (which is an usual situation, e.g. web data analysis). Our method extracts a subset of concepts from the frequent closed itemsets lattice, using an evaluation measure. This method is promising, and first experiments give attractive results.

xv 1 Introductory Overview 1 1.1 The Research Question and Motivation . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Roles and Preferred Characteristics . . . . . . . . . . . . . . . . . . . . 2 1.1.3 Realization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Overview of Contributions...

• • • LIST OF TABLES. LIST OF FIGURES i vi viii PART I: CHAPTER ESTIMATION, TESTING AND MODELING PROCEDURES

Recent developments in the categorical foundations of universal algebra have given an impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott’s representation theorem is then completely natural and leads to a precise Fundamental Theorem showing the essential equivalence between the categorical and more familiar...

Factor mixture models (FMM's) are latent variable models with categorical and continuous latent variables which can be used as a model-based approach to clustering. A previous paper covered the results of a simulation study showing that in the absence of model violations, it is usually possible to choose the correct model when fitting a series of models with different numbers of classes and fac...

Probabilistic inversion within a multiple-point statistics framework is still computationally prohibitive for large-scale problems. To partly address this, we introduce and evaluate a new training-image based simulation and inversion approach for complex geologic media. Our approach relies on a deep neural network of the spatial generative adversarial network (SGAN) type. After training using a...