# 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} }

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…

## 34 Citations

Pattern Decomposition with Complex Combinatorial Constraints: Application to Materials Discovery

- Computer ScienceAAAI
- 2015

CombiFD is introduced, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints, and a new pattern decompositions algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs.

Uncovering Hidden Structure through Parallel Problem Decomposition for the Set Basis Problem

- Computer ScienceAAAI Workshop: Computational Sustainability
- 2015

This work introduces a novel way in which parallelism can be used to exploit hidden structure of hard combinatorial problems, and shows that this strategy leads to a substantial speed-up over a sequential approach, since the aggregated sub-problem solution information often provides key structural insights to the complete solver.

Relaxation Methods for Constrained Matrix Factorization Problems: Solving the Phase Mapping Problem in Materials Discovery

- Computer ScienceCPAIOR
- 2017

A novel “lazy” Iterative Agile Factor Decomposition (IAFD) approach that relaxes and postpones non-convex constraint sets (the lazy constraints), iteratively enforcing them when violations are detected, while still ensuring fast run times.

Uncovering Hidden Structure through Parallel Problem Decomposition

- Computer ScienceAAAI
- 2014

A novel way in which parallelism can be used to exploit hidden structure of hard combinatorial problems, which leads to a significant speed-up over a sequential approach and greatly outperforms state-of-the-art incomplete solvers in terms of solution quality.

An Efficient Relaxed Projection Method for Constrained Non-negative Matrix Factorization with Application to the Phase-Mapping Problem in Materials Science

- Computer ScienceCPAIOR
- 2018

This paper proposes a general relaxation and several algorithms for enforcing constraints in a challenging application: the phase-mapping problem in materials science and shows that the proposed method significantly outperforms previous methods in terms of \(\ell _2\)-norm error and speed.

Automating Crystal-Structure Phase Mapping: Combining Deep Learning with Constraint Reasoning

- Computer ScienceNat. Mach. Intell.
- 2021

It is shown how DRNets require only a modest amount of data and compensate for the limited data by exploiting and magnifying the rich scientific prior knowledge about the thermodynamic rules that govern the mixtures of crystals.

Unsupervised phase mapping of X-ray diffraction data by nonnegative matrix factorization integrated with custom clustering

- Computer Sciencenpj Computational Materials
- 2018

A team led by Ichiro Takeuchi from the University of Maryland and Boian Alexandrov from Los Alamos National Laboratory developed a new computational method based on non-negative matrix factorization and cross-correlation analysis, capable of identifying peak-shifted patterns in XRD datasets.

Pattern Decomposition of Inorganic Materials: Optimizing Computational Algorithm

- Physics
- 2016

Phase pattern decomposition of inorganic materials’ crystalline structure is extremely important for the unearthing of new properties such as superconductivity. Previously, this process had…

Generalized machine learning technique for automatic phase attribution in time variant high-throughput experimental studies

- Materials Science
- 2015

Phase identification is an arduous task during high-throughput processing experiments, which can be exacerbated by the need to reconcile results from multiple measurement techniques to form a…

Fast and interpretable classification of small X-ray diffraction datasets using data augmentation and deep neural networks

- Computer Sciencenpj Computational Materials
- 2019

The scarce data problem intrinsic to novel materials development is overcome by coupling a supervised machine learning approach with a model-agnostic, physics-informed data augmentation strategy using simulated data from the Inorganic Crystal Structure Database (ICSD) and experimental data.

## References

SHOWING 1-10 OF 25 REFERENCES

Length-Lex Ordering for Set CSPs

- Computer ScienceAAAI
- 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 ScienceCPAIOR
- 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 ScienceECAI
- 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 ScienceThe 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 Science2010 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

- Mathematics, ArtTechnometrics
- 2007

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 ScienceJ. 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)

- Computer Science
- 2006

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 ScienceCPAIOR
- 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.