A Non-parametric Spectral Model for Graph Classification
Andrea Gasparetto, Giorgia Minello, Andrea Torsello
2015
Abstract
Graph-based representations have been used with considerable success in computer vision in the abstraction and recognition of object shape and scene structure. Despite this, the methodology available for learning structural representations from sets of training examples is relatively limited. In this paper we take a simple yet effective spectral approach to graph learning. In particular, we define a novel model of structural representation based on the spectral decomposition of graph Laplacian of a set of graphs, but which make away with the need of one-to-one node-correspondences at the base of several previous approaches, and handles directly a set of other invariants of the representation which are often neglected. An experimental evaluation shows that the approach significantly improves over the state of the art.
References
- Aubry, M., Schlickewei, U., and Cremers, D. (2011). The wave kernel signature: A quantum mechanical approach to shape analysis. In Computer Vision Workshops (ICCV Workshops), 2011 IEEE International Conference on, pages 1626-1633.
- Bai, L., Hancock, E., Torsello, A., and Rossi, L. (2013). A quantum jensen-shannon graph kernel using the continuous-time quantum walk. In Kropatsch, W., Artner, N., Haxhimusa, Y., and Jiang, X., editors, Graph-Based Representations in Pattern Recognition, Lecture Notes in Computer Science, pages 121-131. Springer Berlin Heidelberg.
- Biasotti, S., Marini, S., Mortara, M., Patan, G., Spagnuolo, M., and Falcidieno, B. (2003). 3d shape matching through topological structures. In Nystrm, I., Sanniti di Baja, G., and Svensson, S., editors, Discrete Geometry for Computer Imagery, volume 2886 of Lecture Notes in Computer Science, pages 194-203. Springer Berlin Heidelberg.
- Bonev, B., Escolano, F., Lozano, M., Suau, P., Cazorla, M., and Aguilar, W. (2007). Constellations and the unsupervised learning of graphs. In Escolano, F. and Vento, M., editors, Graph-Based Representations in Pattern Recognition, volume 4538 of Lecture Notes in Computer Science, pages 340-350. Springer Berlin Heidelberg.
- Borgwardt, K. M. and peter Kriegel, H. (2005). Shortestpath kernels on graphs. In In Proceedings of the 2005 International Conference on Data Mining, pages 74- 81.
- Bunke, H., Foggia, P., Guidobaldi, C., and Vento, M. (2003). Graph clustering using the weighted minimum common supergraph. In Hancock, E. and Vento, M., editors, Graph Based Representations in Pattern Recognition, volume 2726 of Lecture Notes in Computer Science, pages 235-246. Springer Berlin Heidelberg.
- Estrada, F. and Jepson, A. (2009). Benchmarking image segmentation algorithms. International journal of computer vision, 85(2):167-181.
- Friedman, N. and Koller, D. (2003). Being bayesian about network structure. a bayesian approach to structure discovery in bayesian networks. Machine Learning, 50(1-2):95-125.
- Jensen, L. J., Kuhn, M., Stark, M., Chaffron, S., Creevey, C., Muller, J., Doerks, T., Roth, E., Simonovic, M., Bork, P., and Mering, C. V. (2008). String 8 a global view on proteins and their functional interactions in 630 organisms.
- Kashima, H., Tsuda, K., and Inokuchi, A. (2003). Marginalized kernels between labeled graphs. In Proceedings of the Twentieth International Conference on Machine Learning, pages 321-328. AAAI Press.
- Li, G., Semerci, M., Yener, B., and Zaki, M. J. (2012). Effective graph classification based on topological and label attributes. Stat. Anal. Data Min., pages 265-283.
- Litman, R. and Bronstein, A. M. (2014). Learning spectral descriptors for deformable shape correspondence. IEEE Trans. Pattern Anal. Mach. Intell., 36(1):171- 180.
- Luo, B., Wilson, R. C., and Hancock, E. R. (2006). A spectral approach to learning structural variations in graphs. Pattern Recognition, 39(6):1188 - 1198.
- Nene, S. A., Nayar, S. K., and Murase, H. (1996). Columbia Object Image Library (COIL-20). Technical report.
- Shervashidze, N., Schweitzer, P., van Leeuwen, E. J., Mehlhorn, K., and Borgwardt, K. M. (2011). Weisfeiler-lehman graph kernels. J. Mach. Learn. Res.
- Shervashidze, N., Vishwanathan, S. V. N., Petri, T. H., Mehlhorn, K., and et al. (2009). Efficient graphlet kernels for large graph comparison.
- Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman & Hall, London.
- Todorovic, S. and Ahuja, N. (2006). Extracting subimages of an unknown category from a set of images. In Computer Vision and Pattern Recognition, 2006 IEEE Computer Society Conference on, volume 1, pages 927-934.
- Torsello, A. (2008). An importance sampling approach to learning structural representations of shape. In Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on, pages 1-7.
- Torsello, A., Gasparetto, A., Rossi, L., and Hancock, E. (2014). Transitive State Alignment for the Quantum Jensen-Shannon Kernel.
- Torsello, A. and Hancock, E. (2006). Learning shapeclasses using a mixture of tree-unions. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 28(6):954-967.
- Torsello, A. and Rossi, L. (2011). Supervised learning of graph structure. In Pelillo, M. and Hancock, E. R., editors, SIMBAD, volume 7005 of Lecture Notes in Computer Science, pages 117-132. Springer.
- White, D. and Wilson, R. (2007). Spectral generative models for graphs. In Image Analysis and Processing, 2007. ICIAP 2007. 14th International Conference on, pages 35-42.
Paper Citation
in Harvard Style
Gasparetto A., Minello G. and Torsello A. (2015). A Non-parametric Spectral Model for Graph Classification . In Proceedings of the International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM, ISBN 978-989-758-076-5, pages 312-319. DOI: 10.5220/0005220303120319
in Bibtex Style
@conference{icpram15,
author={Andrea Gasparetto and Giorgia Minello and Andrea Torsello},
title={A Non-parametric Spectral Model for Graph Classification},
booktitle={Proceedings of the International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},
year={2015},
pages={312-319},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005220303120319},
isbn={978-989-758-076-5},
}
in EndNote Style
TY - CONF
JO - Proceedings of the International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,
TI - A Non-parametric Spectral Model for Graph Classification
SN - 978-989-758-076-5
AU - Gasparetto A.
AU - Minello G.
AU - Torsello A.
PY - 2015
SP - 312
EP - 319
DO - 10.5220/0005220303120319