Abstract
We consider applying a functional logistic discriminant procedure to the analysis of handwritten character data. Time-course trajectories corresponding to the X and Y coordinate values of handwritten characters written in the air with one finger are converted into a functional data set via regularized basis expansion. We then apply functional logistic modeling to classify the functions into several classes. In order to select the values of adjusted parameters involved in the functional logistic model, we derive a model selection criterion for evaluating models estimated by the method of regularization. Results indicate the effectiveness of our modeling strategy in terms of prediction accuracy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
ANDO, T., KONISHI, S., and IMOTO, S. (2008),“Nonlinear Regression Modeling Via Regularized Radial Basis Function Networks,” Journal of Statistical Planning and Inference, 138, 3617–3633.
ARAKI, Y., KONISHI, S., and IMOTO, S. (2004), “Functional Discriminant Analysis for Microarray Gene Expression Data Via Radial Basis Function Networks,” in Proceedings of COMPSTAT 2004, Heidelberg: Physica-Verlag/Springer, pp. 613–620.
ARAKI, Y., KONISHI, S., KAWANO, S., and MATSUI, H. (2009), “Functional Regression Modeling Via Regularized Gaussian Basis Expansions”, Annals of the Institute of Statistical Mathematics, 61, 811–833.
BAHLMANN, C., and BURKHARDT, H. (2004), “The Writer Independent Online Handwriting Recognition System Frog on Hand and Cluster Generative Statistical Dynamic TimeWarping”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 299–310.
BIAU, G., BUNEA, F., and WEGKAMP, M. (2005), “Functional Classification in Hilbert Spaces,” IEEE Transactions on Information Theory, 51, 2163–2172.
BISHOP, C.M. (2006), Pattern Recognition and Machine Learning, New York: Springer- Verlag.
BUNKE, H., ROTH, M., and SCHUKAT-TALAMAZZINI, E.G. (1995), “Off-line Cursive Handwriting Recognition Using Hidden Markov Models,” Pattern Recognition, 28, 1399–1413.
FERRATY, F., and VIEU, P. (2006), Nonparametric Functional Data Analysis, London: Springer-Verlag.
FERR´E, L., and VILLA, N. (2006), “Multi-layer Perceptron with Functional Inputs: An Inverse Regression Approach,” Scandinavian Journal of Statistics, 33, 807–823.
FUJII, T., and KONISHI, S. (2006), “Nonlinear Regression Modeling Via Regularized Wavelets and Smoothing Parameter Selection,” Journal of Multivariate Analysis, 97, 2023–2033.
HASTIE, T., BUJA, A., and TIBSHIRANI, R. (1995), “Penalized Discriminant Analysis,” Annals of Statistics, 23, 73–102.
HASTIE, T., TIBSHIRANI, R., and FRIEDMAN, J. (2001), The Elements of Statistical Learning, New York: Springer–Verlag.
JAMES, G., and HASTIE, T. (2001), “Functional Linear Discriminant Analysis for Irregularly Sampled Curves,” Journal of Royal Statistical Society B, 63, 533–550.
JAMES, G. (2002), “Generalized Linear Models with Functional Predictor Variables,” Journal of Royal Statistical Society B, 64, 411–432.
JAMES, G.M., and SILVERMAN, B.W. (2005), “Functional Adaptive Model Estimation,” Journal of the American Statistical Association, 100, 565–576.
KADOUS,M.W. (1999), “Learning Comprehensible Descriptions of Multivariate Time Series”, in Proceedings of the International Conference of Machine Learning, pp. 454–463.
KONISHI, S., ANDO, T., and IMOTO, S. (2004), “Bayesian Information Criteria and Smoothing Parameter Selection in Radial Basis Function Networks,” Biometrika, 91, 27–43.
KONISHI, S., and KITAGAWA, G. (2008), Information Criteria and Statistical Modeling, New York: Springer-Verlag.
LIU, C.L., NAKASHIMA, H., SAKO, H., and FUJISAWA, H. (2003), “Handwritten Digit Recognition: Benchmarking of State-of-the-Art Techniques,” Pattern Recognition, 36, 2271–2285.
MOODY, J., and DARKEN, C.J. (1989), “Fast Learning in Networks of Locally–tuned Processing Units,” Neural Computation, 1, 281–294.
RAMSAY, J.O., and SILVERMAN, B.W. (2002), Applied Functional Data Analysis, New York: Springer-Verlag.
RAMSAY, J.O., and SILVERMAN, B.W. (2005), Functional Data Analysis (2nd ed.), New York: Springer-Verlag.
ROSSI, F., and CONAN-GUEZ, B. (2005), “Functional Multi-layer Perceptron: A Nonlinear Tool for Functional Data Analysis,” Neural Networks, 18, 45–60.
ROSSI, F., and VILLA, N. (2006), “Support Vector Machine for Functional Data Classification,” Neurocomputing, 69, 730–742.
SCHWARZ, G. (1978), “Estimating the Dimension of a Model,” Annals of Statistics, 6, 461–464.
STARNER, T.,WEAVER, J., and PENTLAND, A. (1998), “Real-time American Sign Language Recognition Using Desk and Wearable Computer-based Video,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 20, 1371–1375.
VAN LAARHOVEN, P.J., and AARTS, E.H. (1987), Simulated Annealing: Theory and Applications, Dordrecht: D. Reidel Publishing.
YOON, H.S., SOH, J., MIN, B., and YANG, H.S. (1999), “Recognition of Alphabetical Hand Gestures Using Hidden Markov Model,” IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 82, 1358–1366.
Author information
Authors and Affiliations
Corresponding author
Additional information
The authors would like to thank the anonymous reviewers for constructive and helpful suggestions that improved the quality of the paper considerably.
Rights and permissions
About this article
Cite this article
Matsui, H., Araki, T. & Konishi, S. Multiclass Functional Discriminant Analysis and Its Application to Gesture Recognition. J Classif 28, 227–243 (2011). https://doi.org/10.1007/s00357-011-9082-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00357-011-9082-z