You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We propose an unsupervised object matching method for relational data, which finds matchings between objects in different relational datasets without correspondence information. For example, the proposed method matches documents in different languages in multi-lingual document-word networks without dictionaries nor alignment information. The proposed method assumes that each object has latent vectors, and the probability of neighbor objects is modeled by the inner-product of the latent vectors, where the neighbors are generated by short random walks over the relations. The latent vectors are estimated by maximizing the likelihood of the neighbors for each dataset. The estimated latent vectors contain hidden structural information of each object in the given relational dataset. Then, the proposed method linearly projects the latent vectors for all the datasets onto a common latent space shared across all datasets by matching the distributions while preserving the structural information. The projection matrix is estimated by minimizing the distance between the latent vector distributions with an orthogonality regularizer. To represent the distributions effectively, we use the kernel embedding of distributions that hold high-order moment information about a distribution as an element in a reproducing kernel Hilbert space, which enables us to calculate the distance between the distributions without density estimation. The structural information encoded in the latent vectors are preserved by using the orthogonality regularizer. We demonstrate the effectiveness of the proposed method with experiments using real-world multi-lingual document-word relational datasets and multiple user-item relational datasets.

Cited Abstract(s):
[1]: We propose a method for unsupervised many-to-many object matching from multiple networks, which is the task of finding correspondences between groups of nodes in different networks. For example, the proposed method can discover shared word groups from multi-lingual document-word networks without cross-language alignment information. We assume that multiple networks share groups, and each group has its own interaction pattern with other groups. Using infinite relational models with this assumption, objects in different networks are clustered into common groups depending on their interaction patterns, discovering a matching. The effectiveness of the proposed method is experimentally demonstrated by using synthetic and real relational data sets, which include applications to cross-domain recommendation without shared user item identifiers and multi-lingual word clustering.
The ReMatch method is an unsupervised cluster matching method for relational data [1] . The ReMatch assigns each object into a cluster that is shared across all datasets, and finds correspondence based on the cluster assignments. Therefore, multiple objects assigned into the same cluster cannot be distinguished, and there would be many ties when objects are ranked based on the estimated correspondence. In contrast, the proposed method estimates different continuous feature representations for different objects.