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01-03-2013 | Research Article

Hierarchical and multiple hand action representation using temporal postural synergies

Authors: G. Tessitore, C. Sinigaglia, R. Prevete

Published in: Experimental Brain Research | Issue 1/2013

Abstract

The notion of synergy enables one to provide simplified descriptions of hand actions. It has been used in a number of different meanings ranging from kinematic and dynamic synergies to postural and temporal postural synergies. However, relatively little is known about how representing an action by synergies might take into account the possibility to have a hierarchical and multiple action representation. This is a key aspect for action representation as it has been characterized by action theorists and cognitive neuroscientists. Thus, the aim of the present paper is to investigate whether and to what extent a hierarchical and multiple action representation can be obtained by a synergy approach. To this purpose, we took advantage of representing hand action as a linear combination of temporal postural synergies (TPSs), but on the assumption that TPSs have a tree-structured organization. In a tree-structured organization, a hand action representation can involve a TPS only if the ancestors of the synergy in the tree are themselves involved in the action representation. The results showed that this organization is enough to force a multiple representation of hand actions in terms of synergies which are hierarchically organized.

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We consider high sparsity a mean sparsity value roughly equal to 70 % of the total number of TPSs of each tree. More specifically, the mean sparsity of the tree-based action representations belonging to each training set was computed as \(1-\frac{1}{rn}\sum\nolimits_{j=1}^{n}\|{\bf U}_{j}\|_{0}\), where U _j are the coefficients of the tree-based action representation for jth action of the training set. For the corresponding λ, we found that the reconstruction error \(\frac{1}{2np}\|{\bf X}-{\bf U}{\bf V}^{T}\|_{F}^{2}\) was always lower than 4 × 10⁻³.

Note that all w _j are fixed to 1 in the experiments.

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Title: Hierarchical and multiple hand action representation using temporal postural synergies
Authors: G. Tessitore
C. Sinigaglia
R. Prevete
Publication date: 01-03-2013
Publisher: Springer-Verlag
Published in: Experimental Brain Research / Issue 1/2013
Print ISSN: 0014-4819
Electronic ISSN: 1432-1106
DOI: https://doi.org/10.1007/s00221-012-3344-9

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Hierarchical and multiple hand action representation using temporal postural synergies

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