arXiv subjects

Tom Hanika

Publications and source records attributed to Tom Hanika.

At least 37 records · Page 2Linked to original sources

arXiv2023

Scaling Dimension

Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic definitions are in flux. Our contribution was triggered by the study of concept lattices for tree classifiers and the scaling methods used there. We extend some basic notions, give precise mathematical definitions for them and introduce the concept of scaling dimension. In addition to a detailed discussion of its properties, including an example, we show theoretical bounds related to the order dimension of concept lattices. We also study special subclasses, such as the ordinal and the interordinal scaling dimensions, and show for them first results and examples.

cs.LG↗

arXiv2023

Conceptual Views on Tree Ensemble Classifiers

Random Forests and related tree-based methods are popular for supervised learning from table based data. Apart from their ease of parallelization, their classification performance is also superior. However, this performance, especially parallelizability, is offset by the loss of explainability. Statistical methods are often used to compensate for this disadvantage. Yet, their ability for local explanations, and in particular for global explanations, is limited. In the present work we propose an algebraic method, rooted in lattice theory, for the (global) explanation of tree ensembles. In detail, we introduce two novel conceptual views on tree ensemble classifiers and demonstrate their explanatory capabilities on Random Forests that were trained with standard parameters.

cs.LG↗

arXiv2022

Discovering Locally Maximal Bipartite Subgraphs

Induced bipartite subgraphs of maximal vertex cardinality are an essential concept for the analysis of graphs. Yet, discovering them in large graphs is known to be computationally hard. Therefore, we consider in this work a weaker notion of this problem, where we discard the maximality constraint in favor of inclusion maximality. Thus, we aim to discover locally maximal bipartite subgraphs. For this, we present three heuristic approaches to extract such subgraphs and compare their results to the solutions of the global problem. For the latter, we employ the algorithmic strength of fast SAT-solvers. Our three proposed heuristics are based on a greedy strategy, a simulated annealing approach, and a genetic algorithm, respectively. We evaluate all four algorithms with respect to their time requirement and the vertex cardinality of the discovered bipartite subgraphs on several benchmark datasets

cs.AI↗

arXiv2022

Research Topic Flows in Co-Authorship Networks

In scientometrics, scientific collaboration is often analyzed by means of co-authorships. An aspect which is often overlooked and more difficult to quantify is the flow of expertise between authors from different research topics, which is an important part of scientific progress. With the Topic Flow Network (TFN) we propose a graph structure for the analysis of research topic flows between scientific authors and their respective research fields. Based on a multi-graph and a topic model, our proposed network structure accounts for intratopic as well as intertopic flows. Our method requires for the construction of a TFN solely a corpus of publications (i.e., author and abstract information). From this, research topics are discovered automatically through non-negative matrix factorization. The thereof derived TFN allows for the application of social network analysis techniques, such as common metrics and community detection. Most importantly, it allows for the analysis of intertopic flows on a large, macroscopic scale, i.e., between research topic, as well as on a microscopic scale, i.e., between certain sets of authors. We demonstrate the utility of TFNs by applying our method to two comprehensive corpora of altogether 20 Mio. publications spanning more than 60 years of research in the fields computer science and mathematics. Our results give evidence that TFNs are suitable, e.g., for the analysis of topical communities, the discovery of important authors in different fields, and, most notably, the analysis of intertopic flows, i.e., the transfer of topical expertise. Besides that, our method opens new directions for future research, such as the investigation of influence relationships between research fields.

cs.SI↗

arXiv2022

Mapping Research Trajectories

Steadily growing amounts of information, such as annually published scientific papers, have become so large that they elude an extensive manual analysis. Hence, to maintain an overview, automated methods for the mapping and visualization of knowledge domains are necessary and important, e.g., for scientific decision makers. Of particular interest in this field is the development of research topics of different entities (e.g., scientific authors and venues) over time. However, existing approaches for their analysis are only suitable for single entity types, such as venues, and they often do not capture the research topics or the time dimension in an easily interpretable manner. Hence, we propose a principled approach for \emph{mapping research trajectories}, which is applicable to all kinds of scientific entities that can be represented by sets of published papers. For this, we transfer ideas and principles from the geographic visualization domain, specifically trajectory maps and interactive geographic maps. Our visualizations depict the research topics of entities over time in a straightforward interpr. manner. They can be navigated by the user intuitively and restricted to specific elements of interest. The maps are derived from a corpus of research publications (i.e., titles and abstracts) through a combination of unsupervised machine learning methods. In a practical demonstrator application, we exemplify the proposed approach on a publication corpus from machine learning. We observe that our trajectory visualizations of 30 top machine learning venues and 1000 major authors in this field are well interpretable and are consistent with background knowledge drawn from the entities' publications. Next to producing interactive, interpr. visualizations supporting different kinds of analyses, our computed trajectories are suitable for trajectory mining applications in the future.

cs.DL↗

arXiv2021

Towards Explainable Scientific Venue Recommendations

Selecting the best scientific venue (i.e., conference/journal) for the submission of a research article constitutes a multifaceted challenge. Important aspects to consider are the suitability of research topics, a venue's prestige, and the probability of acceptance. The selection problem is exacerbated through the continuous emergence of additional venues. Previously proposed approaches for supporting authors in this process rely on complex recommender systems, e.g., based on Word2Vec or TextCNN. These, however, often elude an explanation for their recommendations. In this work, we propose an unsophisticated method that advances the state-of-the-art in two aspects: First, we enhance the interpretability of recommendations through non-negative matrix factorization based topic models; Second, we surprisingly can obtain competitive recommendation performance while using simpler learning methods.

cs.IR↗

arXiv2021

Topological Indoor Mapping through WiFi Signals

The ubiquitous presence of WiFi access points and mobile devices capable of measuring WiFi signal strengths allow for real-world applications in indoor localization and mapping. In particular, no additional infrastructure is required. Previous approaches in this field were, however, often hindered by problems such as effortful map-building processes, changing environments and hardware differences. We tackle these problems focussing on topological maps. These represent discrete locations, such as rooms, and their relations, e.g., distances and transition frequencies. In our unsupervised method, we employ WiFi signal strength distributions, dimension reduction and clustering. It can be used in settings where users carry mobile devices and follow their normal routine. We aim for applications in short-lived indoor events such as conferences.

cs.NI↗

arXiv2021

Quantifying the Conceptual Error in Dimensionality Reduction

Dimension reduction of data sets is a standard problem in the realm of machine learning and knowledge reasoning. They affect patterns in and dependencies on data dimensions and ultimately influence any decision-making processes. Therefore, a wide variety of reduction procedures are in use, each pursuing different objectives. A so far not considered criterion is the conceptual continuity of the reduction mapping, i.e., the preservation of the conceptual structure with respect to the original data set. Based on the notion scale-measure from formal concept analysis we present in this work a) the theoretical foundations to detect and quantify conceptual errors in data scalings; b) an experimental investigation of our approach on eleven data sets that were respectively treated with a variant of non-negative matrix factorization.

cs.LG↗

arXiv2021

Topic Space Trajectories: A case study on machine learning literature

The annual number of publications at scientific venues, for example, conferences and journals, is growing quickly. Hence, even for researchers it becomes harder and harder to keep track of research topics and their progress. In this task, researchers can be supported by automated publication analysis. Yet, many such methods result in uninterpretable, purely numerical representations. As an attempt to support human analysts, we present topic space trajectories, a structure that allows for the comprehensible tracking of research topics. We demonstrate how these trajectories can be interpreted based on eight different analysis approaches. To obtain comprehensible results, we employ non-negative matrix factorization as well as suitable visualization techniques. We show the applicability of our approach on a publication corpus spanning 50 years of machine learning research from 32 publication venues. Our novel analysis method may be employed for paper classification, for the prediction of future research topics, and for the recommendation of fitting conferences and journals for submitting unpublished work.

cs.LG↗

arXiv2021

Exploring Scale-Measures of Data Sets

Measurement is a fundamental building block of numerous scientific models and their creation. This is in particular true for data driven science. Due to the high complexity and size of modern data sets, the necessity for the development of understandable and efficient scaling methods is at hand. A profound theory for scaling data is scale-measures, as developed in the field of formal concept analysis. Recent developments indicate that the set of all scale-measures for a given data set constitutes a lattice and does hence allow efficient exploring algorithms. In this work we study the properties of said lattice and propose a novel scale-measure exploration algorithm that is based on the well-known and proven attribute exploration approach. Our results motivate multiple applications in scale recommendation, most prominently (semi-)automatic scaling.

cs.AI↗

arXiv2020

On the Lattice of Conceptual Measurements

We present a novel approach for data set scaling based on scale-measures from formal concept analysis, i.e., continuous maps between closure systems, and derive a canonical representation. Moreover, we prove said scale-measures are lattice ordered with respect to the closure systems. This enables exploring the set of scale-measures through by the use of meet and join operations. Furthermore we show that the lattice of scale-measures is isomorphic to the lattice of sub-closure systems that arises from the original data. Finally, we provide another representation of scale-measures using propositional logic in terms of data set features. Our theoretical findings are discussed by means of examples.

cs.AI↗

arXiv2020

Intrinsic Dimension of Geometric Data Sets

The curse of dimensionality is a phenomenon frequently observed in machine learning (ML) and knowledge discovery (KD). There is a large body of literature investigating its origin and impact, using methods from mathematics as well as from computer science. Among the mathematical insights into data dimensionality, there is an intimate link between the dimension curse and the phenomenon of measure concentration, which makes the former accessible to methods of geometric analysis. The present work provides a comprehensive study of the intrinsic geometry of a data set, based on Gromov's metric measure geometry and Pestov's axiomatic approach to intrinsic dimension. In detail, we define a concept of geometric data set and introduce a metric as well as a partial order on the set of isomorphism classes of such data sets. Based on these objects, we propose and investigate an axiomatic approach to the intrinsic dimension of geometric data sets and establish a concrete dimension function with the desired properties. Our model for data sets and their intrinsic dimension is computationally feasible and, moreover, adaptable to specific ML/KD-algorithms, as illustrated by various experiments.

cs.AI↗

arXiv2020

Knowledge Cores in Large Formal Contexts

Knowledge computation tasks are often infeasible for large data sets. This is in particular true when deriving knowledge bases in formal concept analysis (FCA). Hence, it is essential to come up with techniques to cope with this problem. Many successful methods are based on random processes to reduce the size of the investigated data set. This, however, makes them hardly interpretable with respect to the discovered knowledge. Other approaches restrict themselves to highly supported subsets and omit rare and interesting patterns. An essentially different approach is used in network science, called $k$-cores. These are able to reflect rare patterns if they are well connected in the data set. In this work, we study $k$-cores in the realm of FCA by exploiting the natural correspondence to bi-partite graphs. This structurally motivated approach leads to a comprehensible extraction of knowledge cores from large formal contexts data sets.

cs.AI↗

arXiv2019

FCA2VEC: Embedding Techniques for Formal Concept Analysis

Embedding large and high dimensional data into low dimensional vector spaces is a necessary task to computationally cope with contemporary data sets. Superseding latent semantic analysis recent approaches like word2vec or node2vec are well established tools in this realm. In the present paper we add to this line of research by introducing fca2vec, a family of embedding techniques for formal concept analysis (FCA). Our investigation contributes to two distinct lines of research. First, we enable the application of FCA notions to large data sets. In particular, we demonstrate how the cover relation of a concept lattice can be retrieved from a computational feasible embedding. Secondly, we show an enhancement for the classical node2vec approach in low dimension. For both directions the overall constraint of FCA of explainable results is preserved. We evaluate our novel procedures by computing fca2vec on different data sets like, wiki44 (a dense part of the Wikidata knowledge graph), the Mushroom data set and a publication network derived from the FCA community.

cs.LG↗

arXiv2019

Orometric Methods in Bounded Metric Data

A large amount of data accommodated in knowledge graphs (KG) is actually metric. For example, the Wikidata KG contains a plenitude of metric facts about geographic entities like cities, chemical compounds or celestial objects. In this paper, we propose a novel approach that transfers orometric (topographic) measures to bounded metric spaces. While these methods were originally designed to identify relevant mountain peaks on the surface of the earth, we demonstrate a notion to use them for metric data sets in general. Notably, metric sets of items inclosed in knowledge graphs. Based on this we present a method for identifying outstanding items using the transferred valuations functions 'isolation' and 'prominence'. Building up on this we imagine an item recommendation process. To demonstrate the relevance of the novel valuations for such processes we use item sets from the Wikidata knowledge graph. We then evaluate the usefulness of 'isolation' and 'prominence' empirically in a supervised machine learning setting. In particular, we find structurally relevant items in the geographic population distributions of Germany and France.

cs.AI↗

arXiv2019

Drawing Order Diagrams Through Two-Dimension Extension

Order diagrams are an important tool to visualize the complex structure of ordered sets. Favorable drawings of order diagrams, i.e., easily readable for humans, are hard to come by, even for small ordered sets. Many attempts were made to transfer classical graph drawing approaches to order diagrams. Although these methods produce satisfying results for some ordered sets, they unfortunately perform poorly in general. In this work we present the novel algorithm DimDraw to draw order diagrams. This algorithm is based on a relation between the dimension of an ordered set and the bipartiteness of a corresponding graph.

cs.CG↗

arXiv2019

Collaborative Interactive Learning -- A clarification of terms and a differentiation from other research fields

The field of collaborative interactive learning (CIL) aims at developing and investigating the technological foundations for a new generation of smart systems that support humans in their everyday life. While the concept of CIL has already been carved out in detail (including the fields of dedicated CIL and opportunistic CIL) and many research objectives have been stated, there is still the need to clarify some terms such as information, knowledge, and experience in the context of CIL and to differentiate CIL from recent and ongoing research in related fields such as active learning, collaborative learning, and others. Both aspects are addressed in this paper.

cs.LG↗

arXiv2019

DimDraw -- A novel tool for drawing concept lattices

Concept lattice drawings are an important tool to visualize complex relations in data in a simple manner to human readers. Many attempts were made to transfer classical graph drawing approaches to order diagrams. Although those methods are satisfying for some lattices they unfortunately perform poorly in general. In this work we present a novel tool to draw concept lattices that is purely motivated by the order structure.

cs.CG↗