Generalized RBF feature maps for Eficient Detection

Sreekanth Vempati, Andrea Vedaldi, Andrew Zisserman and C. V. Jawahar

Overview

In this work we propose feature maps for generalized RBF kernels and show how this helps in efficient object detection. Kernel methods yield state-of-the-art performance in certain applications such as image classification and object detection. However, large scale problems require machine learning techniques of at most linear complexity and these are usually limited to linear kernels. This unfortunately rules out gold-standard kernels such as the generalized RBF kernels (e.g. exponential-chisquare). Recently, Maji and Berg (ICCV 2009) and Vedaldi and Zisserman (CVPR 2010) proposed explicit feature maps to approximate the additive kernels (intersection, chi-square, etc.) by linear ones, thus enabling the use of fast machine learning technique in a non-linear context. An analogous technique was proposed by Rahimi and Recht (NIPS 2007) for the translation invariant RBF kernels. In this paper, we complete the construction and combine the two techniques to obtain explicit feature maps for the generalized RBF kernels. Furthermore, we investigate a learning method using l1 regularization to encourage sparsity in the final vector representation, and thus reduce its dimension. We evaluate this technique on the VOC 2007 detection challenge, showing when it can improve on fast additive kernels, and the trade-offs in complexity and accuracy.

Results

Here you can see, how average precision and the testing time vary with different levels of approximation. In the graph we compare AP and testing time for classifying VOC 2007 test data (car category) using exact and approximate versions of exponential and chi-square kernel. We can see that approximate version of exponential chi-square kernel is faster than exact version, with only a slight loss in performance.
Here SVM-dense, SVM-sparse and LR-sparse are the proposed approximate versions of "exponential-chisquare kernel" and "exact exp-chisquare" is the exact version of "exact exponential-chisquare kernel".

In the below figure, we can observe the similar trends for other classes present in the VOC 2007 data.

Top 15 detections for the "car" category of VOC2007 data using approximate exponential-chisquare kernel can be seen below.

Publication

Acknowledgements