#### DMCA

## Learning neighborhoods for metric learning (2012)

Venue: | In ECMLPKDD |

Citations: | 2 - 0 self |

### Citations

2381 | Nonlinear dimensionality reduction by locally linear embedding
- Roweis, Saul
- 2000
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Citation Context ...) 85.63(0.0) 92.05 (3.5) 91.08 (3.5) MNIST 97.66(6.0) 97.66(6.0)= 97.73(6.0)== 96.91 (2.0) 96.97 (2.0) 96.58 (1.5) 96.93 (1.5) 97.09 (3.0) Total Score 33 37.5 41.5 16 16.5 8.5 20 23 manifold learning =-=[11]-=-. Most often the similarity graphs in these methods are constructed in the original space, which nevertheless can be quite different from true manifold on which the data lies. These methods could also... |

1888 |
Theory of linear and integer programming
- Schrijver
- 1986
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Citation Context ...totally unimodular matrix. Thus, the constraint matrix B = [I,−I,A,−A]T in the following equivalent problem also is a totally unimodular matrix (pp.268 Learning Neighborhoods for Metric Learning 7 in =-=[12]-=-). min p pT f s.t. Bp ≤ e e = ( 1, · · · , 1︸ ︷︷ ︸P cl n2cl −n , 0, · · · , 0︸ ︷︷ ︸P cl n2cl −n ,Kmax, · · · ,Kmax︸ ︷︷ ︸ n , Kav ∗ n,−Kmin, · · · ,−Kmin︸ ︷︷ ︸ n ,−Kav ∗ n)T (5) Since e is an integer v... |

1454 | Gradient-based learning applied to document recognition.
- LeCun, Bottou, et al.
- 1998
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Citation Context ...ning repository, Sonar, Ionosphere, Iris, Balance, Wine, Letter, Isolet; four text mining datasets, Function, Alt, Disease and Structure, which were constructed from biological corpora [7]; and MNIST =-=[8]-=-, a handwritten digit recognition problem. A more detailed description of the datasets is given in Table 1. Since LMNN is computationally expensive for datasets with large number of features we applie... |

796 | Distance metric learning with application to clustering with side-information
- Xing, Ng, et al.
- 2003
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Citation Context ... defined as: DM(xi,xj) = (xi − xj)TM(xi − xj) (1) where M is a Positive Semi-Definite (PSD) matrix (M 0) that we will learn. We can reformulate many of the existing metric learning methods, such as =-=[19, 13, 3, 10, 18]-=-, by explicitly parametrizing the target neighborhood relations as follows: min M,Ξ ∑ ij,i 6=j,yi=yj Pij · Fij(M,Ξ) (2) s.t. constraints of the original problem The matrix P,Pij ∈ {0, 1}, describes th... |

677 | Distance metric learning for large margin nearest neighbor classification
- Weinberger, Blitzer, et al.
- 2006
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Citation Context ...eve constraints can be relaxed with the incorporation of slack variables [13, 2, 10, 9]. With a local target neighborhood the satisfiability of the constraints is examined within a local neighborhood =-=[4, 17, 10, 18]-=-. For any given instance we only need to ensure that we satisfy the constraints that involve that instance and instances from its local neighborhood. The resulting problem is considerably less constra... |

556 | A tutorial on spectral clustering.
- Luxburg
- 2007
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Citation Context ... can indeed improve the predictive performance. The target neighborhood matrix P is strongly related to the similarity graphs which are often used in semi-supervised learning [6], spectral clustering =-=[15]-=- and Learning Neighborhoods for Metric Learning 13 Table 2. Accuracy results. The superscripts +−= next to the LN-XXXX accuracy indicate the result of the McNemar’s statistical test result of its comp... |

339 | Information-theoretic metric learning
- Davis, Kulis, et al.
- 2007
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Citation Context ...iting prior knowledge that comes in different forms. The most well studied metric learning paradigm is that of learning the Mahalanobis metric with a steadily expanding literature over the last years =-=[19, 13, 3, 2, 10, 18, 9, 5, 16]-=-. Metric learning for classification relies on two interrelated concepts, similarity and dissimilarity constraints, and the target neighborhood. The latter defines for any given instance the instances... |

333 | Neighbourhood component analysis
- Goldberger, Roweis, et al.
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Citation Context ...nd by f the respective vectorized version of the Fij terms. Then we rewrite Problem 3 as: min p pT f s.t. (Kmax, · · · ,Kmax︸ ︷︷ ︸ n ,Kav ∗ n)T ≥ Ap ≥ (Kmin, · · · ,Kmin︸ ︷︷ ︸ n ,Kav ∗ n)T 1 ≥ pi ≥ 0 =-=(4)-=- The first and second constraints of Problem 3 are reformulated as the first constraint in Problem 4. A is a (n+1)× (∑cl n2cl −n) constraint matrix, where ncl is the number of instances in class cl A ... |

222 | Metric learning by collapsing classes
- Globerson, Roweis
- 2006
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Citation Context ...iting prior knowledge that comes in different forms. The most well studied metric learning paradigm is that of learning the Mahalanobis metric with a steadily expanding literature over the last years =-=[19, 13, 3, 2, 10, 18, 9, 5, 16]-=-. Metric learning for classification relies on two interrelated concepts, similarity and dissimilarity constraints, and the target neighborhood. The latter defines for any given instance the instances... |

191 | Learning a distance metric from relative comparisons
- Schultz, Joachims
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Citation Context ...iting prior knowledge that comes in different forms. The most well studied metric learning paradigm is that of learning the Mahalanobis metric with a steadily expanding literature over the last years =-=[19, 13, 3, 2, 10, 18, 9, 5, 16]-=-. Metric learning for classification relies on two interrelated concepts, similarity and dissimilarity constraints, and the target neighborhood. The latter defines for any given instance the instances... |

155 | Is that you? Metric learning approaches for face identification
- Guillaumin, Verbeek, et al.
- 2009
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61 | Graph construction and b-matching for semisupervised learning
- Jebara, Wang, et al.
- 2009
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Citation Context ...learning the neighborhood can indeed improve the predictive performance. The target neighborhood matrix P is strongly related to the similarity graphs which are often used in semi-supervised learning =-=[6]-=-, spectral clustering [15] and Learning Neighborhoods for Metric Learning 13 Table 2. Accuracy results. The superscripts +−= next to the LN-XXXX accuracy indicate the result of the McNemar’s statistic... |

52 | Stability of feature selection algorithms: a study on high-dimensional spaces
- Kalousis, Prados, et al.
- 2007
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Citation Context ...CI machine learning repository, Sonar, Ionosphere, Iris, Balance, Wine, Letter, Isolet; four text mining datasets, Function, Alt, Disease and Structure, which were constructed from biological corpora =-=[7]-=-; and MNIST [8], a handwritten digit recognition problem. A more detailed description of the datasets is given in Table 1. Since LMNN is computationally expensive for datasets with large number of fea... |

42 |
Some notes on alternating optimization
- Bezdek, Hathaway
- 2002
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Citation Context ...erage number of target neighbor per instance. It holds by construction that Kmax ≥ Kav ≥ Kmin. We should note here that we relax the target neighborhood matrix so that its elements Pij take values in =-=[0, 1]-=- (third constraint). However, we will show later that a solution Pij ∈ {0, 1} is obtained, given some natural constraints on the Kmin, Kmax and Kav parameters. 3.1 Target neighbor assignment rule Unli... |

29 | Linear and Integer Programming: Theory and Practice - Sierksma - 2002 |

12 | Metric Learning with Multiple Kernels
- Wang, Do, et al.
- 2011
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7 | Metric Learning: A Support Vector Approach
- Nguyen, Guo
- 2008
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5 | Geometry-aware metric learning
- Lu, Jain, et al.
- 2009
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1 |
Regularized neighborhood component analysis
- Yang, Laaksonen
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Citation Context ...ance, thus having a small distance, while the others will be pushed further away. NCA thus learns the local target neighborhood as a part of the optimization. Nevertheless it is prone to overfitting, =-=[20]-=-, and does not scale to large datasets. The large margin nearest neighbor method (LMNN) described in [17, 18] learns a distance metric which directly minimizes the distances of each instance to its lo... |