Generalized Unsupervised Manifold Alignment
In this paper, we propose a Generalized Unsupervised Manifold Alignment (GU-MA) method to build the connections between different but correlated datasets without any known correspondences. Based on the assumption that datasets of the same theme usually have similar manifold structures, GUMA is formulated into an explicit integer optimization problem considering the structure matching and preserving criteria, as well as the feature comparability of the corresponding points in the mutual embedding space. The main benefits of this model include: (1) simultaneous discovery and alignment of manifold structures; (2) fully unsupervised matching without any pre-specified correspondences; (3) efficient iterative alignment without computations in all permutation cases. Experimental results on dataset matching and real-world applications demonstrate the effectiveness and the practicability of our manifold alignment method.
This paper proposes an unsupervised method for aligning manifold structures of different datasets and finding correspondence between objects in different datasets. The proposed method is a combination of three objective functions: 1) geometry matching term, 2) feature matching term, and 3) geometry preserving term. In the learning procedures, matching objects and estimating projection matrices are alternately performed so as to maximize the objective function. In the experiments, the authors demonstrate the effectiveness of the proposed method comparing with unsupervised manifold alignment methods.The proposed method is the combination of three related methods as described below. Therefore, the novelty of the proposed method is limited. However, it is interesting to combine related frameworks to solve unsupervised manifold alignment, which is a very difficult problem. The proposed method achieved the good performance in the experiments.The geometry preserving term in the objective function is the same as that of unsupervised manifold alignment methods as described in the paper. The geometry matching term in the objective function is related to unsupervised object matching methods, such as kernelized sorting and least square object matching. Especially equation (3) is the same as that of convex kernelized sorting. Discussion on these unsupervised object matching methods should be added. The feature matching term is related to CCA (canonical correlation analysis) based unsupervised matching methods, such as matching CCA and many-to-many matching latent variable models. These methods find linear projection matrices and object correspondence.[kernelized sorting] Quadrianto, et al, Kernelized sorting, IEEE TPAMI, 2010[least square object matching] Yamada and Sugiyama, Cross-domain object matching with model selection, AISTATS, 2011[convex kernelized sorting] Djuric, et al, Convex kernelized sorting, AAAI, 2012[matching CCA] Haghighi, Learning bilingual lexicons from monolingual corpora, ACL, 2008[many-to-many latent variable model] Iwata et al, Unsupervised Cluster Matching via Probabilistic Latent Variable Models, AAAI, 2013In the face pose experiments, it seems that the similarity between different datasets can be calculated. So, it might be able to solve this task with (supervised) manifold alignment methods. Please clarify it is a task for unsupervised methods.