Cakewalk Sampling

We study the task of finding good local optima in combinatorial optimization problems. Although combinatorial optimization is NP-hard in general, locally optimal solutions are frequently used in practice. Local search methods however typically converge to a limited set of optima that depend on their initialization. Sampling methods on the other hand can access any valid solution, and thus can be used either directly or alongside methods of the former type as a way for finding good local optima. Since the effectiveness of this strategy depends on the sampling distribution, we derive a robust learning algorithm that adapts sampling distributions towards good local optima of arbitrary objective functions. As a first use case, we empirically study the efficiency in which sampling methods can recover locally maximal cliques in undirected graphs. Not only do we show how our adaptive sampler outperforms related methods, we also show how it can even approach the performance of established clique algorithms. As a second use case, we consider how greedy algorithms can be combined with our adaptive sampler, and we demonstrate how this leads to superior performance in k-medoid clustering. Together, these findings suggest that our adaptive sampler can provide an effective strategy to combinatorial optimization problems that arise in practice.Comment: Accepted as a conference paper by AAAI-2020 (oral presentation

Class-Based Feature Matching Across Unrestricted Transformations

We develop a novel method for class-based feature matching across large changes in viewing conditions. The method is based on the property that when objects share a similar part, the similarity is preserved across viewing conditions. Given a feature and a training set of object images, we first identify the subset of objects that share this feature. The transformation of the feature's appearance across viewing conditions is determined mainly by properties of the feature, rather than of the object in which it is embedded. Therefore, the transformed feature will be shared by approximately the same set of objects. Based on this consistency requirement, corresponding features can be reliably identified from a set of candidate matches. Unlike previous approaches, the proposed scheme compares feature appearances only in similar viewing conditions, rather than across different viewing conditions. As a result, the scheme is not restricted to locally planar objects or affine transformations. The approach also does not require examples of correct matches. We show that by using the proposed method, a dense set of accurate correspondences can be obtained. Experimental comparisons demonstrate that matching accuracy is significantly improved over previous schemes. Finally, we show that the scheme can be successfully used for invariant object recognition