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.
The ReMatch method is an unsupervised cluster matching method for relational data @cite_51 . 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.
@cite_51
2261463483 1866515447 2119474464 2101639445
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. Joint matching over a collection of objects aims at aggregating information from a large collection of similar instances (e.g. images, graphs, shapes) to improve maps between pairs of them. Given multiple matches computed between a few object pairs in isolation, the goal is to recover an entire collection of maps that are (1) globally consistent, and (2) close to the provided maps --- and under certain conditions provably the ground-truth maps. Despite recent advances on this problem, the best-known recovery guarantees are limited to a small constant barrier --- none of the existing methods find theoretical support when more than @math of input correspondences are corrupted. Moreover, prior approaches focus mostly on fully similar objects, while it is practically more demanding to match instances that are only partially similar to each other. In this paper, we develop an algorithm to jointly match multiple objects that exhibit only partial similarities, given a few pairwise matches that are densely corrupted. Specifically, we propose to recover the ground-truth maps via a parameter-free convex program called MatchLift, following a spectral method that pre-estimates the total number of distinct elements to be matched. Encouragingly, MatchLift exhibits near-optimal error-correction ability, i.e. in the asymptotic regime it is guaranteed to work even when a dominant fraction @math of the input maps behave like random outliers. Furthermore, MatchLift succeeds with minimal input complexity, namely, perfect matching can be achieved as soon as the provided maps form a connected map graph. We evaluate the proposed algorithm on various benchmark data sets including synthetic examples and real-world examples, all of which confirm the practical applicability of MatchLift. We present a method to automatically learn object categories from unlabeled images. Each image is represented by an unordered set of local features, and all sets are embedded into a space where they cluster according to their partial-match feature correspondences. After efficiently computing the pairwise affinities between the input images in this space, a spectral clustering technique is used to recover the primary groupings among the images. We introduce an efficient means of refining these groupings according to intra-cluster statistics over the subsets of features selected by the partial matches between the images, and based on an optional, variable amount of user supervision. We compute the consistent subsets of feature correspondences within a grouping to infer category feature masks. The output of the algorithm is a partition of the data into a set of learned categories, and a set of classifiers trained from these ranked partitions that can recognize the categories in novel images. We present an efficient method for feature correspondence and object-based image matching, which exploits both photometric similarity and pairwise geometric consistency from local invariant features. We formulate object-based image matching as an unsupervised multi-class clustering problem on a set of candidate feature matches, and propose a novel pairwise dissimilarity measure and a robust linkage model in the framework of hierarchical agglomerative clustering. The algorithm handles significant amount of outliers and deformation as well as multiple clusters, thus enabling simultaneous feature matching and clustering from real-world image pairs with significant clutter and multiple deformable objects. The experimental evaluation on feature correspondence, object recognition, and object-based image matching demonstrates that our method is robust to both outliers and deformation, and applicable to a wide range of image matching problems.