Training a Support Vector Machine in the Primal

By Olivier Chapelle. 2007

898 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Optimization & Training, Statistical Learning Theory, Signal Processing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Computer Vision and Pattern Recognition

In Optimization & Training

In Statistical Learning Theory

In Signal Processing

Citations in the corpus

Interval Coded Scoring: a toolbox for interpretable scoring systems (2018, background): “Due to its formulation, it can be efﬁciently solved in the primal (Chapelle, 2006) with a complexity related to the number of data points rather than the size of the expanded feature space, which is usually greater.”
Fine-Grained Emotion Strength Transfer, Control and Prediction for Emotional Speech Synthesis (2020, methodology): “[17] proposed to estimate the w by solving the following problem through Newton’s method [21]:”
Differentially Private Empirical Risk Minimization (2009, positive): “For Huber SVM, we picked the Huber constant h = 0.5, a typical value (Chapelle, 2007)1.”
Learning in a Large Function Space: Privacy-Preserving Mechanisms for SVM Learning (2009, methodology): “However, note that the SVM primal can be iteratively optimized where each iterate is a function of sums over the data (Chapelle, 2007; Chu et al., 2006).”
Selective Transfer Machine for Personalized Facial Action Unit Detection (2013, methodology): “Using the representer theorem [8], the penalized SVM in (2) can be rewritten as:”
Controlling Emotion Strength with Relative Attribute for End-to-End Speech Synthesis (2019, neutral): “Details can be found in [30].”
Learning to Rank Using Privileged Information (2013, methodology): “Furthermore, in contrast to SVM+, we can use standard SVM packages to solve them, including efficient methods working in primal representation [4], and solvers based on stochastic gradient descent [22].”
Supervised classification and mathematical optimization (2013, background): “However, even though the usual is to work in the dual space, working with the primal problem (18)–(22) is receiving an increasing attention, [56, 132, 161, 223].”
Machine Learning Methods for Attack Detection in the Smart Grid (2015, methodology): “(12) The hyperplanewΨ is computed by solving the following optimization problem in primal or dual form [21], [22], [23]”
A Reduction of the Elastic Net to Support Vector Machines with an Application to GPU Computing (2014, methodology): “Both formulations of the SVM can be solved particularly efﬁciently on modern hardware with Newton’s Method [7, 9], which ofﬂoads the majority of the computation onto matrix operations and therefore can be vectorized and parallelized to achieve near peak computing performance [26].”
Sequential Max-Margin Event Detectors (2014, methodology): “However, unlike [4] we used an efficient line search algorithm adapted to SMMED.”
Sub-Sampled Newton Methods I: Globally Convergent Algorithms (2016, background): “Primal optimizations of linear SVMs have already been studied by [26, 15, 31].”
Approximating Concavely Parameterized Optimization Problems (2012, background): “In the kernel case one has the following primal SVM (see [2]),”
Interval Coded Scoring extensions for larger problems (2017, methodology): “using an iterative conjugated gradient approach as suggested by Chapelle [15].”
Large Margin Gaussian Mixture Models with Differential Privacy (2012, methodology): “For small values of the parameter h, Huber loss has similar characteristics as hinge loss and provides the same accuracy [15].”