A new topological entropy-based approach for measuring similarities among piecewise linear functions

Rucco, Matteo; González-Dı́az, Rocı́o; Jiménez, Manuel García; Atienza, Nieves; Cristalli, Cristina; Concettoni, Enrico; Ferrante, Andrea; Merelli, Emanuela

doi:10.1016/j.sigpro.2016.12.006

Cited by 26 publications

(31 citation statements)

References 22 publications

(15 reference statements)

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“…One summary which we will use in this paper is persistent entropy. 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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“…Definition 5 (Persistent entropy [6]) Given a filtered simplicial complex {K(t) : t ∈ F }, and the corresponding persistence barcode B = {a i = [x i , y i ) : i ∈ I}, the persistent entropy E of the filtered simplicial complex is calculated as follows:…”

Section: Introductionmentioning

confidence: 99%

Towards Emotion Recognition: A Persistent Entropy Application

González-Dı́az

Paluzo-Hidalgo

Quesada

2018

Computational Topology in Image Context

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Emotion recognition and classification is a very active area of research. In this paper, we present a first approach to emotion classification using persistent entropy and support vector machines. A topology-based model is applied to obtain a single real number from each raw signal. These data are used as input of a support vector machine to classify signals into 8 different emotions (calm, happy, sad, angry, fearful, disgust and surprised).

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“…It was defined in its current form in [26] but a precursor of this definition appears in [9]. Some successful applications of persistent entropy have been developed for pattern recognition of signals [21], [27]; complex systems [3] and biological images [1]. A more theoretical approach allows to use persistent entropy to distinguish topological features from noise [2].…”

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confidence: 99%