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If we consider a matching that preserves high-order relationships among points in the same set, we can introduce a hypergraph-matching technique to search for correspondence according to high-order feature values. While graph matc...
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If we consider a matching that preserves high-order relationships among points in the same set, we can introduce a hypergraph-matching technique to search for correspondence according to high-order feature values. While graph matching has been widely studied, there is limited research available regarding hypergraph matching. In this paper, we formulate hypergraph matching in terms of tensors. Then, we reduce the hypergraph matching to a bipartite matching problem that can be solved in polynomial time. We then extend this hypergraph matching to attributed hypergraph matching using a combination of different attributes with different orders. We perform analyses that demonstrate that this method is robust when handling noisy or missing data and can achieve inexact graph matching. To the best of our knowledge, while attributed graph-matching and hypergraph-matching have been heavily researched, methods for attributed hypergraph matching have not been proposed before.
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Feature-based methods for image registration frequently encounter the correspondence problem. In this paper, we formulate feature-based image registration as a manifold alignment problem, and present a novel matching method for fi...
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Feature-based methods for image registration frequently encounter the correspondence problem. In this paper, we formulate feature-based image registration as a manifold alignment problem, and present a novel matching method for finding the correspondences among different images containing the same object. Different from the semi-supervised manifold alignment, our methods map the data sets to the underlying common manifold without using correspondence information. An iterative multiplicative updating algorithm is proposed to optimize the objective, and its convergence is guaranteed theoretically. The proposed approach has been tested for matching accuracy, and robustness to outliers. Its performance on synthetic and real images is compared with the state-of-the-art reference algorithms.
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Feature-based methods for image registration frequently encounter the correspondence problem. In this paper, we formulate feature-based image registration as a manifold alignment problem, and present a novel matching method for fi...
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Feature-based methods for image registration frequently encounter the correspondence problem. In this paper, we formulate feature-based image registration as a manifold alignment problem, and present a novel matching method for finding the correspondences among different images containing the same object. Different from the semi-supervised manifold alignment, our methods map the data sets to the underlying common manifold without using correspondence information. An iterative multiplicative updating algorithm is proposed to optimize the objective, and its convergence is guaranteed theoretically. The proposed approach has been tested for matching accuracy, and robustness to outliers. Its performance on synthetic and real images is compared with the state-of-the-art reference algorithms.
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The joint optimization of fidelity and commensurability (JOFC) manifold matching methodology embeds an omnibus dissimilarity matrix consisting of multiple dissimilarities on the same set of objects. One approach to this embedding ...
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The joint optimization of fidelity and commensurability (JOFC) manifold matching methodology embeds an omnibus dissimilarity matrix consisting of multiple dissimilarities on the same set of objects. One approach to this embedding optimizes the preservation of fidelity to each individual dissimilarity matrix together with commensurability of each given observation across modalities via iterative majorization of a raw stress error criterion by successive Guttman transforms. In this article, we exploit the special structure inherent to JOFC to exactly and efficiently compute the successive Guttman transforms, and as a result we are able to greatly speed up the JOFC procedure for both in-sample and out-of-sample embedding. We demonstrate the scalability of our implementation on both real and simulated data examples.
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Domain adaptation addresses the prediction problem in which the source and target data are sampled from different but related probability distributions. The key problem here lies in properly matching the distributions and learning...
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Domain adaptation addresses the prediction problem in which the source and target data are sampled from different but related probability distributions. The key problem here lies in properly matching the distributions and learning general feature representation for training the prediction model. In this article, we introduce a Domain Invariant and Agnostic Adaptation (DIAA) solution, which matches the source and target joint distributions, and simultaneously aligns the feature and domain label joint distribution to its marginal product. In particular, DIAA matches and aligns the distributions via a feature transformation, and compares the two kinds of distribution disparities uniformly under the Kullback-Leibler (KL) divergence. To approximate the two corresponding KL divergences from observed samples, we derive a linear-regression-like technique that fits linear models to different ratio functions under the quadratic loss. With the estimated KL divergences, learning the DIAA feature transformation is formulated as solving a Grassmannian minimization problem. Experiments on text and image classification tasks with varied nature demonstrate the success of our approach. (C) 2021 Elsevier B.V. All rights reserved.
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This study aimed to provide a basic description of the motor control strategy during bimanual isometric force control in healthy young adults. Thirty healthy young adults (mean age: 27.4 +/- 3.7 years) participated in the study. T...
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This study aimed to provide a basic description of the motor control strategy during bimanual isometric force control in healthy young adults. Thirty healthy young adults (mean age: 27.4 +/- 3.7 years) participated in the study. The subjects were instructed to press both hands simultaneously to match the target force level of 5%, 25%, and 50% bimanual maximum voluntary force using continuous visual feedback. Bimanual motor synergy and bimanual coordination, as well as force asymmetry, force accuracy, and force variability were compared. This study identified the specific motor control strategy of healthy young adults during bimanual isometric force control, indicating that they proportionally increased "good" and "bad" variabilities, resulting in comparable bimanual motor synergy as the target force level increased.
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Manifold matching works to identify embeddings of multiple disparate data spaces into the same low-dimensional space, where joint inference can be pursued. It is an enabling methodology for fusion and inference from multiple and m...
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Manifold matching works to identify embeddings of multiple disparate data spaces into the same low-dimensional space, where joint inference can be pursued. It is an enabling methodology for fusion and inference from multiple and massive disparate data sources. In this paper three methods of manifold matching are considered: PoM, which stands for Multidimensional Scaling (MDS) composed with Procrustes; CCA (Canonical Correlation Analysis) and JOFC (Joint Optimization of Fidelity and Commensura-bility). We present a comparative efficiency investigation of the three methods for a particular text document classification application.
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Image-to-image translation (I2I) has broad application prospects for assisting physicians in diagnosis of medical image missing scenarios. Considering that there is no medical I2I model constructed from a geometric view of simulta...
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Image-to-image translation (I2I) has broad application prospects for assisting physicians in diagnosis of medical image missing scenarios. Considering that there is no medical I2I model constructed from a geometric view of simultaneously preserving local manifold-value and global manifold structure, we propose an I2I model based on manifold-value correction and manifold matching (MMNet) to translate one modal image to another in a paired and unpaired fashion and preserve the texture details of the target model image. For local manifold-value preservation, each manifold-value of the generated image is aligned with the corresponding real image as much as possible by jointly optimizing the distribution corrector and the distribution generator. For global manifold structure preservation, three distance metrics are defined to globally reduce the difference between the manifold of the generated images and the manifold of the real images through optimizing the manifold matching loss. Experimental results demonstrate that the proposed MMNet outperforms multiple state-of-the-art GANs-based methods for MR image translation in both qualitative and quantitative measures.
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The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the action of reparameterization. Using a canonical decom...
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The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the action of reparameterization. Using a canonical decomposition of a path in a principal bundle, we introduce a simple algorithm that finds an optimal matching between two curves by computing the geodesic of the infinite-dimensional manifold of curves that is at all time horizontal to the fibers of the shape bundle. We focus on the elastic metric studied in Le Brigant (J Geom Mech 9(2):131-156, 2017) using the so-called square root velocity framework. The quotient structure of the shape bundle is examined, and in particular horizontality with respect to the fibers. These results are more generally given for any elastic metric. We then introduce a comprehensive discrete framework which correctly approximates the smooth setting when the base manifold has constant sectional curvature. It is itself a Riemannian structure on the product manifold Mn of discrete curves given by n points, and we show its convergence to the continuous model as the size n of the discretization goes to . Illustrations of geodesics and optimal matchings between discrete curves are given in the hyperbolic plane, the plane and the sphere, for synthetic and real data, and comparison with dynamic programming (Srivastava and Klassen in Functional and shape data analysis, Springer, Berlin, 2016) is established.
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At present, deep learning has been well applied in many fields. However, due to the high complexity of hypothesis space, numerous training samples are usually required to ensure the reliability of minimizing experience risk. There...
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At present, deep learning has been well applied in many fields. However, due to the high complexity of hypothesis space, numerous training samples are usually required to ensure the reliability of minimizing experience risk. Therefore, training a classifier with a small number of training examples is a challenging task. From a biological point of view, based on the assumption that rich prior knowledge and analogical association should enable human beings to quickly distinguish novel things from a few or even one example, we proposed a dynamic analogical association algorithm to make the model use only a few labeled samples for classification. To be specific, the algorithm search for knowledge structures similar to existing tasks in prior knowledge based on manifold matching, and combine sampling distributions to generate offsets instead of two sample points, thereby ensuring high confidence and significant contribution to the classification. The comparative results on two common benchmark datasets substantiate the superiority of the proposed method compared to existing data generation approaches for few-shot learning, and the effectiveness of the algorithm has been proved through ablation experiments.
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