Abstract
Motivated by an important and challenging task encountered in material discovery, we consider the problem of finding K basis patterns of numbers that jointly compose N observed patterns while enforcing additional spatial and scaling constraints. We propose a Constraint Programming (CP) model which captures the exact problem structure yet fails to scale in the presence of noisy data about the patterns. We alleviate this issue by employing Machine Learning (ML) techniques, namely kernel methods and clustering, to decompose the problem into smaller ones based on a global data-driven view, and then stitch the partial solutions together using a global CP model. Combining the complementary strengths of CP and ML techniques yields a more accurate and scalable method than the few found in the literature for this complex problem.
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
Powder Diffract. File, JCPDS Internat. Centre Diffract. Data, PA (2004)
Barber, Z.H., Blamire, M.G.: High throughput thin film materials science. Mat. Sci. Tech. 24(7), 757–770 (2008)
Barr, G., Dong, W., Gilmore, C.J.: Polysnap3: a computer program for analysing and visualizing high-throughput data from diffraction and spectroscopic sources. J. Appl. Cryst. 42, 965 (2009)
Baumes, L.A., Moliner, M., Corma, A.: Design of a full-profile-matching solution for high-throughput analysis of multiphase samples through powder x-ray diffraction. Chem. Eur. J. 15, 4258 (2009)
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, NY (2006)
Damoulas, T., Henry, S., Farnsworth, A., Lanzone, M., Gomes, C.: Bayesian Classification of Flight Calls with a novel Dynamic Time Warping Kernel. In: ICMLA 2010, pp. 424–429. IEEE, Los Alamitos (2010)
Gervet, C., Hentenryck, P.V.: Length-lex ordering for set csps. In: AAAI (2006)
Gomes, C.P.: Computational Sustainability: Computational methods for a sustainable environment, economy, and society. The Bridge, NAE 39(4) (2009)
Gregoire, J.M., Dale, D., Kazimirov, A., DiSalvo, F.J., van Dover, R.B.: High energy x-ray diffraction/x-ray fluorescence spectroscopy for high-throughput analysis of composition spread thin films. Rev. Sci. Instrum. 80(12), 123905 (2009)
Gregoire, J.M., Tague, M.E., Cahen, S., Khan, S., Abruna, H.D., DiSalvo, F.J., van Dover, R.B.: Improved fuel cell oxidation catalysis in pt1-xtax. Chem. Mater. 22(3), 1080 (2010)
Hawkins, P., Stuckey, P.J.: Solving set constraint satisfaction problems using robdds. Journal of Artificial Intelligence Research 24, 109–156 (2005)
Van Hentenryck, P., Michel, L.: The steel mill slab design problem revisited. In: Trick, M.A. (ed.) CPAIOR 2008. LNCS, vol. 5015, pp. 377–381. Springer, Heidelberg (2008)
Holm, J., de Lichtenberg, K., Thorup, M.: Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. In: STOC 1998, New York, NY, USA, pp. 79–89 (1998)
Long, C.J., Bunker, D., Karen, V.L., Li, X., Takeuchi, I.: Rapid identification of structural phases in combinatorial thin-film libraries using x-ray diffraction and non-negative matrix factorization. Rev. Sci. Instruments 80(103902) (2009)
Long, C.J., Hattrick-Simpers, J., Murakami, M., Srivastava, R.C., Takeuchi, I., Karen, V.L., Li, X.: Rapid structural mapping of ternary metallic alloy systems using the combinatorial approach and cluster analysis. Rev. Sci. Inst. 78 (2007)
Potyrailo, R.A., Maier, W.F.: Combinatorial and High-Throughput Discovery and Optimization of Catalysts and Materials. CRC Press, Boca Raton (2007)
Prosser, P., Unsworth, C.: A connectivity constraint using bridges. In: ECAI 2006, The Netherlands, pp. 707–708 (2006)
Sakoe, H., Chiba, S.: Dynamic programming algorithm optimization for spoken word recognition. Readings in Speech Recognition, 159 (1990)
Stockmeyer, L.J.: The set basis problem is np-complete. Technical Report Report No. RC-5431, IBM Watson Research Center, East Lansing, Michigan (1975)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
LeBras, R., Damoulas, T., Gregoire, J.M., Sabharwal, A., Gomes, C.P., van Dover, R.B. (2011). Constraint Reasoning and Kernel Clustering for Pattern Decomposition with Scaling. In: Lee, J. (eds) Principles and Practice of Constraint Programming – CP 2011. CP 2011. Lecture Notes in Computer Science, vol 6876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23786-7_39
Download citation
DOI: https://doi.org/10.1007/978-3-642-23786-7_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23785-0
Online ISBN: 978-3-642-23786-7
eBook Packages: Computer ScienceComputer Science (R0)