Computational Topology in Text Mining

Wagner, Hubert; Dłotko, Paweł; Mrożek, Marian

doi:10.1007/978-3-642-30238-1_8

Cited by 25 publications

(13 citation statements)

References 10 publications

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“…In recent years, persistent homology has found applications in data analysis, including neuroscience [32], time series data [33], text mining [34] and shape analysis [35]. In the complex network setting, while some studies analyze the evaluation of a single graph, some studies analyze multiple graphs for graph matching and classification with characterizing the temporal changes in topological features of a network.…”

Section: Algorithms and Applicationsmentioning

confidence: 99%

Persistence homology of networks: methods and applications

2019

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Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, and biological networks. The primary challenge in this domain is measuring similarity or distance between networks based on topology. However, classical graph-theoretic measures are usually local and mainly based on differences between either node or edge measurements or correlations without considering the topology of networks such as the connected components or holes. In recent years, mathematical tools and deep learning based methods have become popular to extract the topological features of networks. Persistent homology (PH) is a mathematical tool in computational topology that measures the topological features of data that persist across multiple scales with applications ranging from biological networks to social networks.In this paper, we provide a conceptual review of key advancements in this area of using PH on complex network science. We give a brief mathematical background on PH, review different methods (i.e. filtrations) to define PH on networks and highlight different algorithms and applications where PH is used in solving network mining problems. In doing so, we develop a unified framework to describe these recent approaches and emphasize major conceptual distinctions. We conclude with directions for future work. We focus our review on recent approaches that get significant attention in the mathematics and data mining communities working on network data. We believe our summary of the analysis of PH on networks will provide important insights to researchers in applied network science.

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Section: Algorithms and Applicationsmentioning

confidence: 99%

Persistence homology of networks: methods and applications

2019

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“…In the study of persistent homology the invariants are in the form of persistence diagrams or barcodes [23]. For interested readers, we suggest papers about point cloud from vector space models [69], and persistent homology [10,12,78].…”

Section: Challenges and Future Researchmentioning

confidence: 99%

Knowledge Discovery from Complex High Dimensional Data

Lee

Holzinger

2016

Solving Large Scale Learning Tasks. Challenges and Algorithms

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Abstract. Modern data analysis is confronted by increasing dimensionality of problems, mainly contributed by higher resolutions available for data acquisition and by our use of larger models with more degrees of freedom to investigate complex systems deeper. High dimensionality constitutes one aspect of "big data", which brings us not only computational but also statistical and perceptional challenges. Most data analysis problems are solved using techniques of optimization, where large-scale optimization requires faster algorithms and implementations. Computed solutions must be evaluated for statistical quality, since otherwise false discoveries can be made. Recent papers suggest to control and modify algorithms themselves for better statistical properties. Finally, human perception puts an inherent limit on our understanding to three dimensional spaces, making it almost impossible to grasp complex phenomena. For aid, we use dimensionality reduction or other techniques, but these usually do not capture relations between interesting objects. Here graph-based knowledge representation has lots of potential, for instance to create perceivable and interactive representations and to perform new types of analysis based on graph theory and network topology. In this article, we show glimpses of new developments in these aspects.

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“…One of the main tasks of applied topology is to find and analyse higher dimensional topological structures in lower dimensional spaces (e.g. point cloud from vector space model as discussed in [80]). A common way to describe topological spaces is to first create simplicial complexes, because a simplicial complex structure on a topological space is an expression of the space as a union of simplices such as points, intervals, triangles, and higher dimensional analogues.…”

Section: Research Track 4 Tdm Topological Data Miningmentioning

confidence: 99%

Machine Learning for Health Informatics

Holzinger¹

2016

Lecture Notes in Computer Science

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Abstract. Machine Learning (ML) studies algorithms which can learn from data to gain knowledge from experience and to make decisions and predictions. Health Informatics (HI) studies the effective use of probabilistic information for decision making. The combination of both has greatest potential to rise quality, efficacy and efficiency of treatment and care. Health systems worldwide are confronted with "big data" in high dimensions, where the inclusion of a human is impossible and automatic ML (aML) show impressive results. However, sometimes we are confronted with complex data, "little data", or rare events, where aMLapproaches suffer of insufficient training samples. Here interactive ML (iML) may be of help, particularly with a doctor-in-the-loop, e.g. in subspace clustering, k-Anonymization, protein folding and protein design. However, successful application of ML for HI needs an integrated approach, fostering a concerted effort of four areas: (1) data science, (2) algorithms (with focus on networks and topology (structure), and entropy (time), (3) data visualization, and last but not least (4) privacy, data protection, safety & security.

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Computational Topology in Text Mining

Cited by 25 publications

References 10 publications

Persistence homology of networks: methods and applications

Persistence homology of networks: methods and applications

Knowledge Discovery from Complex High Dimensional Data

Machine Learning for Health Informatics

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