An Eigendecomposition Approach to Weighted Graph Matching Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Laplace eigenvalues of graphs—a survey
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Almost all trees share a complete set of immanantal polynomials
Journal of Graph Theory
Organizing Large Structural Modelbases
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Quantitative measures of change based on feature organization: eigenvalues and eigenvectors
Computer Vision and Image Understanding
Genetic operators for hierarchical graph clustering
Pattern Recognition Letters
Shock Graphs and Shape Matching
International Journal of Computer Vision
Pattern Recognition Letters - Special issue on pattern recognition in practice VI
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision
Structural Matching in Computer Vision Using Probabilistic Relaxation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Factorization Approach to Grouping
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Inexact Multisubgraph Matching Using Graph Eigenspace and Clustering Models
Proceedings of the Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
On clusterings-good, bad and spectral
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Edit Distance From Graph Spectra
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Dominant Sets and Hierarchical Clustering
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Many-to-many graph matching via metric embedding
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Clustering graphs by weighted substructure mining
ICML '06 Proceedings of the 23rd international conference on Machine learning
Graph embedding using tree edit-union
Pattern Recognition
Graph simplification and matching using commute times
Pattern Recognition
Region-Based Hierarchical Image Matching
International Journal of Computer Vision
Isotree: Tree clustering via metric embedding
Neurocomputing
Size functions for comparing 3D models
Pattern Recognition
Reducing the Dimensionality of Vector Space Embeddings of Graphs
MLDM '07 Proceedings of the 5th international conference on Machine Learning and Data Mining in Pattern Recognition
Clustering Organisms Using Metabolic Networks
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Measuring Graph Similarity Using Spectral Geometry
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
A generalized graph-spectral approach to melodic modeling and retrieval
MIR '08 Proceedings of the 1st ACM international conference on Multimedia information retrieval
An Inexact Graph Comparison Approach in Joint Eigenspace
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Complex Fiedler Vectors for Shape Retrieval
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Quantitative Evaluation on Heat Kernel Permutation Invariants
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Graph Characteristics from the Ihara Zeta Function
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Spectral Embedding of Feature Hypergraphs
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
On Euclidean Corrections for Non-Euclidean Dissimilarities
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
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
A generative model for graph matching and embedding
Computer Vision and Image Understanding
Graph characteristics from the heat kernel trace
Pattern Recognition
Characteristic Polynomial Analysis on Matrix Representations of Graphs
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Dissimilarity Based Vector Space Embedding of Graphs Using Prototype Reduction Schemes
MLDM '09 Proceedings of the 6th International Conference on Machine Learning and Data Mining in Pattern Recognition
Topological and directional logo layout indexing using Hermitian spectra
SPPRA '08 Proceedings of the Fifth IASTED International Conference on Signal Processing, Pattern Recognition and Applications
Geometric characterization and clustering of graphs using heat kernel embeddings
Image and Vision Computing
Classifier ensembles for vector space embedding of graphs
MCS'07 Proceedings of the 7th international conference on Multiple classifier systems
Comparing sets of 3D digital shapes through topological structures
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Graph embedding in vector spaces by means of prototype selection
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
A family of novel graph kernels for structural pattern recognition
CIARP'07 Proceedings of the Congress on pattern recognition 12th Iberoamerican conference on Progress in pattern recognition, image analysis and applications
Manifold embedding for shape analysis
Neurocomputing
Probabilistic matching of lines for their homography
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
3D CAD model search: a regularized manifold learning approach
ROBIO'09 Proceedings of the 2009 international conference on Robotics and biomimetics
Indexing tree and subtree by using a structure network
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Graph embedding for pattern recognition
ICPR'10 Proceedings of the 20th International conference on Recognizing patterns in signals, speech, images, and videos
Learning invariant structure for object identification by using graph methods
Computer Vision and Image Understanding
A generic framework for median graph computation based on a recursive embedding approach
Computer Vision and Image Understanding
Detecting anomalies in people's trajectories using spectral graph analysis
Computer Vision and Image Understanding
Graph descriptors from B-matrix representation
GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
Entropy versus heterogeneity for graphs
GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
Towards performance evaluation of graph-based representation
GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
Characterizing graphs using approximate von Neumann entropy
IbPRIA'11 Proceedings of the 5th Iberian conference on Pattern recognition and image analysis
Discriminating graphs through spectral projections
Computer Networks: The International Journal of Computer and Telecommunications Networking
Graph-based representations of point clouds
Graphical Models
Feature point matching using a hermitian property matrix
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
3D CAD model retrieval with perturbed Laplacian spectra
Computers in Industry
Transforming strings to vector spaces using prototype selection
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Geometric characterisation of graphs
ICIAP'05 Proceedings of the 13th international conference on Image Analysis and Processing
Clustering with proximity knowledge and relational knowledge
Pattern Recognition
Towards the unification of structural and statistical pattern recognition
Pattern Recognition Letters
Pattern analysis with graphs: Parallel work at Bern and York
Pattern Recognition Letters
The dissimilarity representation for structural pattern recognition
CIARP'11 Proceedings of the 16th Iberoamerican Congress conference on Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Graph structure analysis based on complex network
Digital Signal Processing
Graph embedding in vector spaces by node attribute statistics
Pattern Recognition
Similarity-Based Retrieval With Structure-Sensitive Sparse Binary Distributed Representations
Computational Intelligence
Graph characterizations from von Neumann entropy
Pattern Recognition Letters
Invariants of distance k-graphs for graph embedding
Pattern Recognition Letters
Feature selection on node statistics based embedding of graphs
Pattern Recognition Letters
On graph-associated matrices and their eigenvalues for optical character recognition
ANNPR'12 Proceedings of the 5th INNS IAPR TC 3 GIRPR conference on Artificial Neural Networks in Pattern Recognition
Graph complexity from the jensen-shannon divergence
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Improving fuzzy multilevel graph embedding through feature selection technique
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Unsupervised clustering of human pose using spectral embedding
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Human action recognition in video by fusion of structural and spatio-temporal features
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
An incremental structured part model for image classification
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Discriminative prototype selection methods for graph embedding
Pattern Recognition
Graph Kernels from the Jensen-Shannon Divergence
Journal of Mathematical Imaging and Vision
Depth-based complexity traces of graphs
Pattern Recognition
Robust point pattern matching based on spectral context
Pattern Recognition
Spectral graph features for the classification of graphs and graph sequences
Computational Statistics
Hi-index | 0.14 |
Graph structures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low-dimensional space using a number of alternative strategies, including principal components analysis (PCA), multidimensional scaling (MDS), and locality preserving projection (LPP). Experimentally, we demonstrate that the embeddings result in well-defined graph clusters. Our experiments with the spectral representation involve both synthetic and real-world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real-world experiments show that the method can be used to locate clusters of graphs.