Almost all trees share a complete set of immanantal polynomials
Journal of Graph Theory
International Journal of Computer Vision
Embedding tree metrics into low dimensional Euclidean spaces
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Shock Graphs and Shape Matching
International Journal of Computer Vision
Properties of Embedding Methods for Similarity Searching in Metric Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Quantitative Measures of Change based on Feature Organization: Eigenvalues and Eigenvectors
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
A skeletal measure of 2D shape similarity
Computer Vision and Image Understanding
Pattern Vectors from Algebraic Graph Theory
IEEE Transactions on Pattern Analysis and Machine Intelligence
Human Carrying Status in Visual Surveillance
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering
International Journal of Computer Vision
General Tensor Discriminant Analysis and Gabor Features for Gait Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Many-to-many graph matching via metric embedding
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Multi-way clustering using super-symmetric non-negative tensor factorization
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Graph-Based Representations in Pattern Recognition and Computational Intelligence
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part I: Bio-Inspired Systems: Computational and Ambient Intelligence
Improving Graph Classification by Isomap
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Clustering with proximity knowledge and relational knowledge
Pattern Recognition
Information-theoretic selection of high-dimensional spectral features for structural recognition
Computer Vision and Image Understanding
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One of the problems that hinders the spectral analysis of trees is that they have a strong tendency to be co-spectral. As a result, structurally distinct trees possess degenerate graph-spectra, and spectral methods can be reliably used to neither compute distances between trees nor to cluster trees. The aim of this paper is to describe a method that can be used to alleviate this problem. We use the ISOMAP algorithm to embed the trees in a Euclidean space using the pattern of shortest distances between nodes. From the arrangement of nodes in this space, we compute a weighted proximity matrix, and from the proximity matrix a Laplacian matrix is computed. By transforming the graphs in this way we lift the co-spectrality of the trees. The spectrum of the Laplacian matrix for the embedded graphs may be used for purposes of comparing trees and for clustering them. Experiments on sets of shock graphs reveal the utility of the method on real-world data.