Characterisation of the Idiotypic Immune Network Through Persistent Entropy

Rucco, Matteo; Castiglione, Filippo; Merelli, Emanuela; Pettini, Marco

doi:10.1007/978-3-319-29228-1_11

Cited by 64 publications

(57 citation statements)

References 19 publications

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“…This was defined by Chintakunta et al [77] and later Rucco, Atienza, et al [78,79] proved that the construction is continuous. This construction, a modification of Shannon entropy, has found use in several applications [80][81][82].…”

Section: Introductionmentioning

confidence: 99%

Persistent homology of complex networks for dynamic state detection

2019

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In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a compressed, multi-scale representation of the graph that can distinguish between dynamic states such as periodic and chaotic behavior. We show the approach for two graph constructions obtained from the time series. In the first approach the time series is embedded into a point cloud which is then used to construct an undirected k-nearest neighbor graph. The second construct relies on the recently developed ordinal partition framework. In either case, a pairwise distance matrix is then calculated using the shortest path between the graph's nodes, and this matrix is utilized to define a filtration of a simplicial complex that enables tracking the changes in homology classes over the course of the filtration. These changes are summarized in a persistence diagram-a two-dimensional summary of changes in the topological features. We then extract existing as well as new geometric and entropy point summaries from the persistence diagram and compare to other commonly used network characteristics. Our results show that persistence-based point summaries yield a clearer distinction of the dynamic behavior and are more robust to noise than existing graph-based scores, especially when combined with ordinal graphs.

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Section: Introductionmentioning

confidence: 99%

Persistent homology of complex networks for dynamic state detection

2019

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“…Benzekry et al [36] propose that cancer therapy can be guided by changes in the complexity of protein-protein interaction (PPI) networks. They analyze 11 cancer interaction networks and find out that there is a correlation between 1-dimensional Betti Similar to this, Rucco et al [37] use Betti number as persistent entropy to measure the graph complexity. They study the behavior of the idiotypic network of the mammal immune system.…”

Section: Analysis On Single Graphmentioning

confidence: 93%

“…Ignacio et al [44] analyze the patterns and shapes in remittance and migration networks as a directed weighted network via persistent homology to identify flow patterns [41] VR 0 dim PD Brain networks [39] WS 0-2 dim PD Brain Networks [42] VR 0-dim PD Brain Networks [44] VR 0-2 dim PD Migration and remittance networks [37] VR 1 dim PB Simulated idiotypic networks [43] TMP 1-2 dim PD Co-occurrence networks [45] POW 0 dim PB Co-occurrence networks [24] VBCL,kCL 0 dim PD Co-occurrence, brain and collaboration network between multiple countries. They detect both local and global patterns that highlight simultaneous interactions among multiple nodes.…”

Section: Analysis On Single Graphmentioning

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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“…In order to exploit global information from TDA, we use the notion of persistent entropy, introduced in [27], to characterize the environment. This entropy measure is basically calculated using the persistent Betti barcodes.…”

Section: From Persistent Homology To Persistent Entropy: Global Informentioning

confidence: 99%

Topological Characterization of Complex Systems: Using Persistent Entropy

Merelli

Rucco

Sloot

et al. 2015

Entropy

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In this paper, we propose a methodology for deriving a model of a complex system by exploiting the information extracted from topological data analysis. Central to our approach is the S[B] paradigm in which a complex system is represented by a two-level model. One level, the structural S one, is derived using the newly-introduced quantitative concept of persistent entropy, and it is described by a persistent entropy automaton. The other level, the behavioral B one, is characterized by a network of interacting computational agents. The presented methodology is applied to a real case study, the idiotypic network of the mammalian immune system.

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Characterisation of the Idiotypic Immune Network Through Persistent Entropy

Cited by 64 publications

References 19 publications

Persistent homology of complex networks for dynamic state detection

Persistent homology of complex networks for dynamic state detection

Persistence homology of networks: methods and applications

Topological Characterization of Complex Systems: Using Persistent Entropy

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