The use of computers and algorithms to deal with human language, in both spoken and written form, is summarized by the term natural language processing (nlp). Modeling language in a way that is suitable for computers plays an important role in nlp. One idea is to use formalisms from theoretical computer science for that purpose. For example, one can try to find an automaton to capture the valid written sentences of a language. Finding such an automaton by way of examples is called training. In this work, we also consider the structure of sentences by making use of trees. We use weighted tree automata (wta) in order to deal with such tree structures. Those devices assign weights to trees in order to, for example, distinguish between good and bad structures. The well-known expectation-maximization algorithm can be used to train the weights for a wta while the state behavior stays fixed. As a way to adapt the state behavior of a wta, state splitting, i.e. dividing a state into several new states, and state merging, i.e. replacing several states by a single new state, can be used. State splitting, state merging, and the expectation maximization algorithm already were combined into the state splitting and merging algorithm, which was successfully applied in practice. In our work, we formalized this approach in order to show properties of the algorithm. We also examined a new approach – the count-based state merging algorithm – which exclusively relies on state merging. When dealing with trees, another important tool is binarization. A binarization is a strategy to code arbitrary trees by binary trees. For each of three different binarizations we showed that wta together with the binarization are as powerful as weighted unranked tree automata (wuta). We also showed that this is still true if only probabilistic wta and probabilistic wuta are considered.:How to Read This Thesis 1. Introduction 1.1. The Contributions and the Structure of This Work 2. Preliminaries 2.1. Sets, Relations, Functions, Families, and Extrema 2.2. Algebraic Structures 2.3. Formal Languages 3. Language Formalisms 3.1. Context-Free Grammars (CFGs) 3.2. Context-Free Grammars with Latent Annotations (CFG-LAs) 3.3. Weighted Tree Automata (WTAs) 3.4. Equivalences of WCFG-LAs and WTAs 4. Training of WTAs 4.1. Probability Distributions 4.2. Maximum Likelihood Estimation 4.3. Probabilities and WTAs 4.4. The EM Algorithm for WTAs 4.5. Inside and Outside Weights 4.6. Adaption of the Estimation of Corazza and Satta [CS07] to WTAs 5. State Splitting and Merging 5.1. State Splitting and Merging for Weighted Tree Automata 5.1.1. Splitting Weights and Probabilities 5.1.2. Merging Probabilities 5.2. The State Splitting and Merging Algorithm 5.2.1. Finding a Good π-Distributor 5.2.2. Notes About the Berkeley Parser 5.3. Conclusion and Further Research 6. Count-Based State Merging 6.1. Preliminaries 6.2. The Likelihood of the Maximum Likelihood Estimate and Its Behavior While Merging 6.3. The Count-Based State Merging Algorithm 6.3.1. Further Adjustments for Practical Implementations 6.4. Implementation of Count-Based State Merging 6.5. Experiments with Artificial Automata and Corpora 6.5.1. The Artificial Automata 6.5.2. Results 6.6. Experiments with the Penn Treebank 6.7. Comparison to the Approach of Carrasco, Oncina, and Calera-Rubio [COC01] 6.8. Conclusion and Further Research 7. Binarization 7.1. Preliminaries 7.2. Relating WSTAs and WUTAs via Binarizations 7.2.1. Left-Branching Binarization 7.2.2. Right-Branching Binarization 7.2.3. Mixed Binarization 7.3. The Probabilistic Case 7.3.1. Additional Preliminaries About WSAs 7.3.2. Constructing an Out-Probabilistic WSA from a Converging WSA 7.3.3. Binarization and Probabilistic Tree Automata 7.4. Connection to the Training Methods in Previous Chapters 7.5. Conclusion and Further Research A. Proofs for Preliminaries B. Proofs for Training of WTAs C. Proofs for State Splitting and Merging D. Proofs for Count-Based State Merging Bibliography List of Algorithms List of Figures List of Tables Index Table of Variable Names

Visual place recognition is the task of finding same places in a set of database images for a given set of query images. This becomes particularly challenging for long-term applications when the environmental condition changes between or within the database and query set, e.g., from day to night. Visual place recognition in changing environments can be used if global position data like GPS is not available or very inaccurate, or for redundancy. It is required for tasks like loop closure detection in SLAM, candidate selection for global localization, or multi-robot/multi-session mapping and map merging. In contrast to pure image retrieval, visual place recognition can often build upon additional information and data for improvements in performance, runtime, or memory usage. This includes additional data-inherent knowledge about information that is contained in the image sets themselves because of the way they were recorded. Using data-inherent knowledge avoids the dependency on other sensors, which increases the generality of methods for an integration into many existing place recognition pipelines. This thesis focuses on the usage of additional data-inherent knowledge. After the discussion of basics about visual place recognition, the thesis gives a systematic overview of existing data-inherent knowledge and corresponding methods. Subsequently, the thesis concentrates on a deeper consideration and exploitation of four different types of additional data-inherent knowledge. This includes 1) sequences, i.e., the database and query set are recorded as spatio-temporal sequences so that consecutive images are also adjacent in the world, 2) knowledge of whether the environmental conditions within the database and query set are constant or continuously changing, 3) intra-database similarities between the database images, and 4) intra-query similarities between the query images. Except for sequences, all types have received only little attention in the literature so far. For the exploitation of knowledge about constant conditions within the database and query set (e.g., database: summer, query: winter), the thesis evaluates different descriptor standardization techniques. For the alternative scenario of continuous condition changes (e.g., database: sunny to rainy, query: sunny to cloudy), the thesis first investigates the qualitative and quantitative impact on the performance of image descriptors. It then proposes and evaluates four unsupervised learning methods, including our novel clustering-based descriptor standardization method K-STD and three PCA-based methods from the literature. To address the high computational effort of descriptor comparisons during place recognition, our novel method EPR for efficient place recognition is proposed. Given a query descriptor, EPR uses sequence information and intra-database similarities to identify nearly all matching descriptors in the database. For a structured combination of several sources of additional knowledge in a single graph, the thesis presents our novel graphical framework for place recognition. After the minimization of the graph's error with our proposed ICM-based optimization, the place recognition performance can be significantly improved. For an extensive experimental evaluation of all methods in this thesis and beyond, a benchmark for visual place recognition in changing environments is presented, which is composed of six datasets with thirty sequence combinations.