Regionalization approaches for the spatial analysis of extremal dependence

The impact of an extreme climate event depends strongly on its geographical scale. Max-stable processes can be used for the statistical investigation of climate extremes and their spatial dependencies on a continuous area. Most existing parametric models of max-stable processes assume spatial stationarity and are therefore not suitable for the application to data that cover a large and heterogeneous area. For this reason, it has recently been proposed to use a clustering algorithm to divide the area of investigation into smaller regions and to fit parametric max-stable processes to the data within those regions. We investigate this clustering algorithm further and point out that there are cases in which it results in regions on which spatial stationarity is not a reasonable assumption. We propose an alternative clustering algorithm and demonstrate in a simulation study that it can lead to improved results.Comment: 25 pages, 7 figure

New Applications of the Nearest-Neighbor Chain Algorithm

The nearest-neighbor chain algorithm was proposed in the eighties as a way to speed up certain hierarchical clustering algorithms. In the first part of the dissertation, we show that its application is not limited to clustering. We apply it to a variety of geometric and combinatorial problems. In each case, we show that the nearest-neighbor chain algorithm finds the same solution as a preexistent greedy algorithm, but often with an improved runtime. We obtain speedups over greedy algorithms for Euclidean TSP, Steiner TSP in planar graphs, straight skeletons, a geometric coverage problem, and three stable matching models. In the second part, we study the stable-matching Voronoi diagram, a type of plane partition which combines properties of stable matchings and Voronoi diagrams. We propose political redistricting as an application. We also show that it is impossible to compute this diagram in an algebraic model of computation, and give three algorithmic approaches to overcome this obstacle. One of them is based on the nearest-neighbor chain algorithm, linking the two parts together

Hybrid HC-PAA-G3K for novelty detection on industrial systems

Piecewise aggregate approximation (PAA) provides a powerful yet computationally efficient tool for dimensionality reduction and feature extraction. A new distance-based hierarchical clustering (HC) is now proposed to adjust the PAA segment frame sizes. The proposed hybrid HC-PAA is validated by a generic clustering method ‘G3Kmeans’ (G3K). The efficacy of the hybrid HC-PAA-G3K methodology is demonstrated using an application case study based on novelty detection on industrial gas turbines. Results show the hybrid HC-PAA provides improved performance with regard to cluster separation, compared to traditional PAA. The proposed method therefore provides a robust algorithm for feature extraction and novelty detection. There are two main contributions of the paper: 1) application of HC to modify conventional PAA segment frame size; 2) introduction of ‘G3Kmeans’ to improve the performance of the traditional K-means clustering methods

Temporal - spatial recognizer for multi-label data

Pattern recognition is an important artificial intelligence task with practical applications in many fields such as medical and species distribution. Such application involves overlapping data points which are demonstrated in the multi- label dataset. Hence, there is a need for a recognition algorithm that can separate the overlapping data points in order to recognize the correct pattern. Existing recognition methods suffer from sensitivity to noise and overlapping points as they could not recognize a pattern when there is a shift in the position of the data points. Furthermore, the methods do not implicate temporal information in the process of recognition, which leads to low quality of data clustering. In this study, an improved pattern recognition method based on Hierarchical Temporal Memory (HTM) is proposed to solve the overlapping in data points of multi- label dataset. The imHTM (Improved HTM) method includes improvement in two of its components; feature extraction and data clustering. The first improvement is realized as TS-Layer Neocognitron algorithm which solves the shift in position problem in feature extraction phase. On the other hand, the data clustering step, has two improvements, TFCM and cFCM (TFCM with limit- Chebyshev distance metric) that allows the overlapped data points which occur in patterns to be separated correctly into the relevant clusters by temporal clustering. Experiments on five datasets were conducted to compare the proposed method (imHTM) against statistical, template and structural pattern recognition methods. The results showed that the percentage of success in recognition accuracy is 99% as compared with the template matching method (Featured-Based Approach, Area-Based Approach), statistical method (Principal Component Analysis, Linear Discriminant Analysis, Support Vector Machines and Neural Network) and structural method (original HTM). The findings indicate that the improved HTM can give an optimum pattern recognition accuracy, especially the ones in multi- label dataset

Comparison of Various Improved-Partition Fuzzy c-Means Clustering Algorithms in Fast Color Reduction

This paper provides a comparative study of sev- eral enhanced versions of the fuzzy c -means clustering al- gorithm in an application of histogram-based image color reduction. A common preprocessing is performed before clus- tering, consisting of a preliminary color quantization, histogram extraction and selection of frequently occurring colors of the image. These selected colors will be clustered by tested c -means algorithms. Clustering is followed by another common step, which creates the output image. Besides conventional hard (HCM) and fuzzy c -means (FCM) clustering, the so-called generalized improved partition FCM algorithm, and several versions of the suppressed FCM (s-FCM) in its conventional and generalized form, are included in this study. Accuracy is measured as the average color difference between pixels of the input and output image, while efficiency is mostly characterized by the total runtime of the performed color reduction. Nu- merical evaluation found all enhanced FCM algorithms more accurate, and four out of seven enhanced algorithms faster than FCM. All tested algorithms can create reduced color images of acceptable quality

Feedback-Driven Data Clustering

The acquisition of data and its analysis has become a common yet critical task in many areas of modern economy and research. Unfortunately, the ever-increasing scale of datasets has long outgrown the capacities and abilities humans can muster to extract information from them and gain new knowledge. For this reason, research areas like data mining and knowledge discovery steadily gain importance. The algorithms they provide for the extraction of knowledge are mandatory prerequisites that enable people to analyze large amounts of information. Among the approaches offered by these areas, clustering is one of the most fundamental. By finding groups of similar objects inside the data, it aims to identify meaningful structures that constitute new knowledge. Clustering results are also often used as input for other analysis techniques like classification or forecasting. As clustering extracts new and unknown knowledge, it obviously has no access to any form of ground truth. For this reason, clustering results have a hypothetical character and must be interpreted with respect to the application domain. This makes clustering very challenging and leads to an extensive and diverse landscape of available algorithms. Most of these are expert tools that are tailored to a single narrowly defined application scenario. Over the years, this specialization has become a major trend that arose to counter the inherent uncertainty of clustering by including as much domain specifics as possible into algorithms. While customized methods often improve result quality, they become more and more complicated to handle and lose versatility. This creates a dilemma especially for amateur users whose numbers are increasing as clustering is applied in more and more domains. While an abundance of tools is offered, guidance is severely lacking and users are left alone with critical tasks like algorithm selection, parameter configuration and the interpretation and adjustment of results. This thesis aims to solve this dilemma by structuring and integrating the necessary steps of clustering into a guided and feedback-driven process. In doing so, users are provided with a default modus operandi for the application of clustering. Two main components constitute the core of said process: the algorithm management and the visual-interactive interface. Algorithm management handles all aspects of actual clustering creation and the involved methods. It employs a modular approach for algorithm description that allows users to understand, design, and compare clustering techniques with the help of building blocks. In addition, algorithm management offers facilities for the integration of multiple clusterings of the same dataset into an improved solution. New approaches based on ensemble clustering not only allow the utilization of different clustering techniques, but also ease their application by acting as an abstraction layer that unifies individual parameters. Finally, this component provides a multi-level interface that structures all available control options and provides the docking points for user interaction. The visual-interactive interface supports users during result interpretation and adjustment. For this, the defining characteristics of a clustering are communicated via a hybrid visualization. In contrast to traditional data-driven visualizations that tend to become overloaded and unusable with increasing volume/dimensionality of data, this novel approach communicates the abstract aspects of cluster composition and relations between clusters. This aspect orientation allows the use of easy-to-understand visual components and makes the visualization immune to scale related effects of the underlying data. This visual communication is attuned to a compact and universally valid set of high-level feedback that allows the modification of clustering results. Instead of technical parameters that indirectly cause changes in the whole clustering by influencing its creation process, users can employ simple commands like merge or split to directly adjust clusters. The orchestrated cooperation of these two main components creates a modus operandi, in which clusterings are no longer created and disposed as a whole until a satisfying result is obtained. Instead, users apply the feedback-driven process to iteratively refine an initial solution. Performance and usability of the proposed approach were evaluated with a user study. Its results show that the feedback-driven process enabled amateur users to easily create satisfying clustering results even from different and not optimal starting situations