A unifying approach to hard and probabilistic clustering

Zass, Ron; Shashua, Amnon

doi:10.1109/iccv.2005.27

Cited by 115 publications

(115 citation statements)

References 15 publications

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“…Finally, we can ascribe to preference analysis also all the approaches based on higher order clustering [19,20,21,22], where higher order similarity tensors are defined between n-tuple of points as the probability of points to be clustered together measured in terms of residual errors with respect to provisional models. In this way preferences give rise to a hypergraph whose hyperedges encode the existence of a structure able to explain the incident vertices.…”

Section: Preference Analysismentioning

confidence: 99%

Multiple structure recovery with maximum coverage

Magri

Fusiello

2017

Machine Vision and Applications

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We present a general framework for geometric model fitting based on a set coverage formulation, that caters for intersecting structures and outliers in a simple and principled manner. The multi-model fitting problem is formulated in terms of the optimization of a consensus-based global cost function, which allows to sidestep the pitfalls of preference approaches based on clustering and to avoid the difficult trade-off between data fidelity and complexity of other optimization formulations. Two especially appealing characteristics of this method are the ease with which it can be implemented and its modularity with respect to the solver and to the sampling strategy. Few intelligible parameters need to be set and tuned, namely the inlier threshold and the number of desired models. The summary of the experiments is that our method compares favourably with its competitors overall, and it is always either the best performer or almost on par with the best performer in specific scenarios.

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Section: Preference Analysismentioning

confidence: 99%

Multiple structure recovery with maximum coverage

Magri

Fusiello

2017

Machine Vision and Applications

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“…There are several popular ways [12] to construct the affinity matrix, such as the k-nearest neighbor graph and the fully connected graph. The normalization of the affinity matrix is achieved by finding the closest doubly stochastic matrix to the affinity matrix under a certain error measure [18]- [20], while the simple clustering algorithm (e.g. k-means) is used to partition an embedded coordinate system (formed by the principal k eigenvectors of the normalized affinity matrix) in an easier and simpler way.…”

Section: Construction Of the Affinity Matrixmentioning

confidence: 99%

“…In [18], [19], it has been shown that the key difference between Ratio-cut and Normalized-cut is the error measure used to find the closest doubly stochastic approximation of the input affinity matrix during the normalization step. When repeated, the Normalized-cut process converges to the global optimal solution under the relative entropy measure (also called the Kullback-Leibler divergence), while the L 1 normalization leads to the Ratio-cut clustering.…”

Section: Construction Of the Affinity Matrixmentioning

confidence: 99%

“…Then, the leading eigenvectors of the normalized affinity matrix are extracted to perform dimensionality reduction for effective clustering in the lower dimensional subspace. Therefore, the three critical factors that affect the final performance of spectral clustering are [18], [19]: 1) the construction of the affinity matrix, 2) the normalization of the affinity matrix, and 3) the simple clustering algorithm, as shown in Fig. 1.…”

Section: Construction Of the Affinity Matrixmentioning

confidence: 99%

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Efficient Semidefinite Spectral Clustering via Lagrange Duality

Yan

Shen

Wang

2014

IEEE Trans. on Image Process.

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Abstract-We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius normalization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm approximation based algorithm, the proposed algorithm can more accurately find the closest doubly stochastic approximation to the affinity matrix by considering the p.s.d. constraint. In this paper, SSC is formulated as a semidefinite programming (SDP) problem. In order to solve the high computational complexity of SDP, we present a dual algorithm based on the Lagrange dual formalization. Two versions of the proposed algorithm are proffered: one with less memory usage and the other with faster convergence rate. The proposed algorithm has much lower time complexity than that of the standard interior-point based SDP solvers. Experimental results on both UCI data sets and real-world image data sets demonstrate that 1) compared with the state-of-the-art spectral clustering methods, the proposed algorithm achieves better clustering performance; and 2) our algorithm is much more efficient and can solve larger-scale SSC problems than those standard interior-point SDP solvers.

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“…Complex data are handled well by the third class of algorithms (which has made them the state-of-the-art in image segmentation) that consists of the many variants of spectral factorization [8,14,17,15,21,12]. These algorithms do not make make strong assumptions on the shape of clusters, and thus generally perform better on images.…”

Section: Introductionmentioning

confidence: 99%