Efficient Additive Kernels via Explicit Feature Maps

By Andrea Vedaldi, Andrew Zisserman. 2012

1,049 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Representation & Self-Supervised Learning

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 Representation & Self-Supervised Learning

Citations in the corpus

Aggregating Local Image Descriptors into Compact Codes (2012, methodology): “for GMM modeling and in [31], [32] for better separability”
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 l2-normalised (square rooting correspond to the Hellinger’s kernel map [29]).”
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).”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “See also Kar and Karnick (2012), Vedaldi and Zisserman (2012), Le et al. (2013), Pham and Pagh (2013) and references therein for a generalization of this idea.”
Optimal Rates for Random Fourier Features (2015, positive): “In this paper, we provide the first detailed theoretical analysis about the approximation quality of RFFs by establishing optimal (in terms of the RFF dimension) performance guarantees in uniform and Lr (1 ≤ r ∞) norms.”
Compact Bilinear Pooling (2015, methodology): “This was later extended for the intersection kernel, χ(2) kernel and the exponential χ(2) kernel [35, 25, 36].”
Scalable Kernel Methods via Doubly Stochastic Gradients (2014, background): “Explicit random features have been designed for many other kernels, such as dot product kernel [28], additive/multiplicative class of homogeneous kernels [29], e.”
Orthogonal Random Features (2016, background): “2 Related Works Explicit nonlinear random feature maps have been constructed for many types of kernels, such as intersection kernels [15], generalized RBF kernels [22], skewed multiplicative histogram kernels [14], additive kernels [24], and polynomial kernels [11, 18].”
Label-Embedding for Image Classification (2015, neutral): “This includes work on patch encoding (see [40] for a recent comparison), on kernel-based methods [41] with a recent focus on explicit embeddings [42], [43], on dimensionality reduction [41] and on compression [44], [45], [46].”
Three things everyone should know to improve object retrieval (2012, methodology): “This approach has been explored in the context of kernel maps for SVM classifiers by [22, 31].”
Blocks That Shout: Distinctive Parts for Scene Classification (2013, methodology): “In order to use non-linear additive kernels instead of the linear one, the χ(2) explicit feature map of [33] is used (the bag of parts and bag of words histograms are l(1) normalized).”
Learning latent temporal structure for complex event detection (2012, methodology): “In addition, because [16] uses a χ(2)-SVM, we use the method of additive kernels [25] to approximate a χ(2) kernel for our BoW features to maintain efficient processing while increasing discriminative power.”
Vlfeat: an open and portable library of computer vision algorithms (2010, background): “Much better results can be obtained by pre-transforming the data through vl_homkermap, which computes an explicit feature map that“emulates”a non linear χ(2)-kernel as a linear one [16].”