Graph-restricted game approach for investigating human movement qualities K. Kolykhalova 1 , G. Gnecco 2 , M. Sanguineti 1 , A. Camurri 1 , and G. Volpe 1 1 DIBRIS Department, University of Genoa Via all’Opera Pia, 13 Genoa, Italy 16145 2 IMT School for Advanced Studies Piazza S. Francesco, 19 Lucca, Italy 55100 ABSTRACT A novel computational method for the analysis of expressive full- body movement qualities is introduced, which exploits concepts and tools from graph theory and game theory. e human skele- tal structure is modeled as an undirected graph, where the joints are the vertices and the edge set contains both physical and non- physical links. Physical links correspond to connections between adjacent physical body joints (e.g., the forearm, which connects the elbow to the wrist). Nonphysical links act as “bridges” between parts of the body not directly connected by the skeletal structure, but sharing very similar feature values. e edge weights depend on features obtained by using Motion Capture data. en, a math- ematical game is constructed over the graph structure, where the vertices represent the players and the edges represent communica- tion channels between them. Hence, the body movement is modeled in terms of a game built on the graph structure. Since the vertices and the edges contribute to the overall quality of the movement, the adopted game-theoretical model is of cooperative nature. A game-theoretical concept, called Shapley value, is exploited as a centrality index to estimate the contribution of each vertex to a shared goal (e.g., to the way a particular movement quality is trans- ferred among the vertices). e proposed method is applied to a data set of Motion Capture data of subjects performing expressive movements, recorded in the framework of the H2020-ICT-2015 EU Project WhoLoDance, Project no. 688865. Preliminary results are presented. CCS CONCEPTS •Human-centered computing → HCI theory, concepts and models; Empirical studies in HCI; •Computing methodologies → Activity recognition and understanding; Biometrics; •Applied computing → Performing arts; Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permied. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. MOCO ’17, London, United Kingdom © 2017 Copyright held by the owner/author(s). Publication rights licensed to ACM. 978-1-4503-5209-3/17/06. . . $15.00 DOI: hp://dx.doi.org/10.1145/3077981.3078030 KEYWORDS Human movement qualities, graph theory, game theory ACM Reference format: K. Kolykhalova 1 , G. Gnecco 2 , M. Sanguineti 1 , A. Camurri 1 , and G. Volpe 1 . 2017. Graph-restricted game approach for investigating human movement qualities . In Proceedings of MOCO ’17, London, United Kingdom, June 28-30, 2017, 4 pages. DOI: hp://dx.doi.org/10.1145/3077981.3078030 1 INTRODUCTION e main purpose of this work is the development of a novel ap- proach and the associated computational method for the analysis of expressive full-body movement qualities, combining tools and methods from graph theory and cooperative game theory. e proposed method first models the human skeletal structure as an undirected graph, where the joints are the vertices and the edge set contains both physical and nonphysical links. e edge weights depend on features obtained by using Motion Capture data. Physical links correspond to connections between adjacent physical body joints (e.g., the forearm, which connects the elbow to the wrist). Nonphysical links act as “bridges” between parts of the body not directly connected by the skeletal structure, but sharing very similar feature values. en, we construct a mathematical game over this skeletal graph, in which the vertices represent the players of the game, and the edges represent communication channels between the agents. e body movement is modeled in terms of a cooperative game built on the graph structure. Since the vertices and the edges contribute to the overall quality of the movement, the adopted game-theoretical model is a cooperative one. e so- called Shapley value, which provides a criterion to rank the players according to their importance, is then computed for such a game and used as a centrality index to estimate the contribution of each vertex to a shared goal (e.g., to the way a particular movement quality is transferred among the vertices). e methodology is applied on a data set of Motion Capture data of subjects performing expressive movements, recorded in the framework of the H2020-ICT-2015 EU Project WhoLoDance. Pre- liminary results are presented. Using this approach for the analysis of movement features related to expressive gestures and emotional communication can enable the design of multimodal interfaces involving full-body human interaction, which communicate the non-verbal expressive and emotional content.