Paper:
Quantized Kernel Learning for Feature Matching
Matching local visual features is a crucial problem in computer vision and its accuracy greatly depends on the choice of similarity measure. As it is generally very difficult to design by hand a similarity or a kernel perfectly adapted to the data of interest, learning it automatically with as few assumptions as possible is preferable. However, available techniques for kernel learning suffer from several limitations, such as restrictive parametrization or scalability. In this paper, we introduce a simple and flexible family of non-linear kernels which we refer to as Quantized Kernels (QK). QKs are arbitrary kernels in the index space of a data quantizer, i.e., piecewise constant similarities in the original feature space. Quantization allows to compress features and keep the learning tractable. As a result, we obtain state-of-the-art matching performance on a standard benchmark dataset with just a few bits to represent each feature dimension. QKs also have explicit non-linear, low-dimensional feature mappings that grant access to Euclidean geometry for uncompressed features.

Review:
The paper provides a new algorithm for learning quantized kernels: kernels based on piecewise constant mappings of the features into a finite index space. The main motivation and application is identifying similar pairs in vision tasks. The method achieves significant improvement over state-of-the-art on a task of identifying patch pairs between images.Pros:1. The experimental results, while confined to a specific task, are very strong. The method, while slightly slower, improves ginificantly over state-of-the-art in several metrics and experimental conditions (e.g. explicit feature maps, compact codes).2. The experimental analysis of the learned kernels is deep and insightful to the nature of the specific problem and the way quantized kernels help approach it.3. The approach is novel. Quantized and compact descriptors have been hugely successful in vision applications. This paper takes these ideas into the realm of kernels and offers an interesting way to adaptively learn a quantized kernel.Cons:1. The paper is hard to follow, especially the technical details in section 3. Some examples:a. The definition of a quantizer is cumbersome, instead of just a function q:R^D -> {1,...,N}.b. The optimization algorithm is presented for the one-dimensional case with 2 labels. That is in itself a very easy problem to solve, with no need for the more complicated machinery as brought in the paper, which made it harder to follow for me. Later, there is mention of how to (very approximately) reduce the multi-dimensional, multi-label case to this simple case. This whole line of thought should be made more explicit and easier to follow.c. Last line of page 4: isn't b_1 the same for all t? If so, which t to choose? d. Should I conclude from lines 246-247 that the AQK kernel is actually a diagonal kernel?e. The logic of the subsection about sharing kernel matrices is particularly hard to follow, at least for someone not very familiar with these methods.I think the paper could benefit from an "algorithm" box stating explicitly how to solve the full dimensional, arbitrary N case, for both AQK and BQK. Misc.:1. The problem attempts to classify pairs in negative and positive pairs. Obviously not all pairs can be used for large datasets, especially since most will be negative. How are the pairs chosen in the experiments?2. In other similarity learning tasks it is common to learn a bilinear form such that a triplet order is preserved instead of positive and negative pairs. For example in "Learning a Distance Metric from a Network" by Shaw et al., NIPS 2011. Has this been tried in the context of the tasks used in this paper?3. Line 315 and table 1: it seems that for Adaptive+ the Optimized version does NOT improve performance significantly. It is on the same order as in the Adaptive case, where the authors claim there is no improvement.