## Clustering through Ranking on Manifolds (2005)

### Cached

### Download Links

- [cervisia.org]
- [markus-breitenbach.com]
- [www.cs.colorado.edu]
- [www.machinelearning.org]
- DBLP

### Other Repositories/Bibliography

Venue: | In Proceedings of the 22nd international conference on Machine learning |

Citations: | 11 - 1 self |

### BibTeX

@INPROCEEDINGS{Breitenbach05clusteringthrough,

author = {Markus Breitenbach and Gregory Z. Grudic},

title = {Clustering through Ranking on Manifolds},

booktitle = {In Proceedings of the 22nd international conference on Machine learning},

year = {2005},

pages = {73--80},

publisher = {ACM Press}

}

### OpenURL

### Abstract

Clustering aims to find useful hidden structures in data. In this paper we present a new clustering algorithm that builds upon the consistency method (Zhou, et.al., 2003), a semi-supervised learning technique with the property of learning very smooth functions with respect to the intrinsic structure revealed by the data. Other methods, e.g. Spectral Clustering, obtain good results on data that reveals such a structure. However, unlike Spectral Clustering, our algorithm effectively detects both global and within-class outliers, and the most representative examples in each class. Furthermore, we specify an optimization framework that estimates all learning parameters, including the number of clusters, directly from data. Finally, we show that the learned cluster-models can be used to add previously unseen points to clusters without re-learning the original cluster model. Encouraging experimental results are obtained on a number of real world problems.

### Citations

1882 |
Data Mining Concepts and Techniques
- Han, Kamber
- 2001
(Show Context)
Citation Context ...pic in machine learning and pattern recognition. The problem of finding clusters that have a compact shape has been widely studied in literature. One of the most widely used approaches is the K-Means =-=[1]-=- method for vectorial data. Despite the success these methods have with real life data, they fail to handle data that exposes a manifold structure, i.e. data that is not shaped in the form of point cl... |

1097 | On spectral clustering: Analysis and an algorithm
- Ng, Jordan, et al.
- 2001
(Show Context)
Citation Context ..., they fail to handle data that exposes a manifold structure, i.e. data that is not shaped in the form of point clouds, but forms paths through a high-dimensional space. Recently, Spectral Clustering =-=[2, 3]-=- has attracted a lot of attention for its ability to handle this type of data very well. Although Spectral Clustering algorithms have achieved Appearing in Proceedings of the 22 nd International Confe... |

876 | The Architecture of Cognition
- Anderson
- 1983
(Show Context)
Citation Context ... class using the classifying function: yi = arg maxj≤c Fij. We define a matrix U as: U = β (I − αS) −1 = � u T 1 , ..., u T � n (3) and note that U defines a graph or diffusion kernel as described in =-=[7, 8]-=-. The entries in the columns of U (we symbolize column i of matrix U by the column vector uT i ) contain the “activation” of all the points in the data set if point i were used for labeling. That mean... |

490 | Semisupervised learning using gaussian fields and harmonic functions
- Zhu, Ghahramani, et al.
- 2003
(Show Context)
Citation Context ... the algorithm was unable to find the “right” solution automatically. 3.1. Synthetic Data In this experiment, we consider the two-moon and spiral synthetic data sets. The spiral data that was used in =-=[11]-=- and two-moon has been used as an example in numerous other manifold related experiments [5, 4]. Note that these synthetic data sets can not be clustered in a meaningful way by methods that assume a c... |

434 | Learning with local and global consistency - Zhou, Bousquet, et al. |

433 | From few to many: Illumination cone models for face recognition under variable lighting and pose
- Georghiades, Belhumeur, et al.
(Show Context)
Citation Context ...ecifying the number of clusters, Self-Tuning Spectral Clustering results in an error rate of 0.5. 3.5. Yale Face-Database B We now consider the setup used the in [12] and use the Yale Face Database B =-=[13]-=-. We use images of individuals 2, 5 and 10 and down-sample each image to 30x40 pixels. This σ 0.2 0.3 0.4 0.6 0.8 Error, α = 0.99 0.59 0.476 0.656 0.83 0.83 Error, α = 0.8 0.49 0.201 0.666 0.52 0.52 E... |

188 | Self-tuning spectral clustering
- Zelnik-Manor, Perona
- 2004
(Show Context)
Citation Context ...ster. In general, these learning parameters are set manually, making spectral clustering difficult to use in practice. Recently, an automated way of choosing these learning parameters was proposed in =-=[4]-=-. However, this algorithm has two main disadvantages: First, there is no framework for assigning points outside of the training set to clusters; second, although the algorithm works well on synthetic ... |

93 | Ranking on data manifolds
- Zhou, Weston, et al.
- 2004
(Show Context)
Citation Context ...means that Uii is the largest number in column i, and the remaining values in Ui get smaller the further the points are away from the centroid, but according to the underlying intrinsic structure. In =-=[9]-=- these values were used to rank with respect to the intrinsic manifold structure, i.e. the activation was used as similarity measure between the points. The ordering of these distances along each mani... |

59 | A comparison of spectral clustering algorithms
- Verma, Meilă
- 2003
(Show Context)
Citation Context ..., they fail to handle data that exposes a manifold structure, i.e. data that is not shaped in the form of point clouds, but forms paths through a high-dimensional space. Recently, Spectral Clustering =-=[2, 3]-=- has attracted a lot of attention for its ability to handle this type of data very well. Although Spectral Clustering algorithms have achieved Appearing in Proceedings of the 22 nd International Confe... |

31 | A new GPCA algorithm for clustering subspaces by fitting, differentiating and dividing polynomials
- Vidal, Ma, et al.
- 2004
(Show Context)
Citation Context ...for different sigmas is in table 3. Specifying the number of clusters, Self-Tuning Spectral Clustering results in an error rate of 0.5. 3.5. Yale Face-Database B We now consider the setup used the in =-=[12]-=- and use the Yale Face Database B [13]. We use images of individuals 2, 5 and 10 and down-sample each image to 30x40 pixels. This σ 0.2 0.3 0.4 0.6 0.8 Error, α = 0.99 0.59 0.476 0.656 0.83 0.83 Error... |

19 |
Observation of phase transitions in spreading activation networks
- Shrager, Hogg, et al.
- 1987
(Show Context)
Citation Context ... class using the classifying function: yi = arg maxj≤c Fij. We define a matrix U as: U = β (I − αS) −1 = � u T 1 , ..., u T � n (3) and note that U defines a graph or diffusion kernel as described in =-=[7, 8]-=-. The entries in the columns of U (we symbolize column i of matrix U by the column vector uT i ) contain the “activation” of all the points in the data set if point i were used for labeling. That mean... |

9 | Topological mapping with multiple visual manifolds
- Grudic, Mulligan
- 2005
(Show Context)
Citation Context ...ring learning. Section 3 presents detailed experimental results on both synthetic and real data. Section 4 concludes with future work. An extension of this work to the robotics domain can be found in =-=[6]-=-. Matlab code implementing the proposed clustering algorithm is available for download from the authors homepages. 2. Algorithm 2.1. Semi-Supervised Learning In [5] Zhou et.al. introduced the consiste... |