Learning a Mahalanobis Metric from Equivalence Constraints

By Aharon Bar-Hillel, Tomer Hertz, Noam Shental, Daphna Weinshall. Journal of machine learning research, 2005

589 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/85ca6bf1968fe41603a0c08e097220652654c04e

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Citations in the corpus

Randomized Clustering Forests for Image Classification (2008, methodology): “This function is generally inspired by the Mahalanobis distance dðx; yÞ 1⁄4 ðx yÞAðx yÞ, as in [35] or, more recently, [58], [22], [50], [3], [21], [56].”
Survey on distance metric learning and dimensionality reduction in data mining (2014, methodology): “The goal of RCA is to 550 F. Wang, J. Sun find a transformation that amplifies relevant variability and suppresses irrelevant variability .”
PCCA: A new approach for distance learning from sparse pairwise constraints (2012, background): “Therefore, many approaches have tried to learn the distance using domain specific constraints [1, 10, 11, 14, 19, 21, 27, 30, 31, 33].”
Fast image search for learned metrics (2008, methodology): “Recent work has yielded various approaches to metric learning, including several techniques to learn a combination of existing kernels [19, 29], as well as methods to learn a Mahalanobis metric [30, 3, 8], and methods to learn example-specific local distance functions [10].”
Is that you? Metric learning approaches for face identification (2009, methodology): “In this section we present three methods to learn Mahalanobis metrics for visual identiﬁcation.”
Semi-Supervised Dimensionality Reduction (2007, methodology): “Utilizing domain knowledge has been an important issue in many data mining tasks [1, 16, 17].”
A Survey on Metric Learning for Feature Vectors and Structured Data (2013, unknown): “Relevant Component Analysis20 (Shental et al., 2002; Bar-Hillel et al., 2003, 2005) makes use of positive pairs only and is based on subsets of the training examples called “chunklets”.”
Recurrent Convolutional Network for Video-Based Person Re-identification (2016, methodology): “Various methods have been proposed based on this idea such as, Relaxed Pairwise Learning (PRLM) [14], Large Margin Nearest-Neighbour (LMNN) [44], and Relevance Component Analysis (RCA) [2].”
Distance Metric Learning for Large Margin Nearest Neighbor Classification (2006, methodology): “Finally, we briefly review relevant component analysis (RCA) (Shental et al., 2002; Bar-Hillel et al., 2006) in the context of distance metric learning.”
Image retrieval: Ideas, influences, and trends of the new age (2008, methodology): “One way to achieve this is to learn a generalized Mahalanobis distance metric, such as those general-purpose methods proposed in [Xing et al. 2003; Bar-hillel et al. 2005].”
On Deep Multi-View Representation Learning (2015, background): “ge. Metric l earning often uses side information in the form of pairs of similar/dissimilar samples, which may be known a priori or derived from class labels (Xing et al., 2003; Shental et al., 2002; Bar-Hillel et al., 2005; Tsang and Kwok, 2003; Schultz and Joachims,2004;Goldberger et al.,2005;Hoi ”
An introduction to domain adaptation and transfer learning (2018, background): “In order to avoid that the Mahalanobis metric pushes samples from different classes closer together for the sake of mapping source to target, it is necessary to include some constraints [10].”
Heterogeneous Metric Learning with Joint Graph Regularization for Cross-Media Retrieval (2013, background): “However, an underlying assumption shared by most of the metric learning methods (Bar-Hillel et al. 2005; Davis et al. 2007; K.Weinberger, Blitzer, and Saul 2006; Xing et al. 2002; Hoi, Liu, and Chang 2008; Park et al. 2011) is that all of the data share the same data representation.”
Distance Metric Learning for Large Margin Nearest Neighbor Classification (2005, methodology): “3 RELEVANT COMPONENT ANALYSIS Finally, we briefly review relevant component analysis (RCA) (Shental et al., 2002; Bar-Hillel et al., 2006) in the context of distance metric learning.”
Learning Distance Metrics with Contextual Constraints for Image Retrieval (2006, methodology): “The relevant dimensions are estimated by chunklets [2], each of them is deﬁned as a group of data instances linked together with positive constraints.”
Jointly Attentive Spatial-Temporal Pooling Networks for Video-Based Person Re-identification (2017, methodology): “In the meantime, metric learning methods such as large margin nearest neighbor (LMNN) [29], Ma-halanobis distance metric (RCA) [2], Locally Adaptive Decision Function (LADF) [13] and RankSVM [38] have also been applied to person re-id task.”
Hierarchical learning : theory with applications in speech and vision (2009, background): “Several recent attempts [7, 24, 101] have been made to construct a distance based on ideas related to PCA, and can in fact be summarized as “anti-PCA”: the goal is to learn a projection of the data under which variance along coordinates with a large amount of within-class scatter is eliminated.”
Dimensionality Reduction: A Comparative Review (2008, background): “Linear Discriminant Analysis [46], Generalized Discriminant Analysis [9], and Neighborhood Components Analysis [53, 106], and recently proposed metric learners [32, 8, 51, 137] are not included in the review, because of their supervised nature.”