Classi cation by Pairwise Coupling

By Trevor J. Hastie, Robert Tibshirani. 1998

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Citations in the corpus

Auditing black-box models for indirect influence (2016, methodology): “We built two models that are notoriously opaque to simple examination; SVMs 6 [12] and feedforward neural networks (FNNs).”
Special Invited Paper-Additive logistic regression: A statistical view of boosting (2000, background): “By considering all of the classes simultaneously, the symmetric multiclass model is better able to take advantage of simple pairwise boundaries when they exist [Hastie and Tibshirani (1998)].”
On building ensembles of stacked denoising auto-encoding classifiers and their further improvement (2018, methodology): “There are two basic binarization techniques, One versus One (OvO) and One versus Rest (OvR) [49,50] .”
Boosting for Tumor Classification with Gene Expression Data (2003, unknown): “More sophisticated and computationally more expensive approaches for reducing multiclass to binary problems also exist, see Hastie and Tibshirani (1998) or Allwein et al. (2000) for a thorough discussion.”
Multi-group support vector machines with measurement costs: A biobjective approach (2008, methodology): “Now we compare the deﬁnition of separability given in Deﬁnition 1 with those existing in the literature, [1, 19, 20, 32].”
Analysing the classification of imbalanced data-sets with multiple classes: Binarization techniques and ad-hoc approaches (2013, methodology): “The OVO approach [34] tries to train a classiﬁer for each possible pair of classes, ignoring the examples that do not belong to the related classes.”
Matrix estimation by Universal Singular Value Thresholding (2012, background): “Numerous extensions and applications have been proposed, for example [54, 3, 82, 80, 71, 72, 58].”
Transforming classifier scores into accurate multiclass probability estimates (2002, methodology): “This method was proposed as an extension to the pairwise coupling method [14] matrices.”
Multi-class Classification without Multi-class Labels (2019, unknown): “The most well-known strategies are "one-vs-all" (Anand et al., 1995; Rifkin & Klautau, 2004) and "one-vs-one" (Knerr et al., 1990; Hastie & Tibshirani, 1998; Wu et al., 2004).”
Multicategory Support Vector Machines, Theory, and Application to the Classiﬁcation of Microarray Data and Satellite Radiance Data (2002, methodology): “…have been attempts to map outputs of classi ers to conditional probabilities for various classi - cation methods, including the SVM, in multiclass problems (see Zadrozny and Elkan 2002; Passerini, Pontil, and Frasconi 2002; Price, Knerr, Personnaz, and Dreyfus 1995; Hastie and Tibshirani 1998).”
Beyond One-hot Encoding: lower dimensional target embedding (2018, background): “The reason is the fact that random gaussian matrices tend to follow the coding properties described in the literature [12, 19], such as row and column orthogonality.”
Round Robin Classification (2002, methodology): “Along similar lines, there have been several proposals for combining the class probability estimates of the pairwise classiﬁers into class probability distributions for the multi-class problems (Price et al., 1995; Hastie and Tibshirani, 1998).”
A Unified View on Multi-class Support Vector Classification (2016, unknown): “As an OVO approach inevitably requires some additional non-canonical decision making procedure diﬀerent from (1) (e.g., Hastie and Tibshirani, 1998; Platt et al., 2000; Chang and Lin, 2011) and the optimal choice of this procedure is highly task-dependent, OVO-type approaches are out of the scope…”
Multilabel classification via calibrated label ranking (2008, background): “…performance for neural networks (Knerr et al. 1990, 1992; Price et al. 1995; Lu and Ito 1999), support vector machines (Schmidt and Gish 1996; Hastie and Tibshirani 1998; Kreßel 1999; Hsu and Lin 2002), statistical learning (Bradley and Terry 1952; Friedman 1996), rule and decision tree…”
A comparative study of feature selection and multiclass classification methods for tissue classification based on gene expression (2004, background): “One-versus-the-restmethod(Scholkopf and Smola, 2002; Bottou et al ., 1994), pairwise comparison (Kreeel, 1999; Hastie and Tibshirani, 1998; Friedman, 1996), error-correcting output coding (Dietterich and Bakiri, 1991, 1995; Allwein et al ., 2000) and multiclass objective functions (Weston and…”
Statistical ranking and combinatorial Hodge theory (2008, methodology): “Such methods are also getting increasing attention from the machine learning community as they may be adapted for studying classiﬁcation problems [19, 17, 20].”
On the Learnability and Design of Output Codes for Multiclass Problems (2002, methodology): “Several family of codes have been suggested and tested so far, such as, comparing each class against the rest, comparing all pairs of classes [11, 2], random codes [8, 19, 2], exhaustive codes [8, 2], and linear error correcting codes [8].”
Binarized Support Vector Machines (2010, methodology): “In this paper, we restrict ourselves to the case in which two classes exist, (cid:1) = (cid:7) − 1 (cid:8) 1 (cid:9) , since the multiclass case can be reduced to a series of two-class problems, as has been suggested, e.g., in Hastie and Tibshirani (1998), Herbrich (2002), and Vapnik (1998).”