Neural Information Processing Systems http://nips.cc/

The problem of matching not just two, but m different sets of objects to each other arises in a variety of contexts, including finding the correspondence between feature points across multiple images in computer vision. At present it is usually solved by matching the sets pairwise, in series. In contrast, we propose a new method, permutation synchronization, which finds all the matchings jointly, in one shot, via a relaxation to eigenvector decomposition. The resulting algorithm is both computationally efficient, and, as we demonstrate with theoretical arguments as well as experimental results, much more stable to noise than previous methods.

W e propose an efficient and robust iterative solution to the multi-object matching problem.

Weaknesses: - The presentation can be largely improved: some of the sentences do not help the reader and currently the draft is not easy to read. For instance, the transition to the second paragraph of the introduction is quite abrupt: while the first paragraph talks about keypoints and images, the keypoints disappear when talking about the permutation synchronization. Moreover, the sigma is not properly defined. Similarly, Section 4.1 is hard to read: while the overall idea is clear, the reader gets trapped in too many details, such as those in lines 196-199. Similar comments hold for Section 4.2: why presenting two techniques when you recommend using only one? While I understand the desire of the authors to be comprehensive, mentioning too many details may compromise clarity.

The problem of matching not just two, but m different sets of objects to each other arises in many contexts, including finding the correspondence between feature points across multiple images in computer vision. At present it is usually solved by matching the sets pairwise, in series. In contrast, we propose a new method, Permutation Synchronization, which finds all the matchings jointly, in one shot, via a relaxation to eigenvector decomposition. The resulting algorithm is both computationally efficient, and, as we demonstrate with theoretical arguments as well as experimental results, much more stable to noise than previous methods.

We propose a novel non-negative spherical relaxation for optimization problems over binary matrices with injectivity constraints, which in particular has applications in multi-matching and clustering. We relax respective binary matrix constraints to the (high-dimensional) non-negative sphere. To optimize our relaxed problem, we use a conditional power iteration method to iteratively improve the objective function, while at same time sweeping over a continuous scalar parameter that is (indirectly) related to the universe size (or number of clusters). Opposed to existing procedures that require to fix the integer universe size before optimization, our method automatically adjusts the analogous continuous parameter. Furthermore, while our approach shares similarities with spectral multi-matching and spectral clustering, our formulation has the strong advantage that we do not rely on additional post-processing procedures to obtain binary results. Our method shows compelling results in various multi-matching and clustering settings, even when compared to methods that use the ground truth universe size (or number of clusters).

We propose an efficient and robust iterative solution to the multi-object matching problem. We first clarify serious limitations of current methods as well as the inappropriateness of the standard iteratively reweighted least squares procedure. In view of these limitations, we suggest a novel and more reliable iterative reweighting strategy that incorporates information from higher-order neighborhoods by exploiting the graph connection Laplacian. We demonstrate the superior performance of our procedure over state-of-the-art methods using both synthetic and real datasets.

The problem of matching not just two, but m different sets of objects to each other arises in a variety of contexts, including finding the correspondence between feature points across multiple images in computer vision. At present it is usually solved by matching the sets pairwise, in series. In contrast, we propose a new method, permutation synchronization, which finds all the matchings jointly, in one shot, via a relaxation to eigenvector decomposition. The resulting algorithm is both computationally efficient, and, as we demonstrate with theoretical arguments as well as experimental results, much more stable to noise than previous methods. Papers published at the Neural Information Processing Systems Conference.

The algorithmic advancement of synchronizing maps is important in order to solve a wide range of practice problems with possible large-scale dataset. In this paper, we provide theoretical justifications for spectral techniques for the map synchronization problem, i.e., it takes as input a collection of objects and noisy maps estimated between pairs of objects, and outputs clean maps between all pairs of objects. We show that a simple normalized spectral method that projects the blocks of the top eigenvectors of a data matrix to the map space leads to surprisingly good results. As the noise is modelled naturally as random permutation matrix, this algorithm NormSpecSync leads to competing theoretical guarantees as state-of-the-art convex optimization techniques, yet it is much more efficient. We demonstrate the usefulness of our algorithm in a couple of applications, where it is optimal in both complexity and exactness among existing methods.

The problem of matching not just two, but m different sets of objects to each other arises in a variety of contexts, including finding the correspondence between feature points across multiple images in computer vision. At present it is usually solved by matching the sets pairwise, in series. In contrast, we propose a new method, permutation synchronization, which finds all the matchings jointly, in one shot, via a relaxation to eigenvector decomposition. The resulting algorithm is both computationally efficient, and, as we demonstrate with theoretical arguments as well as experimental results, much more stable to noise than previous methods.