For hierarchical clustering, dendrograms provide convenient and powerful visualization. Although many visualization methods have been suggested for partitional clustering, their usefulness deteriorates quickly with increasing dimensionality of the data and/or they fail to represent structure between and within clusters simultaneously. In this paper we extend (dissimilarity) matrix shading with several reordering steps based on seriation. Both methods, matrix shading and seriation, have been well-known for a long time. However, only recent algorithmic improvements allow to use seriation for larger problems. Furthermore, seriation is used in a novel stepwise process (within each cluster and between clusters) which leads to a visualization technique that is independent of the dimensionality of the data. A big advantage is that it presents the structure between clusters and the micro-structure within clusters in one concise plot. This not only allows for judging cluster quality but also makes mis-specification of the number of clusters apparent. We give a detailed discussion of the construction of dissimilarity plots and demonstrate their usefulness with several examples. / Series: Research Report Series / Department of Statistics and Mathematics

Recent advances in tractography allow for connectomes to be constructed in vivo. These have applications for example in brain tumor surgery and understanding of brain development and diseases. The large size of the data produced by these methods lead to a variety problems, including how to evaluate tractography outputs, development of faster processing algorithms for tractography and clustering, and the development of advanced visualization methods for verification and exploration. This thesis presents several advances in these fields. First, an evaluation is presented for the robustness to noise of multiple commonly used tractography algorithms. It employs a Monte–Carlo simulation of measurement noise on a constructed ground truth dataset. As a result of this evaluation, evidence for obustness of global tractography is found, and algorithmic sources of uncertainty are identified. The second contribution is a fast clustering algorithm for tractography data based on k–means and vector fields for representing the flow of each cluster. It is demonstrated that this algorithm can handle large tractography datasets due to its linear time and memory complexity, and that it can effectively integrate interrupted fibers that would be rejected as outliers by other algorithms. Furthermore, a visualization for the exploration of structural connectomes is presented. It uses illustrative rendering techniques for efficient presentation of connecting fiber bundles in context in anatomical space. Visual hints are employed to improve the perception of spatial relations. Finally, a visualization method with application to exploration and verification of probabilistic tractography is presented, which improves on the previously presented Fiber Stippling technique. It is demonstrated that the method is able to show multiple overlapping tracts in context, and correctly present crossing fiber configurations.

In this dissertation, we propose and develop innovative data modeling and analysis methods for extracting meaningful and specific information about disease mechanisms from microarray gene expression data. To provide a high-level overview of gene expression data for easy and insightful understanding of data structure, we propose a novel statistical data clustering and visualization algorithm that is comprehensively effective for multiple clustering tasks and that overcomes some major limitations of existing clustering methods. The proposed clustering and visualization algorithm performs progressive, divisive hierarchical clustering and visualization, supported by hierarchical statistical modeling, supervised/unsupervised informative gene/feature selection, supervised/unsupervised data visualization, and user/prior knowledge guidance through human-data interactions, to discover cluster structure within complex, high-dimensional gene expression data. For the purpose of selecting suitable clustering algorithm(s) for gene expression data analysis, we design an objective and reliable clustering evaluation scheme to assess the performance of clustering algorithms by comparing their sample clustering outcome to phenotype categories. Using the proposed evaluation scheme, we compared the performance of our newly developed clustering algorithm with those of several benchmark clustering methods, and demonstrated the superior and stable performance of the proposed clustering algorithm. To identify the underlying active biological processes that jointly form the observed biological event, we propose a latent linear mixture model that quantitatively describes how the observed gene expressions are generated by a process of mixing the latent active biological processes. We prove a series of theorems to show the identifiability of the noise-free model. Based on relevant geometric concepts, convex analysis and optimization, gene clustering, and model stability analysis, we develop a robust blind source separation method that fits the model to the gene expression data and subsequently identify the underlying biological processes and their activity levels under different biological conditions. Based on the experimental results obtained on cancer, muscle regeneration, and muscular dystrophy gene expression data, we believe that the research work presented in this dissertation not only contributes to the engineering research areas of machine learning and pattern recognition, but also provides novel and effective solutions to potentially solve many biomedical research problems, for improving the understanding about disease mechanisms. / Ph. D.

For scientific or socio-economic reasons it is often necessary or desirable that biological material be identified. Given that there are an estimated 10 million living organisms on Earth, the identification of biological material can be problematic. Consequently the services of taxonomist specialists are often required. However, if such expertise is not readily available it is necessary to attempt an identification using an alternative method. Some of these alternative methods are unsatisfactory or can lead to a wrong identification. One of the most common problems encountered when identifying specimens is that important diagnostic features are often not easily observed, or may even be completely absent. A number of techniques can be used to try to overcome this problem, one of which, the Self Organizing Map (or SOM), is a particularly appealing technique because of its ability to handle missing data. This thesis explores the use of SOMs as a technique for the identification of indigenous trees of the Acacia species in KwaZulu-Natal, South Africa. The ability of the SOM technique to perform exploratory data analysis through data clustering is utilized and assessed, as is its usefulness for visualizing the results of the analysis of numerical, multivariate botanical data sets. The SOM’s ability to investigate, discover and interpret relationships within these data sets is examined, and the technique’s ability to identify tree species successfully is tested. These data sets are also tested using the C5 and CN2 classification techniques. Results from both these techniques are compared with the results obtained by using a SOM commercial package. These results indicate that the application of the SOM to the problem of biological identification could provide the start of the long-awaited breakthrough in computerized identification that biologists have eagerly been seeking. / Dissertation (MSc)--University of Pretoria, 2011. / Computer Science / unrestricted

Data clustering is a highly used knowledge extraction technique and is applied in more and more application domains. Over the last years, a lot of algorithms have been proposed that are often complicated and/or tailored to specific scenarios. As a result, clustering has become a hardly accessible domain for non-expert users, who face major difficulties like algorithm selection and parameterization. To overcome this issue, we develop a novel feedback-driven clustering process using a new perspective of clustering. By substituting parameterization with user-friendly feedback and providing support for result interpretation, clustering becomes accessible and allows the step-by-step construction of a satisfying result through iterative refinement.

This thesis is about visualizing a kind of data that is trivial to process by computers but difficult to imagine by humans because nature does not allow for intuition with this type of information: high-dimensional data. Such data often result from representing observations of objects under various aspects or with different properties. In many applications, a typical, laborious task is to find related objects or to group those that are similar to each other. One classic solution for this task is to imagine the data as vectors in a Euclidean space with object variables as dimensions. Utilizing Euclidean distance as a measure of similarity, objects with similar properties and values accumulate to groups, so-called clusters, that are exposed by cluster analysis on the high-dimensional point cloud. Because similar vectors can be thought of as objects that are alike in terms of their attributes, the point cloud\''s structure and individual cluster properties, like their size or compactness, summarize data categories and their relative importance. The contribution of this thesis is a novel analysis approach for visual exploration of high-dimensional point clouds without suffering from structural occlusion. The work is based on implementing two key concepts: The first idea is to discard those geometric properties that cannot be preserved and, thus, lead to the typical artifacts. Topological concepts are used instead to shift away the focus from a point-centered view on the data to a more structure-centered perspective. The advantage is that topology-driven clustering information can be extracted in the data\''s original domain and be preserved without loss in low dimensions. The second idea is to split the analysis into a topology-based global overview and a subsequent geometric local refinement. The occlusion-free overview enables the analyst to identify features and to link them to other visualizations that permit analysis of those properties not captured by the topological abstraction, e.g. cluster shape or value distributions in particular dimensions or subspaces. The advantage of separating structure from data point analysis is that restricting local analysis only to data subsets significantly reduces artifacts and the visual complexity of standard techniques. That is, the additional topological layer enables the analyst to identify structure that was hidden before and to focus on particular features by suppressing irrelevant points during local feature analysis. This thesis addresses the topology-based visual analysis of high-dimensional point clouds for both the time-invariant and the time-varying case. Time-invariant means that the points do not change in their number or positions. That is, the analyst explores the clustering of a fixed and constant set of points. The extension to the time-varying case implies the analysis of a varying clustering, where clusters appear as new, merge or split, or vanish. Especially for high-dimensional data, both tracking---which means to relate features over time---but also visualizing changing structure are difficult problems to solve.

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.