An expectation–maximisation framework for segmentation and grouping

Robles-Kelly, Antonio; Hancock, Edwin R.

doi:10.1016/s0262-8856(02)00062-8

Cited by 8 publications

(6 citation statements)

References 32 publications

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“…In related work, both Perona and Freeman [24], and Sarkar and Boyer [29] have shown how the thresholded leading eigenvector of the weighted adjacency matrix can be used for grouping points and line-segments. Robles-Kelly and Hancock [26] have developed a statistical variant of the method which avoids thresholding the leading eigenvector and instead employs the EM algorithm to iteratively locate clusters of objects.…”

Section: Related Literaturementioning

confidence: 99%

Pattern vectors from algebraic graph theory

Wilson

Hancock

Luo

2005

IEEE Trans. Pattern Anal. Machine Intell.

187

110

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Graph structures have proved 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 * This research is partially supported by the National Natural Science Foundation of China(No. 60375010)1 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.

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Section: Related Literaturementioning

confidence: 99%

Pattern vectors from algebraic graph theory

Wilson

Hancock

Luo

2005

IEEE Trans. Pattern Anal. Machine Intell.

187

110

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“…The ÿrst of these is the EM algorithm described in Ref. [24], which uses a mixture of Bernoulli distributions. This algorithm does not however use modal decomposition of the link-weight matrix.…”

Section: Methodsmentioning

confidence: 99%

“…In fact in related work, we have developed an EM algorithm for grouping using a mixture of Bernoulli distributions [24]. However, the method proved slow to converge and resulted in overlapped clusters.…”

Section: Contributionmentioning

confidence: 99%

A probabilistic spectral framework for grouping and segmentation

ROBLESKELLY¹

2004

Pattern Recognition

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This paper presents an iterative spectral framework for pairwise clustering and perceptual grouping. Our model is expressed in terms of two sets of parameters. Firstly, there are cluster memberships which represent the a nity of objects to clusters. Secondly, there is a matrix of link weights for pairs of tokens. We adopt a model in which these two sets of variables are governed by a Bernoulli model. We show how the likelihood function resulting from this model may be maximised with respect to both the elements of link-weight matrix and the cluster membership variables. We establish the link between the maximisation of the log-likelihood function and the eigenvectors of the link-weight matrix. This leads us to an algorithm in which we iteratively update the link-weight matrix by repeatedly reÿning its modal structure. Each iteration of the algorithm is a three-step process. First, we compute a link-weight matrix for each cluster by taking the outer-product of the vectors of current cluster-membership indicators for that cluster. Second, we extract the leading eigenvector from each modal link-weight matrix. Third, we compute a revised link weight matrix by taking the sum of the outer products of the leading eigenvectors of the modal link-weight matrices.

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“…Recall that, in previous sections, we intro- Note that we can use this posteriors in a number of ways. These can be viewed as class indicator variables, such as those employed in [63]. Other options include taking a classifier ensemble approach such as boosting [64], where each of the variables α i (·) can be combined making use of a purposely recovered rule.…”

Section: Shape Categorisation and Matchingmentioning

confidence: 99%

Graph attribute embedding via Riemannian submersion learning

Zhao

Robles-Kelly

Zhou

et al. 2011

Computer Vision and Image Understanding

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In this paper, we tackle the problem of embedding a set of relational structures into a metric space for purposes of matching and categorisation. To this end, we view the problem from a Riemannian perspective and make use of the concepts of charts on the manifold to define the embedding as a mixture of class-specific submersions. Formulated in this manner, the mixture weights are recovered using a probability density estimation on the embedded graph node coordinates. Further, we recover these class-specific submersions making use of an iterative trust-region method so as to minimise the L2 norm between the hard limit of the graph-vertex posterior probabilities and their estimated values. The method presented here is quite general in nature and allows tasks such as matching, categorisation and retrieval. We show results on graph matching, shape categorisation and digit classification on synthetic data, the MNIST dataset and the MPEG-7 database.

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An expectation–maximisation framework for segmentation and grouping

Cited by 8 publications

References 32 publications

Pattern vectors from algebraic graph theory

Pattern vectors from algebraic graph theory

A probabilistic spectral framework for grouping and segmentation

Graph attribute embedding via Riemannian submersion learning

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