# The pyramid match kernel: discriminative classification with sets of image features

@article{Grauman2005ThePM, title={The pyramid match kernel: discriminative classification with sets of image features}, author={Kristen Grauman and Trevor Darrell}, journal={Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1}, year={2005}, volume={2}, pages={1458-1465 Vol. 2} }

Discriminative learning is challenging when examples are sets of features, and the sets vary in cardinality and lack any sort of meaningful ordering. Kernel-based classification methods can learn complex decision boundaries, but a kernel over unordered set inputs must somehow solve for correspondences epsivnerally a computationally expensive task that becomes impractical for large set sizes. We present a new fast kernel function which maps unordered feature sets to multi-resolution histograms…

## 1,606 Citations

Pyramid Match Kernels: Discriminative Classification with Sets of Image Features (version 2)

- Computer Science
- 2006

A new fast kernel function is presented which maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in this space and is shown to be positive-definite, making it valid for use in learning algorithms whose optimal solutions are guaranteed only for Mercer kernels.

The Pyramid Match Kernel: Efficient Learning with Sets of Features

- Mathematics, Computer ScienceJ. Mach. Learn. Res.
- 2007

The pyramid match maps unordered feature sets to multi-resolution histograms and computes a weighted histogram intersection in order to find implicit correspondences based on the finest resolution histogram cell where a matched pair first appears.

Efficient Match Kernel between Sets of Features for Visual Recognition

- Computer Science, MathematicsNIPS
- 2009

It is shown that bag-of-words representations commonly used in conjunction with linear classifiers can be viewed as special match kernels, which count 1 if two local features fall into the same regions partitioned by visual words and 0 otherwise.

Dimension Amnesic Pyramid Match Kernel

- Computer ScienceAAAI
- 2008

A general, data-independent kernel to quantify the feature-set similarities is proposed, which gives an upper bound of approximation error independent of the dimension of local features, and achieves the desirable dimension-free property.

Probabilistic Kernel Combination for Hierarchical Object Categorization

- Computer Science
- 2009

This paper describes hierarchical discriminative probabilistic techniques for learning visual object category models, which recovers a nested set of object categories with chosen kernel combinations for discrimination at each level of the tree using a Gaussian Process based framework.

Multiple kernel learning with ICA: Local discriminative image descriptors for recognition

- Mathematics, Computer ScienceThe 2010 International Joint Conference on Neural Networks (IJCNN)
- 2010

This paper shows that the Kernel ICA descriptors based MKL supervised learning approach perform better than other descriptors for object recognition, since the ICA-based representation is localized.

Support Kernel Machines for Object Recognition

- Mathematics, Computer Science2007 IEEE 11th International Conference on Computer Vision
- 2007

Recent kernel learning techniques are exploited that show how learning SKMs can be formulated as a convex optimization problem, which can be solved efficiently using Sequential Minimal Optimization.

Efficient image matching with distributions of local invariant features

- Mathematics, Computer Science2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05)
- 2005

This work presents a method for efficiently comparing images based on their discrete distributions of distinctive local invariant features, without clustering descriptors, and evaluates the method with scene, object, and texture recognition tasks.

The Pyramid Match: Efficient Learning with Partial Correspondences

- Computer ScienceAAAI
- 2007

A general approximate matching technique is developed called pyramid match that measures partial match similarity in time linear in the number of feature vectors per set and forms a Mercer kernel, making it valid for use in many existing kernel-based learning methods.

Multiple kernel learning from sets of partially matching image features

- Mathematics, Computer Science2008 19th International Conference on Pattern Recognition
- 2008

This paper shows that MKL problem with a enhanced spatial pyramid match kernel can be solved efficiently using projected gradient method, and demonstrates the algorithm on classification tasks, which is based on a linear combination of the proposed kernels computed at multiple pyramid levels of image encoding.

## References

SHOWING 1-10 OF 35 REFERENCES

Building kernels from binary strings for image matching

- Medicine, Computer ScienceIEEE Transactions on Image Processing
- 2005

In the theoretical contribution of this work, it is shown that histogram intersection is a Mercer's kernel and the modifications under which a similarity measure based on the notion of Hausdorff distance is also a Mercer’s kernel are determined.

Non-Mercer Kernels for SVM Object Recognition

- Computer Science, MathematicsBMVC
- 2004

The Mercer property of matching kernels which mimic classical matching algorithms used in techniques based on points of interest are studied, and a new statistical approach of kernel positiveness is introduced, which can provide bounds on the probability that the Gram matrix is actually positive definite for kernels in large class of functions.

Shape matching and object recognition using low distortion correspondences

- Mathematics, Computer Science2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05)
- 2005

This work approaches recognition in the framework of deformable shape matching, relying on a new algorithm for finding correspondences between feature points, and shows results for localizing frontal and profile faces that are comparable to special purpose approaches tuned to faces.

A Kullback-Leibler Divergence Based Kernel for SVM Classification in Multimedia Applications

- Computer Science, MathematicsNIPS
- 2003

This paper suggests an alternative procedure to the Fisher kernel for systematically finding kernel functions that naturally handle variable length sequence data in multimedia domains and derives a kernel distance based on the Kullback-Leibler (KL) divergence between generative models.

Support vector machines for histogram-based image classification

- Mathematics, Computer ScienceIEEE Trans. Neural Networks
- 1999

It is observed that a simple remapping of the input x(i)-->x(i)(a) improves the performance of linear SVM's to such an extend that it makes them, for this problem, a valid alternative to RBF kernels.

Learning to detect objects in images via a sparse, part-based representation

- Computer Science, MedicineIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2004

A learning-based approach to the problem of detecting objects in still, gray-scale images that makes use of a sparse, part-based representation is developed and a critical evaluation of the approach under the proposed standards is presented.

SVMs for Histogram Based Image Classification

- Mathematics
- 1999

Traditional classification approaches generalize poorly on image classification tasks, because of the high dimensionality of the feature space. This paper shows that Support Vector Machines (SVM) can…

Recognition with local features: the kernel recipe

- Computer ScienceProceedings Ninth IEEE International Conference on Computer Vision
- 2003

Large-scale recognition results are presented, which demonstrate that SVMs with the proposed kernel perform better than standard matching techniques on local features and that local feature representations significantly outperform global approaches.

Learning over Sets using Kernel Principal Angles

- Mathematics, Computer ScienceJ. Mach. Learn. Res.
- 2003

A new positive definite kernel f(A,B) defined over pairs of matrices A,B is derived based on the concept of principal angles between two linear subspaces and it is shown that the principal angles can be recovered using only inner-products between pairs of column vectors of the input matrices thereby allowing the original column vectors to be mapped onto arbitrarily high-dimensional feature spaces.

Multiresolution histograms and their use for recognition

- Computer Science, MedicineIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2004

A simple yet novel matching algorithm based on the multiresolution histogram that uses the differences between histograms of consecutive image resolutions to achieve or exceed the performance obtained with more complicated features.