Abstract
In this paper we develop a new formulation of probabilistic relaxation labeling for the task of data classification using the theory of diffusion processes on graphs. The state space of our process as the nodes of a support graph which represent potential object-label assignments. The edge-weights of the support graph encode data-proximity and label consistency information. The state-vector of the diffusion process represents the object-label probabilities. The state vector evolves with time according to the Fokker-Planck equation. We show how the solution state vector can be estimated using the spectrum of the Laplacian matrix for the weighted support graph. Experiments on various data clustering tasks show effectiveness of our new algorithm.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Agarwal, A., Triggs, B.: Tracking articulated motion using a mixture of autoregressive models. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3023, pp. 54–65. Springer, Heidelberg (2004)
Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. NIPS (2001)
Chung, F.R.K.: Spectral Graph Theory. American Mathematical Society (1997)
Blake, C.L., Newman, D.J., Hettich, S., Merz, C.J.: UCI repository of machine learning databases (1998)
Faugeras, O., Berthod, M.: Improving consistency and reducing ambiguity in stochastic labeling: An optimization approach. IEEE Trans. PAMI, vol. 3(4) (1981)
Fischer, I., Poland, J.: New methods for spectral clustering. Technical Report IDSIA-12-04, IDSIA (2004)
Hancock, E.R., Kittler, J.: Edge-labeling using dictionary based relaxation. IEEE Trans. PAMI 12, 165–181 (1990)
Hummel, R.A., Zucker, S.W.: On the foundations of relaxation labeling processes. IEEE Trans. PAMI, l.PAMI-5, 267 (1983)
Kittler, J., Hancock, E.R.: Combining evidence in probabilistic relaxation. Int. J. Pattern Recognition And Artificial Inteligence 3(1), 29–51 (1989)
Kondor, R.I., Lafferty, J.: Diffusion kernels on graphs and other discrete input spaces. In: ICML, pp. 315–322 (2002)
Lafon, S., Lee, A.B.: Diffusion Maps and Coarse-Graining: A Unified Framework for Dimensionality Reduction, Graph Partitioning and Data Set Parameterization. IEEE Trans. PAMI 28, 1393–1403 (2006)
Moler, C., van Loan, C.: Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review 45(1), 3–49 (2003)
Nadler, B., Lafon, S., Coifman, R.R., Kevrekidis, I.G.: Diffusion maps, spectral clustering and eigenfunctions of Fokker-Planck operators. NIPS (2005)
Okuma, K., Taleghani, A., de Freitas, N., Little, J., Lowe, D.: A boosted particle filter: Multitarget detection and tracking. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 28–39. Springer, Heidelberg (2004)
Pelillo, M., Refice, M.: Learning compatibility coefficients for relaxation labeling processes. IEEE Trans. PAMI 16(9), 933–945 (1994)
Rosenfeld, A., Hummel, R., Zucker, S.: Scene labeling by relaxation operations. IEEE Trans. Systems. Man and Cybernetics 6, 420–433 (1976)
Smola, A.J., Kondor, R.: Kernels and regularization on graphs. In: Warmuth, M., Schökopf, B. (eds) COLT/KW 2003 (2003)
Sudderth, E.B., Ihler, A.T., Freeman, W.T., Willsky, A.S.: Nonparametric belief propagation. In: CVPR, pp. 605–612 (2003)
Szummer, M., Jaakkola, T.: Partially labeled classification with Markov random walks. In: NIPS 15 (2002)
Tishby, N., Slonim, N.: Data clustering by Markovian relaxation and the information bottleneck method. In: NIPS 13 (2000)
Tsuda, K., Noble, W.S.: Learning kernels from biological networks by maximizing entropy. Bioinformatics 20, 326–333 (2004)
Vert, J.-P., Kanehisa, M.: Graph-driven feature extraction from microarray data using diffusion kernels and kernel CCA. In: NIPS (2002)
Waltz, D.L.: Generating semantic descriptions from drawings of scenes with shadows. Technical Report 271, MIT AI Lab (1972)
Weiss, Y.: Interpreting images by propagating Baysian beliefs. In: ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS, pp. 908–914 (1997)
Zheng, Y., Doermann, D.: Robust point matching for two-dimensional nonrigid shapes. In: Proceedings IEEE Conf. on Computer Vision, pp. 1561–1566 (2005)
Zhou, D., Schölkopf, B.: Learning from labeled and unlabeled data using random walks. In: Proceedings of the 26th DAGM Symposium, pp. 237–244 (2004)
Zhu, X., Ghahramani, Z., Lafferty, J.: Semi-supervised learning using Gaussian fields and harmonic functions. In: ICML, pp. 1561–1566 (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, HF., Hancock, E.R. (2007). Probabilistic Relaxation Labeling by Fokker-Planck Diffusion on a Graph. In: Escolano, F., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2007. Lecture Notes in Computer Science, vol 4538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72903-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-72903-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72902-0
Online ISBN: 978-3-540-72903-7
eBook Packages: Computer ScienceComputer Science (R0)