Constraint selection in metric learning

Capitaine, Hoël Le

doi:10.1016/j.knosys.2018.01.026

Cited by 13 publications

(13 citation statements)

References 24 publications

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“…For example, considering a two class problem having 100 instances in each class, the number of possible triplets is 1, 980, 000. Since dealing with a huge number of triplets causes prohibitive computations, a small subset of triplets are sometimes used in practice (e.g., [10]) though the optimality of such a sub-sampling strategy is not clearly understood. Our safe triplet screening enables the identification of triplets which can be safely removed from the optimization problem without losing the optimality of the resulting metric.…”

Section: Introductionmentioning

confidence: 99%

Safe Triplet Screening for Distance Metric Learning

Yoshida

Takeuchi

Karasuyama

2018

Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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We study safe screening for metric learning. Distance metric learning can optimize a metric over a set of triplets, each one of which is defined by a pair of same class instances and an instance in a different class. However, the number of possible triplets is quite huge even for a small dataset. Our safe triplet screening identifies triplets which can be safely removed from the optimization problem without losing the optimality. Compared with existing safe screening studies, triplet screening is particularly significant because of (1) the huge number of possible triplets, and (2) the semi-definite constraint in the optimization. We derive several variants of screening rules, and analyze their relationships. Numerical experiments on benchmark datasets demonstrate the effectiveness of safe triplet screening.

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Section: Introductionmentioning

confidence: 99%

Safe Triplet Screening for Distance Metric Learning

Yoshida

Takeuchi

Karasuyama

2018

Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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“…The Manhattan distance is used instead of the Euclidean distance. We do not need to consider the absolute values of w (t,k) because the weights are restricted by condition (5) such that their values are non-negative. Moreover, we rewrite the second term in the following form:…”

Section: The Disdf Training and Testingmentioning

confidence: 99%

“…The numerical experiments illustrate the proposed distance metric algorithm. of supervised distance metric learning is cast into pairwise constraints: the equivalence constraints where pairs of data points that belong to the same classes, and inequivalence constraints where pairs of data points belong to different classes.Metric learning approaches were reviewed in [1,5,14,29]. The basic idea underlying the metric learning solution is that the distance between similar objects should be smaller than the distance between different objects.…”

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confidence: 99%

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Discriminative Metric Learning with Deep Forest

Utkin

Ryabinin

2019

Int. J. Artif. Intell. Tools

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A Discriminative Deep Forest (DisDF) as a metric learning algorithm is proposed in the paper. It is based on the Deep Forest or gcForest proposed by Zhou and Feng and can be viewed as a gcForest modification. The case of the fully supervised learning is studied when the class labels of individual training examples are known. The main idea underlying the algorithm is to assign weights to decision trees in random forest in order to reduce distances between objects from the same class and to increase them between objects from different classes. The weights are training parameters. A specific objective function which combines Euclidean and Manhattan distances and simplifies the optimization problem for training the DisDF is proposed. The numerical experiments illustrate the proposed distance metric algorithm. of supervised distance metric learning is cast into pairwise constraints: the equivalence constraints where pairs of data points that belong to the same classes, and inequivalence constraints where pairs of data points belong to different classes.Metric learning approaches were reviewed in [1,5,14,29]. The basic idea underlying the metric learning solution is that the distance between similar objects should be smaller than the distance between different objects. If we have two observation vectors x i ∈ R m and x j ∈ R m from a training set, and the similarity of objects is defined by their belonging to the same class, then the distance d(x i , x j ) between the vectors should be minimized if x i and x j belong to the same class, and it should be maximized if x i and x j are from different classes. Several review papers analyze various methods and algorithms of metric learning [12,19,27]. A powerful implementation of the metric learning dealing with non-linear data structures is the so-called Siamese neural network introduced by Bromley et al. [4] in order to solve signature verification as a problem of image matching. This network consists of two identical sub-networks joined at their outputs. The two sub-networks extract features from two input examples during training, while the joining neuron measures the distance between the two feature vectors. The Siamese architecture has been exploited in many applications, for example, in face verification [7], in the one-shot learning in which predictions are made given only a single example of each new class [13], in constructing an inertial gesture classification [2], in deep learning [24], in extracting speaker-specific information [6], for face verification in the wild [11]. This is only a part of successful applications of Siamese neural networks. Many modifications of Siamese networks have been developed, including fully-convolutional Siamese networks [3], Siamese networks combined with a gradient boosting classifier [15], Siamese networks with the triangular similarity metric [29].A new powerful method, which can be viewed as an alternative to deep neural networks, is the deep forest proposed by Zhou and Feng [30] and called the gcForest. It can be compared with ...

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“…It is pointed out by Bellet et al [1] in their review paper that the metric learning aims to adapt the pairwise real-valued metric function, for example, the Mahalanobis distance or the Euclidean distance, to a problem of interest using the information provided by training data. A detailed description of the metric learning approaches is also represented by Le Capitaine [5] and by Kulis [14]. The basic idea underlying the metric learning solution is that the distance between similar objects should be smaller than the distance between different objects.…”

Section: Introductionmentioning

confidence: 99%