# Constraint Reasoning and Kernel Clustering for Pattern Decomposition with Scaling

@inproceedings{LeBras2011ConstraintRA,
title={Constraint Reasoning and Kernel Clustering for Pattern Decomposition with Scaling},
author={Ronan Le Bras and Theodoros Damoulas and J. Gregoire and Ashish Sabharwal and Carla P. Gomes and R. B. van Dover},
booktitle={CP},
year={2011}
}
• Published in CP 12 September 2011
• Computer Science
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…
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## References

SHOWING 1-10 OF 25 REFERENCES
Length-Lex Ordering for Set CSPs
• Computer Science
AAAI
• 2006
A dual view of set variables is taken that encodes directly cardinality and lexicographic information, by totally ordering a set domain with a length-lex ordering, and the resulting set solver achieves a pruning comparable to the hybrid domain of Sadler and Gervet at a fraction of the computational cost.
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 4th International Conference, CPAIOR 2007, Brussels, Belgium, May 23-26, 2007, Proceedings
• Computer Science
CPAIOR
• 2007
Minimum Cardinality Matrix Decomposition into Consecutive-Ones Matrices: CP and IP Approaches.- Connections in Networks: Hardness of Feasibility Versus Optimality.- Modeling the Regular Constraint
A Connectivity Constraint Using Bridges
• Computer Science
ECAI
• 2006
A specialised constraint for enforcing graph connectivity that is founded on the depth first search (dfs) process and ensures that no critical edge may be deleted from A, i.e. an edge that if deleted disconnects the graph.
Rapid identification of structural phases in combinatorial thin-film libraries using x-ray diffraction and non-negative matrix factorization.
• Computer Science
The Review of scientific instruments
• 2009
The use of NMF is applied to the problem of analyzing hundreds of x-ray microdiffraction patterns from a combinatorial materials library to reduce the arduous task to the much smaller task of identifying only nine microXRD patterns.
PolySNAP3: a computer program for analysing and visualizing high-throughput data from diffraction and spectroscopic sources
• Computer Science
• 2009
Cluster analysis, multivariate data analysis and extensive data visualization routines are used to automatically classify the patterns into groups, validate the classification, and thus identify polymorphs, mixtures and salts.
Bayesian Classification of Flight Calls with a Novel Dynamic Time Warping Kernel
• Computer Science
2010 Ninth International Conference on Machine Learning and Applications
• 2010
A probabilistic classification algorithm with a novel Dynamic Time Warping (DTW) kernel to automatically recognize flight calls of different species of birds that is competitive to human expert recognition levels and outperforms other classifiers trained on a variety of feature extraction approaches.
Pattern Recognition and Machine Learning
This book covers a broad range of topics for regular factorial designs and presents all of the material in very mathematical fashion and will surely become an invaluable resource for researchers and graduate students doing research in the design of factorial experiments.
Solving Set Constraint Satisfaction Problems using ROBDDs
• Computer Science
J. Artif. Intell. Res.
• 2005
It is shown that it is possible to construct an efficient set domain propagator which compactly represents many set domains and set constraints using ROBDDs and how to incorporate less strict consistency notions into the ROBDD framework, such as set bounds, cardinality bounds and lexicographic bounds consistency.
Pattern Recognition and Machine Learning (Information Science and Statistics)
Looking for competent reading resources? We have pattern recognition and machine learning information science and statistics to read, not only read, but also download them or even check out online.
The Steel Mill Slab Design Problem Revisited
• Computer Science
CPAIOR
• 2008
This paper shows that a simple search procedure breaking symmetries dynamically leads to a constraint program solving the problem in a few seconds, while maintaining the completeness of the approach and removing the need for large neighborhood search.