Skip to main content

Advertisement

Log in

Analyzing movement trajectories using a Markov bi-clustering method

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

In this study we treat scribbling motion as a compositional system in which a limited set of elementary strokes are capable of concatenating amongst themselves in an endless number of combinations, thus producing an unlimited repertoire of complex constructs. We broke the continuous scribblings into small units and then calculated the Markovian transition matrix between the trajectory clusters. The Markov states are grouped in a way that minimizes the loss of mutual information between adjacent strokes. The grouping algorithm is based on a novel markov-state bi-clustering algorithm derived from the Information-Bottleneck principle. This approach hierarchically decomposes scribblings into increasingly finer elements. We illustrate the usefulness of this approach by applying it to human scribbling.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Berthier, N. E. (1996). Learning to reach: A mathematical model. Developmental Psychology, 32, 811–823.

    Article  Google Scholar 

  • Bizzi, E., Tresch, M. C., Saltiel, P., & dAvella, A. (2000). New perspectives on spinal motor systems. Nature Reviews. Neuroscience, 1, 101–108.

    Article  CAS  PubMed  Google Scholar 

  • Dempster, A., Laird, N., & Rubin, D. (1977). Maximum likelihood estimation from incomplete data via the em algorithm. Journal of the Royal Statistical Society. Series B, 39, 1–38.

    Google Scholar 

  • Dhillon, I. S., Mallela, S., & Modha, D. S. (2003). Information-theoretic co-clustering. In International conference on knowledge discovery and data mining (KDD).

  • Flash, T., & Henis, E. A. (1991). Arm trajectory modification during reaching towards visual targets. Journal of Cognitive Neuroscience, 3, 220–230.

    Article  Google Scholar 

  • Flash, T., & Hochner, B. (2005). Primitives in vertebrates and invertebrates. Current Opinion in Neurobiology, 15, 660–666.

    Article  CAS  PubMed  Google Scholar 

  • Flash, T., & Hogan, N. (1985). Coordination of arm movements: An experimentally confirmed mathematical model. Journal of Neuroscience, 5, 1688–1703.

    CAS  PubMed  Google Scholar 

  • Ge, X., Parise, S., & Smyth, P. (2003). Clustering Markov states into equivalence classes using svd and heuristic search algorithms. AISTATS.

  • Georgopolulos, A. P., Kalaska, J. F., Caminiti, R., & Massey, J. T. (1982). On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex. Journal of Neuroscience, 2, 1527–1537.

    Google Scholar 

  • Giszter, S., Bizzi, E., & Mussa-Ivaldi, F. A. (1991). Computations underlying the execution of movement: A novel biological perspective. Science, 253, 287–291.

    Article  PubMed  Google Scholar 

  • Hofsten, C. (1991). Structuring of early reaching movements: A longitudinal study. Journal of Motor Behavior, 23, 280–292.

    Google Scholar 

  • Konczak, J., Borutta, M., Topka, H., & Dichgans, J. (1995). The development of goal-directed reaching in infants: Hand trajectory formation and joint force control. Experimental Brain Research, 106, 156–168.

    Article  CAS  Google Scholar 

  • Krebs, H. I., Aisen, M. L., Volpe, B. T., & Hogan, N. (1999). Quantization of continuous arm movements in humans with brain injury. Proceedings of the National Academy of Sciences, 96, 4645–4649.

    Article  CAS  Google Scholar 

  • Lacquaniti, F., Terzuolo, C., & Viviani, P. (1983). The law relating kinematic and figural aspects of drawing movements. ACTA Psychologica, 54, 115–130.

    Article  CAS  PubMed  Google Scholar 

  • Mataric, M. J. (2001). Sensory-motor primitives as a basis for imitation: Linking perception to action and biology to robotics. In Imitation in animals and artifacts. Cambridge: MIT.

    Google Scholar 

  • Meila, M., & Shi, J. (2001). A random walks view of spectral segmentation. AISTATS.

  • Mussa-Ivaldi, F. A., & Bizzi, E. (2000). Motor learning through the combination of primitives. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 355, 1755–1769.

    Article  CAS  PubMed  Google Scholar 

  • Slonim, N., & Weiss, Y. (2003). Maximum likelihood and the information bottleneck. Proceedings of neural information processing systems.

  • Slonim, N., Friedman, N., & Tishby, N. (2002). Unsupervised document classification using sequential information maximization. ACM SIGIR, 129–136.

  • Slonim, N., Friedman, N., & Tishby, N. (2006). Multivariate information bottleneck. Neural Computation, 18, 1739–1789.

    Article  PubMed  Google Scholar 

  • Sosnik, R., Shemesh, M., & Abeles, M. (2007). The point of no return in planar hand movements: An indication of the existence of high level motion primitives. Cognitive Neurodynamics, 1, 341–358.

    Article  PubMed  Google Scholar 

  • Stark, E., Drori, R., Asher, I., Ben-Shaul, Y., & Abeles, M. (2007). Distinct movement parameters are represented by different neurons in the motor cortex. European Journal of Neuroscience, 26, 1055–1066.

    Article  PubMed  Google Scholar 

  • Tappert, C. C. (1982). Cursive script recognition by elastic matching. IBM Journal of Research and Development, 26, 765–771.

    Article  Google Scholar 

  • Thoroughman, K. A., & Shadmehr, R. (2000). Learning of action through adaptive combination of motor primitives. Nature, 407, 742–747.

    Article  CAS  PubMed  Google Scholar 

  • Tishby, N., Pereira, F., & Bialek, W. (1999). The information bottleneck method. In Proc. of the annual Allerton conference on communication, control and computing.

  • Viviani, P., & Schneider, R. (1991). A developmental study of the relationship between geometry and kinematics in drawing movements. Journal of Experimental Psychology, 17, 198–218.

    CAS  PubMed  Google Scholar 

Download references

Acknowledgement

This work was supported in part by the Deutsch-Israelische Projectkooperation (DIP).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jacob Goldberger.

Additional information

Action Editor: Jonathan David Victor

Rights and permissions

Reprints and permissions

About this article

Cite this article

Erez, K., Goldberger, J., Sosnik, R. et al. Analyzing movement trajectories using a Markov bi-clustering method. J Comput Neurosci 27, 543–552 (2009). https://doi.org/10.1007/s10827-009-0168-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-009-0168-0

Keywords

Navigation