This paper addresses the problem of set-to-set matching, which involves matching two different sets of items based on some criteria, especially in the case of high-dimensional items like images. Although neural networks have been applied to solve this problem, most machine learning-based approaches assume that the training and test data follow the same distribution, which is not always true in real-world scenarios. To address this limitation, we introduce SHIFT15M, a dataset that can be used to evaluate set-to-set matching models when the distribution of data changes between training and testing. We conduct benchmark experiments that demonstrate the performance drop of naive methods due to distribution shift. Additionally, we provide software to handle the SHIFT15M dataset in a simple manner, with the URL for the software to be made available after publication of this manuscript. We believe proposed SHIFT15M dataset provide a valuable resource for evaluating set-to-set matching models under the distribution shift.

The problem of matching two sets of multiple elements, namely set-to-set matching, has received a great deal of attention in recent years. In particular, it has been reported that good experimental results can be obtained by preparing a neural network as a matching function, especially in complex cases where, for example, each element of the set is an image. However, theoretical analysis of set-to-set matching with such black-box functions is lacking. This paper aims to perform a generalization error analysis in set-to-set matching to reveal the behavior of the model in that task.

Matching two sets of items, called set-to-set matching problem, is being recently raised. The difficulties of set-to-set matching over ordinary data matching lie in the exchangeability in 1) set-feature extraction and 2) set-matching score; the pair of sets and the items in each set should be exchangeable. In this paper, we propose a deep learning architecture for the set-to-set matching that overcomes the above difficulties, including two novel modules: 1) a cross-set transformation and 2) cross-similarity function. The former provides the exchangeable set-feature through interactions between two sets in intermediate layers, and the latter provides the exchangeable set matching through calculating the cross-feature similarity of items between two sets. We evaluate the methods through experiments with two industrial applications, fashion set recommendation, and group re-identification. Through these experiments, we show that the proposed methods perform better than a baseline given by an extension of the Set Transformer, the state-of-the-art set-input function.