An Eigendecomposition Approach to Weighted Graph Matching Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Normalized convergence in stochastic optimization
Annals of Operations Research
Vector quantization and signal compression
Vector quantization and signal compression
The Minimization of Semicontinuous Functions: Mollifier Subgradients
SIAM Journal on Control and Optimization
A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
On a relation between graph edit distance and maximum common subgraph
Pattern Recognition Letters
A Linear Programming Approach for the Weighted Graph Matching Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
A RKHS Interpolator-Based Graph Matching Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Self-organizing map for clustering in the graph domain
Pattern Recognition Letters - In memory of Professor E.S. Gelsema
Similarity Measures for Structured Representations
EWCBR '93 Selected papers from the First European Workshop on Topics in Case-Based Reasoning
The Anchors Hierarchy: Using the Triangle Inequality to Survive High Dimensional Data
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Efficient Regular Data Structures and Algorithms for Location and Proximity Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Central Clustering of Attributed Graphs
Machine Learning
Graph-Theoretic Techniques for Web Content Mining
Graph-Theoretic Techniques for Web Content Mining
Learning Shape-Classes Using a Mixture of Tree-Unions
IEEE Transactions on Pattern Analysis and Machine Intelligence
IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Graph-Based k-Means Clustering: A Comparison of the Set Median versus the Generalized Median Graph
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
The Journal of Machine Learning Research
Graph clustering using the weighted minimum common supergraph
GbRPR'03 Proceedings of the 4th IAPR international conference on Graph based representations in pattern recognition
ACM attributed graph clustering for learning classes of images
GbRPR'03 Proceedings of the 4th IAPR international conference on Graph based representations in pattern recognition
Report on the second symbol recognition contest
GREC'05 Proceedings of the 6th international conference on Graphics Recognition: ten Years Review and Future Perspectives
A graph matching based approach to fingerprint classification using directional variance
AVBPA'05 Proceedings of the 5th international conference on Audio- and Video-Based Biometric Person Authentication
Least squares quantization in PCM
IEEE Transactions on Information Theory
A self-organizing map for adaptive processing of structured data
IEEE Transactions on Neural Networks
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Vector quantization (VQ) is a lossy data compression technique from signal processing, which is restricted to feature vectors and therefore inapplicable for combinatorial structures. This contribution aims at extending VQ to the quantization of graphs in a theoretically principled way in order to overcome practical limitations known in the context of prototype-based clustering of graphs. For this, we present the following results: (i) A proof of the necessary Lloyd-Max conditions for optimality of a graph quantizer, (ii) consistency statements for optimal graph quantizer design, and (iii) an accelerated version of competitive learning graph quantization. In order to achieve the proposed results, we present graphs as points in some orbifold. The orbifold framework will introduce sufficient mathematical structure to allow an extension of VQ to graph quantization in a theoretically sound way without discarding the relational information of the graphs. In doing so the proposed approach provides a template of how to link structural pattern recognition methods other than graph quantization to statistical pattern recognition.