Convergence properties of the softassign quadratic assignment algorithm
Neural Computation
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Clustering and Embedding Using Commute Times
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Classification Based on Dissimilarity Space Embedding
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Feature Ranking Algorithms for Improving Classification of Vector Space Embedded Graphs
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
Group-Wise Point-Set Registration Using a Novel CDF-Based Havrda-Charvát Divergence
International Journal of Computer Vision
Learning Gaussian mixture models with entropy-based criteria
IEEE Transactions on Neural Networks
Geometric characterization and clustering of graphs using heat kernel embeddings
Image and Vision Computing
Entropy-based variational scheme for fast bayes learning of Gaussian mixtures
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Graph matching through entropic manifold alignment
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Information-Theoretic dissimilarities for graphs
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
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In this paper, we introduce a novel concept: Inverse Embedding. We formulate inverse embedding in the following terms: given a set of multi-dimensional points coming directly or indirectly from a given spectral embedding, find the mininal complexity graph (following a MDL criterion) which satisfies the embedding constraints. This means that when the inferred graph is embedded it must provide the same distribution of squared distances between the original multi-dimensional vectors. We pose the problem in terms of a Lagrangian and find that a fraction of the multipliers (the smaller ones) resulting from the deterministic annealing process provide the positions of the edges of the unknown graph. We proof the convergence of the algorithm through an analysis of the dynamics of the deterministic annealing process and test the method with some significant sample graphs.