Multicategory Support Vector Machines, Theory, and Application to the Classiﬁcation of Microarray Data and Satellite Radiance Data

By Yoonkyung Lee, Yi Lin, Grace Wahba, I. J. Schoenberg Professor. 2002

Subfields: Statistical Learning Theory, Computational Biology & Bioinformatics

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Citations in the corpus

Estimating Individualized Treatment Rules Using Outcome Weighted Learning (2012, background): “The case of multicategory SVM has been studied recently (Lee, Lin, and Wahba 2004; Wang and Shen 2006), and a similar generalization may be possible for ﬁnding ITRs involving three or more treatments.”
Robust LogitBoost and Adaptive Base Class (ABC) LogitBoost (2010, methodology): “, the sum-to-zero constraint, is usually adopted [8, 7, 17, 11, 16, 19, 18].”
Robust Truncated Hinge Loss Support Vector Machines (2007, background): “We note that our extension of the SVM from the binary case to the multicategory case is not unique; some other extensions include those of Vapnik (1998), Weston and Watkins (1999), Bredensteiner and Bennett (1999), and Lee, Lin, and Wahba (2004).”
Ultrahigh dimensional feature selection: beyond the linear model (2009, methodology): “For the multicategory classification we use the loss function proposed by Lee et al. (2004). Denote the coefficients for the kth class by β0k and βk for k = 1, 2, 3, 4, and let B = ((β01,β T 1 ) T , (β02,β T 2 ) T , (β03,β T 3 ) T , (β04,β T 4 ) T ).”
A Unified View on Multi-class Support Vector Classification (2016, methodology): “In addition to these popular methods, we consider the machine by Lee et al. (2004), a variant proposed by Liu and Yuan (2011), as well as multi-class maximum margin regression (Szedmak et al., 2006).”
Cross-Entropy Loss Functions: Theoretical Analysis and Applications (2023, background): “For multiclass classification, the authors derived such guarantees for the so-called sum-losses, such as the sum-exponential loss function of Weston & Watkins (1998), and constrained losses, such as the loss function of Lee et al. (2004), where the scores (logits) must sum to zero.”
Good Practice in Large-Scale Learning for Image Classification (2014, unknown): “[46] introduced a statistically consistent version of multi-class SVM, which can be thought of a “hinge-loss” counterpart of multinomial classiﬁcation.”
Recent Advances of Large-Scale Linear Classification (2012, methodology): “In contrast to using many binary models, some have proposed solving a single optimization problem for multiclass classification [59]–[61].”
Vector valued reproducing kernel Hilbert spaces and universality (2008, background): “In machine learning there is an increasing interest for vector valued learning algorithms, see [ 20 , 12, 4]. In this framework, the basic object is a Hilbert space of functions f from a set X into a normed vector space Y with the property that, for any x ∈ X, k f(x)k ≤ Cx k f k for a positive const”