We present a multiway fusion algorithm capable of directly processing uncertain pairwise affinities. In contrast to existing works that require initial pairwise associations, our MIXER algorithm improves accuracy by leveraging the additional information provided by pairwise affinities. Our main contribution is a multiway fusion formulation that is particularly suited to processing non-binary affinities and a novel continuous relaxation whose solutions are guaranteed to be binary, thus avoiding the typical, but potentially problematic, solution binarization steps that may cause infeasibility. A crucial insight of our formulation is that it allows for three modes of association, ranging from non-match, undecided, and match. Exploiting this insight allows fusion to be delayed for some data pairs until more information is available, which is an effective feature for fusion of data with multiple attributes/information sources. We evaluate MIXER on typical synthetic data and benchmark datasets and show increased accuracy against the state of the art in multiway matching, especially in noisy regimes with low observation redundancy. Additionally, we collect RGB data of cars in a parking lot to demonstrate MIXER's ability to fuse data having multiple attributes (color, visual appearance, and bounding box). On this challenging dataset, MIXER achieves 74% F1 accuracy and is 49x faster than the next best algorithm, which has 42% accuracy. Open source code is available at https://github.com/mit-acl/mixer.

翻译：我们提出了一种能够直接处理不确定成对亲和度的多路融合算法。与现有需要初始成对关联的方法不同，我们的MIXER算法通过利用成对亲和度提供的额外信息来提高精度。主要贡献在于提出了一种特别适合处理非二元亲和度的多路融合公式，以及一种新颖的连续松弛方法，其解保证为二元形式，从而避免了典型但可能因解的二值化步骤导致不可行性的问题。该公式的一个关键洞见是允许三种关联模式：不匹配、未定和匹配。利用这一洞见，可以在获取更多信息之前延迟对某些数据对的融合，这是融合具有多个属性/信息源的数据的有效特性。我们在典型合成数据和基准数据集上评估了MIXER，结果表明其在多路匹配中相较于现有技术提高了精度，尤其是在观测冗余度低的高噪声场景下。此外，我们收集了停车场中汽车的RGB数据，以展示MIXER融合具有多个属性（颜色、视觉外观和边界框）数据的能力。在此具有挑战性的数据集中，MIXER达到了74%的F1精度，且速度比次优算法（42%精度）快49倍。开源代码可通过https://github.com/mit-acl/mixer获取。