The Pyramid Match Kernel: Efficient Learning with Sets of Features

By Kristen Grauman, Trevor Darrell. 2007

426 citations recorded by the source corpus.

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Citations in the corpus

Nonparametric kernel estimators for image classification (2012, methodology): “For example, the shapes of objects can be represented by sets of local descriptors at edges and corner points [8].”
Approximate Nearest Neighbor: Towards Removing the Curse of Dimensionality (2012, background): “From a more general perspective, the existence of fast approximate nearest neighbor algorithms for high-dimensional (cid:96) 1 spaces enabled solving this problem for other metrics, by embedding them into (cid:96) 1 with low distortion.”
Visual Causal Feature Learning (2014, background): “Alternatives include other Lp-induced metrics, distances in implicit feature spaces induced by image kernels (Harchaoui and Bach, 2007; Grauman and Darrell, 2007; Bosch et al., 2007; Vishwanathan, 2010) and distances in learned representation spaces (Bengio et al., 2013).”
On Valid Optimal Assignment Kernels and Applications to Graph Classification (2016, methodology): “This includes structured data like images [2, 5, 11], 3d shapes [1], chemical compounds [8] and proteins [4], which are often represented by graphs.”
Learning query-dependent prefilters for scalable image retrieval (2009, background): “In [5], M sorted lists of projection values are maintained, so that an approximate minimum of |hq−hi| over all i can be found.”
Random Fourier Approximations for Skewed Multiplicative Histogram Kernels (2010, background): “A cheaper variant is the histogram intersection kernel [17], for which a computational trick for fast testing is available [18].”
Metric Learning: A Survey (2013, background): “For example, the pyramid match kernel [29] defines a notion of similarity between images based on comparing sets of local features between the images; this kernel has the property that, while the underlying representation of the feature space is extremely high dimensional, the kernel itself can be c”
Matching Node Embeddings for Graph Similarity (2017, methodology): “…is then defined as follows: kΔ(G1, G2) = I(H L G1 , H L G2) + L−1∑ l=0 1 2L−l ( I(H lG1 , H l G2) − I(H l+1G1 , H l+1G2 ) ) (6) The pyramid match kernel is a Mercer kernel (Grauman and Darrell 2007), hence, by computing it for all pairs of graphs, we can build a positive semidefinite kernel matrix.”
Differentially Private Learning with Kernels (2013, background): “However, their algorithms are restricted to the class of translation invariant kernels and does not capture a wide variety of kernels, e.g., polynomial kernels or pyramid match kernel from the computer vision domain (Grauman & Darrell, 2007).”
Fast and robust Earth Mover's Distances (2009, unknown): “Grauman and Darrell [13] substituted L 1 with histogram intersection in order to approximate partial matching.”
Efficient Subwindow Search: A Branch and Bound Framework for Object Localization (2009, unknown): “The former is popular in the context of the pyramid match kernel [17].”
Exploring Large Feature Spaces with Hierarchical Multiple Kernel Learning (2008, methodology): “We are currently investigating application s t other kernels, such as the pyramid match kernel [15], string kernels, and graph kernels [2].”
Data-driven suggestions for creativity support in 3D modeling (2010, methodology): “To overcome this problem, we use the pyramid match kernel [Grauman and Darrell 2007].”
Large scale image annotation: learning to rank with joint word-image embeddings (2010, background): “Much research in the literature has in fact concentrated on extracting better image features, then training independently simple classiﬁers such as linear or kernel SVMs for each category (for example Grauman and Darrell 2007).”
Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling (2010, methodology): “It can be done simply by presuming the kernels, or learning the mixture of kernels using techniques such as MKL (Multiple Kernel Learning), or PMK (Pyramid Match Kernel) (Lanckriet et al., 2004; Grauman and Darrell, 2007; Bosch et al., 2007).”
A survey on graph kernels (2019, methodology): “Additionally, they propose an alternative solution based on the pyramid match kernel, a generic kernel for comparing sets of features [75].”
Efficient Classification for Additive Kernel SVMs (2013, background): “There are two important classes of additive kernels used in the computer vision, which we describe next.”
Empowering Visual Categorization With the GPU (2011, background): “An example of the use of multiple features with weights is the spatial pyramid [46], [47].”
Palette power: enabling visual search through colors (2013, result): “Bag-of-Word (BoW) Based Approaches: This technique refers to representing an image by an orderless collection of local features [9].”