Clustering and Embedding Using Commute Times
@article{Qiu2007ClusteringAE, title={Clustering and Embedding Using Commute Times}, author={Huaijun Qiu and Edwin R. Hancock}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, year={2007}, volume={29} }
This paper exploits the properties of the commute time between nodes of a graph for the purposes of clustering and embedding and explores its applications to image segmentation and multibody motion tracking. Our starting point is the lazy random walk on the graph, which is determined by the heat kernel of the graph and can be computed from the spectrum of the graph Laplacian. We characterize the random walk using the commute time (that is, the expected time taken for a random walk to travel…
Figures and Tables from this paper
245 Citations
Edge-aware image smoothing using commute time distances
- Computer Science2016 IEEE International Conference on Image Processing (ICIP)
- 2016
This paper exploits the properties of the commute time to extend the notion of “similarity” in this context, and employs a multiscale algorithm for approximating the eigenvector computation efficiently.
Euclidean commute time distance embedding and its application to spectral anomaly detection
- Mathematics, Computer ScienceDefense + Commercial Sensing
- 2012
This paper quantifies the random walk using a quantity known as the average commute time distance and finds a nonlinear transformation that embeds the nodes of a graph in a Euclidean space where the separation between them is equal to the square root of this quantity.
Commute time distance transformation applied to spectral imagery and its utilization in material clustering
- Computer Science
- 2012
A transformation based on a Markov-chain model of a random walk on a graph via application to spectral image clustering is introduced and results are shown for standard clustering algorithms applied to hyperspectral data sets.
Link-based Community Detection with the Commute-Time Kernel
- Computer Science
- 2007
This methodology provides good results, outperforming the spherical k-means and spectral clustering, on a document clustering problem involving the newsgroups database, where the set of documents is viewed as a graph.
Commute-Time Convolution Kernels for Graph Clustering
- Computer ScienceSSPR/SPR
- 2010
This paper begins by computing the commute time distance in graphs, then uses a Gaussian convolution kernel to compare distributions and uses kernel kmeans for clustering and kernel PCA for illustration using the COIL object recognition database.
A Random Walk Approach to Query Informative Constraints for Clustering
- Computer ScienceIEEE Transactions on Cybernetics
- 2018
A random walk approach to the problem of querying informative constraints for clustering, based on the properties of the commute time, that is the expected time taken for a random walk to travel between two nodes and return, on the adjacency graph of data.
Graph nodes clustering with the sigmoid commute-time kernel: A comparative study
- Computer ScienceData Knowl. Eng.
- 2009
Dirichlet densifiers for improved commute times estimation
- Computer Science, MathematicsPattern Recognit.
- 2019
Large Scale Spectral Clustering Using Approximate Commute Time Embedding
- Computer ScienceArXiv
- 2011
This work proposes a fast and accurate spectral clustering approach using an approximate commute time embedding, which is similar to the spectral embedding and uses random projection and a linear time solver to find the approximate embedding.
Visualization of Large Dataset Using Approximate Commute Time Embedding
- Computer Science
- 2019
This paper proposes how to reduce the distortion by preserving the properties the normalized graph Laplacian matrix should be symmetric and positive semidefinite even after its approximation by sampling process.
References
SHOWING 1-10 OF 68 REFERENCES
Image Segmentation using Commute Times
- Mathematics, Computer ScienceBMVC
- 2005
The lazy random walk is characterised using the commute time between nodes, and it is shown how this quantity may be computed from the Laplacian spectrum using the discrete Green’s function.
The Principal Components Analysis of a Graph, and Its Relationships to Spectral Clustering
- Computer Science, MathematicsECML
- 2004
The Principal Components Analysis (PCA) of a graph is defined as the subspace projection that preserves as much variance as possible, in terms of the ECTD, a principal components analysis of the graph based on a Markov-chain model of random walk through the graph.
Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck Operators
- Computer ScienceNIPS
- 2005
A diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian is presented.
Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization
- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2006
It is shown that the quantization distortion in diffusion space bounds the error of compression of the operator, thus giving a rigorous justification for k-means clustering in diffusionspace and a precise measure of the performance of general clustering algorithms.
A Random Walks View of Spectral Segmentation
- Computer ScienceAISTATS
- 2001
It is proved that the Normalized Cut method arises naturally from the framework and a complete characterization of the cases when the Normalization Cut algorithm is exact is provided.
A new graph-theoretic approach to clustering and segmentation
- Computer Science, Mathematics2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings.
- 2003
A framework for the image segmentation problem based on a new graph-theoretic formulation of clustering, motivated by the analogies between the intuitive concept of a cluster and that of a dominant set of vertices, which establishes a correspondence between dominant sets and the extrema of a quadratic form over the standard simplex.
An Experimental Investigation of Graph Kernels on a Collaborative Recommendation Task
- Computer ScienceSixth International Conference on Data Mining (ICDM'06)
- 2006
Results indicate that a simple nearest-neighbours rule based on the similarity measure provided by the regularized Laplacian, the Markov diffusion and the commute time kernels performs best and is recommended for computing similarities between elements of a database.
Amplifying the Block Matrix Structure for Spectral Clustering.
- Computer Science
- 2005
Three improvements to spectral decomposition are proposed which show promising performance on both artiflcial and real-world data sets and include the K-lines algorithm.
Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering
- Computer Science, MathematicsNIPS
- 2001
The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering.
Segmentation using eigenvectors: a unifying view
- Computer ScienceProceedings of the Seventh IEEE International Conference on Computer Vision
- 1999
A unified treatment of eigenvectors of block matrices based on eigendecompositions in the context of segmentation is given, and close connections between them are shown while highlighting their distinguishing features.