Efficient Kernels for identifying unbounded-order spatial features

Higher order spatial features, such as doublets or triplets have been used to incorporate spatial information into the bag-of-local-features model. Due to computational limits, researchers have only been using features up to the 3rd order, i.e., triplets, since the number of features increases exponentially with the order. We propose an algorithm for identifying high-order spatial features efficiently. The algorithm directly evaluates the inner product of the feature vectors from two images to be compared, identifying all high-order features automatically. The algorithm hence serves as a kernel for any kernel-based learning algorithms. The algorithm is based on the idea that if a high-order spatial feature co-occurs in both images, the occurrence of the feature in one image would be a translation from the occurrence of the same feature in the other image. This enables us to compute the kernel in time that is linear to the number of local features in an image (same as the bag of local features approach), regardless of the order. Therefore, our algorithm does not limit the upper bound of the order as in previous work. The experiment results on the object categorization task show that high order features can be calculated efficiently and provide significant improvement in object categorization performance.