Research Group of Prof. Dr. C. Sminchisescu
Mathematical Sciences




RandFeat: Random Fourier Approximations for Skewed Multiplicative Histogram Kernels

Fuxin Li, Catalin Ionescu and Cristian Sminchisescu


Version 1.0, released on 7th October 2010



This is our implementation of RandFeat. It includes a number of other methods of approximation for different kernels and allows one to compare among them. It includes the following kernels:

Kernel Type Formula Approximation
Gaussian multiplicative Monte Carlo [Rahimi and Recht 2007]
Laplacian multiplicative Monte Carlo [Rahimi and Recht 2007]
Intersection additive Signal Theoretic [Vedaldi and Zisserman 2010]
additive Signal Theoretic [Vedaldi and Zisserman 2010]
skewed multiplicative Monte Carlo [Li, Ionescu and Sminchisescu 2010]

The system has been tested on MATLAB 7.9 and 7.10 on a Linux 64-bit machine with 8 Gb of memory.
For details see the README file in the package below.

Download RandFeat: [code].
This package is free for academic use only. No warranty.



References:

Random Fourier Approximations for Skewed Multiplicative Histogram Kernels
Fuxin Li, Catalin Ionescu, Cristian Sminchisescu
Lecture Notes in Computer Science 6376. Proceedings of 32nd DAGM Symposium. DAGM prize paper

If you use our system, please cite the paper, and the current website for the particular release:

@inproceedings{lis_dagm10,
title = {Random Fourier Approximations for Skewed Multiplicative Histogram Kernels},
author = {Fuxin Li and Catalin Ionescu and Cristian Sminchisescu},
year = {2010},
month = {September},
booktitle = {Lecture Notes for Computer Science. Proceedings of the DAGM Symposium.},
note = {DAGM paper prize},
pdf = {http://sminchisescu.ins.uni-bonn.de/papers/lis_dagm10.pdf}
}

@misc{randfeat-release1,
author = "Fuxin Li, Catalin Ionescu, Cristian Sminchisescu",
title = "RandFeat: Random Fourier Approximations for Skewed Multiplicative Histogram Kernels, Release 1",
howpublished = "http://sminchisescu.ins.uni-bonn.de/code/randfeat/randfeat-release1.tar.gz"}



Performance:

Error on approximation of a HOG kernel with 1700 input dimension:


Classification performance with the bow_features.mat (in the package) extracted from PASCAL VOC'09 training set.

>> DEMO_classification
Training model with linear kernel.
Accuracy = 33.1043% (530/1601)
Training model with random Fourier features on additive chi-square kernel.
Accuracy = 59.4628% (952/1601)
Training model with random Fourier features on Gaussian kernel.
Accuracy = 60.6496% (971/1601)
Training model with random Fourier features on Laplacian kernel.
Accuracy = 61.8364% (990/1601)
Training model with random Fourier features on skewed chi-square kernel.
Accuracy = 64.5222% (1033/1601)