@misc{VuLitzelKoch2025, author = {Vu, Thi Huong and Litzel, Ida and Koch, Thorsten}, title = {Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives}, arxiv = {http://arxiv.org/abs/2506.04045}, year = {2025}, abstract = {Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution. While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science -- containing about 70 million articles and a billion citations -- poses significant challenges. We analyze potentials and challenges of the approach from both mathematical and computational perspectives. Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the problem's structure. Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data.}, language = {en} } @misc{GalliatHuisingaDeuflhard1999, author = {Galliat, Tobias and Huisinga, Wilhelm and Deuflhard, Peter}, title = {Self-Organizing Maps Combined with Eigenmode Analysis for Automated Cluster Identification}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4279}, number = {SC-99-38}, year = {1999}, abstract = {One of the important tasks in Data Mining is automated cluster analysis. Self-Organizing Maps (SOMs) introduced by {\sc Kohonen} are, in principle, a powerful tool for this task. Up to now, however, its cluster identification part is still open to personal bias. The present paper suggests a new approach towards automated cluster identification based on a combination of SOMs with an eigenmode analysis that has recently been developed by {\sc Deuflhard et al.} in the context of molecular conformational dynamics. Details of the algorithm are worked out. Numerical examples from Data Mining and Molecular Dynamics are included.}, language = {en} } @misc{Galliat1999, author = {Galliat, Tobias}, title = {Clustering Data of Different Information Levels}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4319}, number = {SC-99-42}, year = {1999}, abstract = {For using Data Mining, especially cluster analysis, one needs measures to determine the similarity or distance between data objects. In many application fields the data objects can have different information levels. In this case the widely used euclidean distance is an inappropriate measure. The present paper describes a concept how to use data of different information levels in cluster analysis and suggests an appropriate similarity measure. An example from practice is included, that shows the usefulness of the concept and the measure in combination with {\sc Kohonens} Self-Organizing Map algorithm, a well-known and powerful tool for cluster analysis.}, language = {en} } @misc{GalliatDeuflhard2000, author = {Galliat, Tobias and Deuflhard, Peter}, title = {Adaptive hierarchical cluster analysis by Self-Organizing Box Maps}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5815}, number = {00-13}, year = {2000}, abstract = {The present paper aims at an extension of {\sc Kohonen's} Self-Organizing Map (SOM) algorithm to be called Self-Organizing Box Map (SOBM) algorithm; it generates box codebooks in lieu of point codebooks. Box codebooks just like point codebooks indirectly define a Voronoi tessellation of the input space, so that each codebook vector represents a unique set of points. Each box codebook vector comprises a multi-dimensional interval that approximates the related partition of the Voronoi tessellation. Upon using the automated cluster identification method that has recently been developed by the authors, the codebook vectors can be grouped in such a way that each group represents a point cluster in the input space. Since the clustering usually depends on the size of the SOM, one cannot be sure, whether the clustering comes out to be optimal. Refinement of part of the identified clusters would often improve the results. This paper presents the concept of an adaptive multilevel cluster algorithm that performs such refinements automatically. Moreover the paper introduces a concept of essential dimensions and suggests a method for their identification based on our herein suggested box codebooks. Applications of the algorithm to molecular dynamics will be described in a forthcoming paper.}, language = {en} } @misc{GalliatDeuflhardRoitzschetal.2000, author = {Galliat, Tobias and Deuflhard, Peter and Roitzsch, Rainer and Cordes, Frank}, title = {Automatic Identification of Metastable Conformations via Self-Organized Neural Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6197}, number = {00-51}, year = {2000}, abstract = {As has been shown recently, the identification of metastable chemical conformations leads to a Perron cluster eigenvalue problem for a reversible Markov operator. Naive discretization of this operator would suffer from combinatorial explosion. As a first remedy, a pre-identification of essential degrees of freedom out of the set of torsion angles had been applied up to now. The present paper suggests a different approach based on neural networks: its idea is to discretize the Markov operator via self-organizing (box) maps. The thus obtained box discretization then serves as a prerequisite for the subsequent Perron cluster analysis. Moreover, this approach also permits exploitation of additional structure within embedded simulations. As it turns out, the new method is fully automatic and efficient also in the treatment of biomolecules. This is exemplified by numerical results.}, language = {en} }