In object recognition, the Bag-of-Words model assumes: i) extraction of local descriptors from images, ii) embedding these descriptors by a coder to a given visual vocabulary space which results in so-called mid-level features, iii) extracting statistics from mid-level features with a pooling operator that aggregates occurrences of visual words in images into so-called signatures. As the last step aggregates only occurrences of visual words, it is called as First-order Occurrence Pooling. This paper investigates higher-order approaches. We propose to aggregate over co-occurrences of visual words, derive Bag-of-Words with Second- and Higher-order Occurrence Pooling based on linearisation of so-called Minor Polynomial Kernel, and extend this model to work with adequate pooling operators. For bi- and multi-modal coding, a novel higher-order fusion is derived. We show that the well-known Spatial Pyramid Matching and related methods constitute its special cases. Moreover, we propose Third-order Occurrence Pooling directly on local image descriptors and a novel pooling operator that removes undesired correlation from the image signatures. Finally, Uni- and Bi-modal First-, Second-, and Third-order Occurrence Pooling are evaluated given various coders and pooling operators. The proposed methods are compared to other approaches (e.g. Fisher Vector Encoding) in the same testbed and attain state-of-the-art results.
