Efficient additive kernels via explicit feature maps

By Andrea Vedaldi, Andrew Zisserman. 2010

299 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical Learning Theory

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Citations in the corpus

Aggregating Local Image Descriptors into Compact Codes (2012, neutral): “Variance stabilizing transforms have previously been applied to BOW histograms, e.g. in [30] for GMM modeling and in [31], [32] for better separability of linear classiﬁers.”
Return of the Devil in the Details: Delving Deep into Convolutional Nets (2014, methodology): “Before use in classiﬁcation, the vector is signed-square-rooted and l 2 -normalised (square rooting correspond to the Hellinger’s kernel map [25]).”
A Multi-View Embedding Space for Modeling Internet Images, Tags, and Their Semantics (2012, methodology): “To handle large numbers of images and high-dimensional features, we propose a scalable approach based on the idea of approximate kernel maps (Maji and Berg, 2009; Perronnin et al., 2010; Rahimi and Recht, 2007; Vedaldi and Zisserman, 2010).”
Optimal Rates for Random Fourier Features (2015, background): “…this bottleneck, numerous solutions have been proposed, such as low-rank matrix approximations [28, 9, 1], explicit feature maps designed for additive kernels [26, 14], hashing [22, 12], and random Fourier features (RFF) [16] constructed for shift-invariant kernels, the focus of the current paper.”
Quasi-Monte Carlo Feature Maps for Shift-Invariant Kernels (2014, background): “Vedaldi and Zisserman [2011] developed feature maps for γ -homogeneous kernels.”
Video Representation Learning Using Discriminative Pooling (2018, methodology): “We avoid this issue by restricting our formulation to use only homogeneouskernels [49], as such kernels have explicit linear feature map embeddings on which a linear SVM can be trained directly.”
Orthogonal Random Features (2016, background): “Explicit nonlinear random feature maps have been constructed for many types of kernels, such as intersection kernels [16], generalized RBF kernels [23], skewed multiplicative histogram kernels [15], additive kernels [25], and polynomial kernels [12, 19].”
3D Object Detection with Multiple Kinects (2012, methodology): “We achieve a classiﬁcation accuracy of 57.8% with nearest-neighbors [15] and 59.4% with χ 2 kernel SVM [23], while [12] reports 64.7% using Spin Image [11] with a Gaussian kernel SVM.”
Generalization Properties of Learning with Random Features (2016, methodology): “In contrast with the previous examples, [43] suggest to select ω 1 , . . . , ω m by using a deterministic approach, in order to achieve a better accuracy, with respect to the random sampling with respect to π .”
Detecting activities of daily living in first-person camera views (2012, methodology): “We experimented with various histogram kernels [41], but found a simple linear kernel deﬁned on an L1-normalized feature to work well.”
The devil is in the details: an evaluation of recent feature encoding methods (2011, methodology): “Here all encodings are used in combination with linear SVMs (potentially after the computation of a suitable feature map as explained above), so that the optimal normalization is l2 [22].”