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Linear SVM-based recognition of elementary juggling movements using correlation dimension of Euler Angles of a single arm

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Abstract

Recognizing the human arm movements has several applications, and it can be performed in a number of ways through the use of one or more sensor devices that the technology offers. This paper aims to exploit the exercises performed by jugglers in order to recognize the arm movements on the basis of the only information on the arm orientation provided by the Euler Angles. The proposed recognizer has two modules, i.e., a feature extractor and a classifier. The former reconstructs the dynamics of the system and estimates three correlation dimensions, each associated with a given Euler Angle. The latter is formed by a Linear Support Vector Machine. Extensive experimentations show the effectiveness of the proposed approach.

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Notes

  1. Dynamics has to be intended in terms of a dynamical system, namely a system where a mathematical function describes the dependence of a point in a geometrical space.

  2. A manifold (http://en.wikipedia.org/wiki/Manifold) is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be more complicated. In a one-dimensional manifold every point has a neighborhood that looks like a line segment; in a two-dimensional manifold the neighborhood looks like a disk. \(\mathbb {R}^n\) is a n-dimensional manifold.

  3. In dynamical systems, an attractor is a set of numerical values toward a system tends to evolve asymptotically, as time increases, for a wide variety of initial conditions of the system [38].

  4. Takens–Mañé embedding theorem is a consequence of a Whitney Embedding Theorem [47] stating that a generic map from an S-dimensional manifold to a \((2S+1)\)-dimensional Euclidean space is an embedding, i.e., the image of the S-dimensional manifold is completely unfolded in the larger space. Therefore, two data points in the S-dimensional manifold do not map to the same point in the \((2S+1)\)-dimensional space.

  5. Colibri is a registered trademark of Trivisio Prototyping GmbH.

  6. The maximum number of balls, for few seconds, that a professional juggler is able to handle in his movements is seven.

  7. The database is available, on request, for further investigations.

  8. A KNN experiment can be performed by LVQ-pak command: eveninit -noc 2 -din fileinput -cout fileoutput -knn 3 where noc stands for the number of codevectors (i.e., 2), din corresponds to the name of input data file, cout provides the name of the codevector file, and knn denotes the number of k nearest neighbors (i.e., 3).

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Acknowledgments

Firstly, the authors are indebted to the anonymous reviewers for their valuable comments. The research was developed when Francesco Esposito was at the Department of Science and Technology, University of Naples Parthenope, as B. Sc. student in Computer Science. Francesco Camastra and Antonino Staiano were funded by Sostegno alla ricerca individuale per il triennio 2015–17 project of University of Naples Parthenope. Finally, the authors wish to thank Lara De Vinco for her help in preparing the paper.

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  1. Department of Science and Technology, University of Naples Parthenope, Centro Direzionale Isola C4, 80143, Naples, Italy

    Francesco Camastra, Francesco Esposito & Antonino Staiano

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  1. Francesco Camastra
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  2. Francesco Esposito
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  3. Antonino Staiano
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Correspondence to Antonino Staiano.

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Camastra, F., Esposito, F. & Staiano, A. Linear SVM-based recognition of elementary juggling movements using correlation dimension of Euler Angles of a single arm. Neural Comput & Applic 29, 1005–1013 (2018). https://doi.org/10.1007/s00521-016-2616-x

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