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.
@cite_37: The goal of cross-domain object matching (CDOM) is to find correspondence between two sets of objects in different domains in an unsupervised way. Photo album summarization is a typical application of CDOM, where photos are automatically aligned into a designed frame expressed in the Cartesian coordinate system. CDOM is usually formulated as finding a mapping from objects in one domain (photos) to objects in the other domain (frame) so that the pairwise dependency is maximized. A state-of-the-art CDOM method employs a kernel-based dependency measure, but it has a drawback that the kernel parameter needs to be determined manually. In this paper, we propose alternative CDOM methods that can naturally address the model selection problem. Through experiments on image matching, unpaired voice conversion, and photo album summarization tasks, the effectiveness of the proposed methods is demonstrated.
@cite_1: Kernelized sorting is a method for aligning objects across two domains by considering within-domain similarity, without a need to specify a cross-domain similarity measure. In this paper we present the Convex Kernelized Sorting method where, unlike in the previous approaches, the cross-domain object matching is formulated as a convex optimization problem, leading to simpler optimization and global optimum solution. Our method outputs soft alignments between objects, which can be used to rank the best matches for each object, or to visualize the object matching and verify the correct choice of the kernel. It also allows for computing hard one-to-one alignments by solving the resulting Linear Assignment Problem. Experiments on a number of cross-domain matching tasks show the strength of the proposed method, which consistently achieves higher accuracy than the existing methods.
@cite_32: We present a method for learning bilingual translation lexicons from monolingual corpora. Word types in each language are characterized by purely monolingual features, such as context counts and orthographic substrings. Translations are induced using a generative model based on canonical correlation analysis, which explains the monolingual lexicons in terms of latent matchings. We show that high-precision lexicons can be learned in a variety of language pairs and from a range of corpus types.
@cite_56: Matching of samples refers to the problem of inferring unknown co-occurrence or alignment between observations in two data sets. Given two sets of equally many samples, the task is to nd for each sample a representative sample in the other set, without prior knowledge on a distance measure between the sets. Recently a few alternative solutions have been suggested, based on maximization of joint likelihood or various measures of between-data statistical dependency. In this work we present an variational Bayesian solution for the problem, learning a Bayesian canonical correlation analysis model with a permutation parameter for re-ordering the samples in one of the sets. We approximate the posterior over the permutations, and demonstrate that the resulting matching algorithm clearly outperforms all of the earlier solutions.
@cite_23: Matching of object refers to the problem of inferring unknown co-occurrence or alignment between observations or samples in two data sets. Given two sets of equally many samples, the task is to find for each sample a representative sample in the other set, without prior knowledge on a distance measure between the sets. Given a distance measure, the problem would correspond to a linear assignment problem, the problem of finding a permutation that re-orders samples in one set to minimize the total distance. When no such measure is available, we need to consider more complex solutions. Typical approaches maximize statistical dependency between the two sets, whereas in this work we present a Bayesian solution that builds a joint model for the two sources. We learn a Bayesian canonical correlation analysis model that includes a permutation parameter for re-ordering the samples in one of the sets. We provide both variational and sampling-based inference for approximative Bayesian analysis, and demonstrate on three data sets that the resulting methods outperform the earlier solutions.
@cite_58: 
A number of unsupervised object matching methods have been proposed @cite_32 @cite_58 @cite_1 @cite_56 @cite_23 @cite_37 , such as kernelized sorting @cite_58 and Bayesian object matching @cite_23 . However, these methods are not for relational data. In addition, these methods do not scale to large data since they find correspondence by estimating a (probabilistic) permutation matrix with the size of the square of the number of objects. On the other hand, the proposed method scales well since it estimates a projection matrix with the size of the square of the latent space dimensionality, which is much smaller than the number of objects.