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In this article, a semisupervised weighting method for feature dimension based on entropy is proposed for classification, dimension reduction, and correlation analysis. For real-world data, different feature dimensions usually show different importance. Generally, data in the same class are supposed to be similar, so their entropy should be small; and those in different classes are supposed to be dissimilar, so their entropy should be large. According to this, we propose a way to construct the weights of feature dimensions with the whole entropy and the innerclass entropies. The weights indicate the contribution of their corresponding feature dimensions in classification. They can be used to improve the performance of classification by giving a weighted distance metric and can be applied to dimension reduction and correlation analysis as well. Some numerical experiments are given to test the proposed method by comparing it with some other representative methods. They demonstrate that the proposed method is feasible and efficient in classification, dimension reduction, and correlation analysis.

Three-dimensional (3-D) data have many applications in the field of computer vision and a point cloud is one of the most popular modalities. Therefore, how to establish a good representation for a point cloud is a core issue in computer vision, especially for 3-D object recognition tasks. Existing approaches mainly focus on the invariance of representation under the group of permutations. However, for point cloud data, it should also be rotation invariant. To address such invariance, in this article, we introduce a relation of equivalence under the action of rotation group, through which the representation of point cloud is located in a homogeneous space. That is, two point clouds are regarded as equivalent when they are only different from a rotation. Our network is flexibly incorporated into existing frameworks for point clouds, which guarantees the proposed approach to be rotation invariant. Besides, a sufficient analysis on how to parameterize the group SO(3) into a convolutional network, which captures a relation with all rotations in 3-D Euclidean space [Formula: see text]. We select the optimal rotation as the best representation of point cloud and propose a solution for minimizing the problem on the rotation group SO(3) by using its geometric structure. To validate the rotation invariance, we combine it with two existing deep models and evaluate them on ModelNet40 dataset and its subset ModelNet10. Experimental results indicate that the proposed strategy improves the performance of those existing deep models when the data involve arbitrary rotations.

Transfer learning (TL) can effectively improve diagnosis accuracy of single-modal-imaging-based computer-aided diagnosis (CAD) by transferring knowledge from other related imaging modalities, which offers a way to alleviate the small-sample-size problem. However, medical imaging data generally have the following characteristics for the TL-based CAD: 1) The source domain generally has limited data, which increases the difficulty to explore transferable information for the target domain; 2) Samples in both domains often have been labeled for training the CAD model, but the existing TL methods cannot make full use of label information to improve knowledge transfer. In this work, we propose a novel doubly supervised transfer classifier (DSTC) algorithm. In particular, DSTC integrates the support vector machine plus (SVM+) classifier and the low-rank representation (LRR) into a unified framework. The former makes full use of the shared labels to guide the knowledge transfer between the paired data, while the latter adopts the block-diagonal low-rank (BLR) to perform supervised TL between the unpaired data. Furthermore, we introduce the Schatten-p norm for BLR to obtain a tighter approximation to the rank function. The proposed DSTC algorithm is evaluated on the Alzheimer's disease neuroimaging initiative (ADNI) dataset and the bimodal breast ultrasound image (BBUI) dataset. The experimental results verify the effectiveness of the proposed DSTC algorithm.

The Kullback-Leibler divergence (KLD), which is widely used to measure the similarity between two distributions, plays an important role in many applications. In this article, we address the KLD metric-learning task, which aims at learning the best KLD-type metric from the distributions of datasets. Concretely, first, we extend the conventional KLD by introducing a linear mapping and obtain the best KLD to well express the similarity of data distributions by optimizing such a linear mapping. It improves the expressivity of data distribution, which means it makes the distributions in the same class close and those in different classes far away. Then, the KLD metric learning is modeled by a minimization problem on the manifold of all positive-definite matrices. To deal with this optimization task, we develop an intrinsic steepest descent method, which preserves the manifold structure of the metric in the iteration. Finally, we apply the proposed method along with ten popular metric-learning approaches on the tasks of 3-D object classification and document classification. The experimental results illustrate that our proposed method outperforms all other methods.

In this paper, we propose a novel probabilistic variant of iterative closest point (ICP) dubbed as CoBigICP. The method leverages both local geometrical information and global noise characteristics. Locally, the 3D structure of both target and source clouds are incorporated into the objective function through bidirectional correspondence. Globally, error metric of correntropy is introduced as noise model to resist outliers. Importantly, the close resemblance between normal-distributions transform (NDT) and correntropy is revealed. To ease the minimization step, an on-manifold parameterization of the special Euclidean group is proposed. Extensive experiments validate that CoBigICP outperforms several well-known and state-of-the-art methods., Comment: 6 pages, 4 figures. Accepted to IROS2020

Graph has been widely used in various applications, while how to optimize the graph is still an open question. In this paper, we propose a framework to optimize the graph structure via structure evolution on graph manifold. We first define the graph manifold and search the best graph structure on this manifold. Concretely, associated with the data features and the prediction results of a given task, we define a graph energy to measure how the graph fits the graph manifold from an initial graph structure. The graph structure then evolves by minimizing the graph energy. In this process, the graph structure can be evolved on the graph manifold corresponding to the update of the prediction results. Alternatively iterating these two processes, both the graph structure and the prediction results can be updated until converge. It achieves the suitable structure for graph learning without searching all hyperparameters. To evaluate the performance of the proposed method, we have conducted experiments on eight datasets and compared with the recent state-of-the-art methods. Experiment results demonstrate that our method outperforms the state-of-the-art methods in both transductive and inductive settings.

Graph-based semi-supervised learning methods have been used in a wide range of real-world applications. However, existing methods limited along with high computational complexity or not facilitating incremental learning, which may not be powerful to deal with large-scale data, whose scale may continuously increase, in real world. This paper proposes a new method called Data Distribution Based Graph Learning (DDGL) for semi-supervised learning on large-scale data. This method can achieve a fast and effective label propagation and supports incremental learning. The key motivation is to propagate the labels along smaller-scale data distribution model parameters, rather than directly dealing with the raw data as previous methods, which accelerate the data propagation significantly. It also improves the prediction accuracy since the loss of structure information can be alleviated in this way. To enable incremental learning, we propose an adaptive graph updating strategy when there is distribution bias between new data and already seen data. We have conducted comprehensive experiments on multiple datasets with sizes increasing from seven thousand to five million. Experimental results on the classification task on large-scale data demonstrate that our proposed DDGL method improves the classification accuracy by a large margin while consuming much less time compared to state-of-art methods.

The accuracy of classification and retrieval significantly depends on the metric used to compute the similarity between samples. For preserving the geometric structure, the symmetric positive definite (SPD) manifold is introduced into the metric learning problem. However, the SPD constraint is too strict to describe the real data distribution. In this paper, we extend the intrinsic metric learning problem to semi-definite case, by which the data distribution is better described for various classification tasks. First, we formulate the metric learning as a minimization problem to the SPD manifold on subspace, which not only considers to balance the information between inner classes and inter classes by an adaptive tradeoff parameter but also improves the robustness by the low-rank subspaces presentation. Thus, it benefits to design a structure-preserving algorithm on subspace by using the geodesic structure of the SPD subspace. To solve this model, we develop an iterative strategy to update the intrinsic metric and the subspace structure, respectively. Finally, we compare our proposed method with ten state-of-the-art methods on four data sets. The numerical results validate that our method can significantly improve the description of the data distribution, and hence, the performance of the image classification task.

Background Robust evidence has shown that abnormal function networks, particularly the salience network (SN), are observed in depressed patients. Although white matter structural connectivity may predict time-varying functional connectivity, including symptom phenotype, in psychiatric disorders, there is still a gap in elucidating the concurrent dynamic functional and structural connectivity profiles of the SN in depressed patients. Methods We measured static and dynamic functional connectivity (FC) of the SN using resting-state fMRI BOLD time series in 76 subjects (21 with major depressive disorder (MDD), 27 with bipolar depression (BD), and 28 healthy controls (HC)). Hamilton Depression Scale total score was used to measure depression severity. Furthermore, we investigated the concurrent structural connectivity using diffusion kurtosis imaging (DKI)-based tractography. Results Our findings suggested that in the presence of MDD, both structural and dynamic (but not static) FC were reduced in the SN, particularly affecting the left prefronto-insular pathways (L.aPFC-L.insula). MDD patients showed decreased connectivity variability within the SN compared with HC. The aberrant dynamic FC in the prefronto-insular pathways of the SN related to severity of depressive symptoms in MDD. Furthermore, compared with BD patients, those with MDD showed significantly decreased dynamic FC in the left prefronto-parietal system (L.aPFC-lateral parietal cortex). Limitations The generalizability of our findings is, to some extent, constrained by the small sample size. Conclusions The integrity of SN connectivity, particularly the prefronto-insular pathway, appears to be a crucial signature of MDD. The perturbed dynamic interaction of SN with prefrontal regions may underlie the clinical severity in depressed patients.

In the field of autonomous driving, carriers are equipped with a variety of sensors, including cameras and LiDARs. However, the camera suffers from problems of illumination and occlusion, and the LiDAR encounters motion distortion, degenerate environment and limited ranging distance. Therefore, fusing the information from these two sensors deserves to be explored. In this paper, we propose a fusion network which robustly captures both the image and point cloud descriptors to solve the place recognition problem. Our contribution can be summarized as: (1) applying the trimmed strategy in the point cloud global feature aggregation to improve the recognition performance, (2) building a compact fusion framework which captures both the robust representation of the image and 3D point cloud, and (3) learning a proper metric to describe the similarity of our fused global feature. The experiments on KITTI and KAIST datasets show that the proposed fused descriptor is more robust and discriminative than the single sensor descriptor.

Elastography ultrasound (EUS) provides additional bio-mechanical information about lesion for B-mode ultrasound (BUS) in the diagnosis of breast cancers. However, joint utilization of both BUS and EUS is not popular due to the lack of EUS devices in rural hospitals, which arouses a novel modality imbalance problem in computer-aided diagnosis (CAD) for breast cancers. Current transfer learning (TL) pay little attention to this special issue of clinical modality imbalance, that is, the source domain (EUS modality) has fewer labeled samples than those in the target domain (BUS modality). Moreover, these TL methods cannot fully use the label information to explore the intrinsic relation between two modalities and then guide the promoted knowledge transfer. To this end, we propose a novel doubly supervised TL network (DDSTN) that integrates the Learning Using Privileged Information (LUPI) paradigm and the Maximum Mean Discrepancy (MMD) criterion into a unified deep TL framework. The proposed algorithm can not only make full use of the shared labels to effectively guide knowledge transfer by LUPI paradigm, but also perform additional supervised transfer between unpaired data. We further introduce the MMD criterion to enhance the knowledge transfer. The experimental results on the breast ultrasound dataset indicate that the proposed DDSTN outperforms all the compared state-of-the-art algorithms for the BUS-based CAD.

Deep learning has been successfully applied to the single-image super-resolution (SISR) task with superior performance in recent years. However, most convolutional neural network (CNN) based SR models have a large number of parameters to be optimized, which requires heavy computation and thereby limits their real-world applications. In this work, a novel lightweight SR network, named Adaptive Weighted Super-Resolution Network (LW-AWSRN), is proposed to address this issue. A novel local fusion block (LFB) is developed in LW-AWSRN for efficient residual learning, which consists of several stacked adaptive weighted residual units (AWRU) and a local residual fusion unit (LRFU). Moreover, an adaptive weighted multi-scale (AWMS) module is proposed to make full use of features for the reconstruction of HR images. The AWMS module includes several convolutions with multiple scales, and the redundancy scale branch can be removed according to the contribution of adaptive weights for the lightweight network. The experimental results on the commonly used datasets show that the proposed LW-AWSRN achieves superior performance on × 2, × 3, × 4, and × 8 scale factors compared to state-of-the-art methods with similar parameters and computational overhead. It suggests that LW-AWSRN has a better trade-off between reconstruction quality and model size.

In this paper, we address the semisupervised distance metric learning problem and its applications in classification and image retrieval. First, we formulate a semisupervised distance metric learning model by considering the metric information of inner classes and interclasses. In this model, an adaptive parameter is designed to balance the inner metrics and intermetrics by using data structure. Second, we convert the model to a minimization problem whose variable is symmetric positive-definite matrix. Third, in implementation, we deduce an intrinsic steepest descent method, which assures that the metric matrix is strictly symmetric positive-definite at each iteration, with the manifold structure of the symmetric positive-definite matrix manifold. Finally, we test the proposed algorithm on conventional data sets, and compare it with other four representative methods. The numerical results validate that the proposed method significantly improves the classification with the same computational efficiency.

In this paper, we address the unsupervised subspace learning from a geometric viewpoint. First, we formulate the subspace learning as an inverse problem on Grassmannian manifold by considering all subspaces as points on it. Then, to make the model computable, we parameterize the Grassmannian manifold by using an orbit of rotation group action on all standard subspaces, which are spanned by the orthonormal basis. Further, to improve the robustness, we introduce a low-rank regularizer which makes the dimension of subspace as low as possible. Thus, the subspace learning problem is transferred to a minimization problem with variables of rotation and dimension. Then, we adopt the alternately iterative strategy to optimize the variables, where a structure-preserving method, based on the geodesic structure of the rotation group, is designed to update the rotation. Finally, we compare the proposed approach with six state-of-the-art methods on three different kinds of real datasets. The experimental results validate that our proposed method outperforms all compared methods.

Nonlinear registration is an important technique to align two different images and widely applied in medical image analysis. In this paper, we develop a novel nonlinear registration framework based on the diffeomorphic demons, where a reciprocal regularizer is introduced to assume that the deformation between two images is an exact diffeomorphism. In detail, first, we adopt a bidirectional metric to improve the symmetry of the energy functional, whose variables are two reciprocal deformations. Secondly, we slack these two deformations into two independent variables and introduce a reciprocal regularizer to assure the deformations being the exact diffeomorphism. Then, we utilize an alternating iterative strategy to decouple the model into two minimizing subproblems, where a new closed form for the approximate velocity of deformation is calculated. Finally, we compare our proposed algorithm on two data sets of real brain MR images with two relative and conventional methods. The results validate that our proposed method improves accuracy and robustness of registration, as well as the gained bidirectional deformations are actually reciprocal.

Normalizing all images in a large data set into a common space is a key step in many clinical and research studies, e.g., for brain development, maturation, and aging. Recently, groupwise registration has been developed for simultaneous alignment of all images without selecting a particular image as template, thus potentially avoiding bias in the registration. However, most conventional groupwise registration methods do not explore the data distribution during the image registration. Thus, their performance could be affected by large inter-subject variations in the data set under registration. To solve this potential issue, we propose to use a graph to model the distribution of all image data sitting on the image manifold, with each node representing an image and each edge representing the geodesic pathway between two nodes (or images). Then, the procedure of warping all images to their population center turns to the dynamic shrinking of the graph nodes along their graph edges until all graph nodes become close to each other. Thus, the topology of image distribution on the image manifold is always preserved during the groupwise registration. More importantly, by modeling the distribution of all images via a graph, we can potentially reduce registration error since every time each image is warped only according to its nearby images with similar structures in the graph. We have evaluated our proposed groupwise registration method on both infant and adult data sets, by also comparing with the conventional group-mean based registration and the ABSORB methods. All experimental results show that our proposed method can achieve better performance in terms of registration accuracy and robustness.

In this study, the authors address a two-dimensional (2D) shape registration problem on data with anisotropic-scale deformation and noise. First, the model is formulated under the iterative closest point (ICP) framework, which is one of the most popular methods for shape registration. To overcome the effect of noise, the expectation maximisation algorithm is used to improve the model. Then, the structure of Lie groups is adopted to parameterise the proposed model, which provides a unified framework to deal with the shape registration problems. Such representation makes it possible to introduce some suitable constraints to the model, which improves the robustness of the algorithm. Thereby, the 2D shape registration problem is turned to an optimisation problem on the matrix Lie group. Furthermore, a sequence of quadratic programming is designed to approximate the solution for the model. Finally, several comparative experiments are carried out to validate that the authors’ algorithm performs well in terms of robustness, especially in the presence of outliers.

Changing the metric on the data may change the data distribution, hence a good distance metric can promote the performance of learning algorithm. In this paper, we address the semi-supervised distance metric learning (ML) problem to obtain the best nonlinear metric for the data. First, we describe the nonlinear metric by the multiple kernel representation. By this approach, we project the data into a high dimensional space, where the data can be well represented by linear ML. Then, we reformulate the linear ML by a minimization problem on the positive definite matrix group. Finally, we develop a two-step algorithm for solving this model and design an intrinsic steepest descent algorithm to learn the positive definite metric matrix. Experimental results validate that our proposed method is effective and outperforms several state-of-the-art ML methods.

The iterative closet point (ICP) method is a dominant method for data registration that has attracted extensive attention. In this paper, a unified mathematical model of ICP based on Lie group representation is established. Under the framework, the registration problem is formulated into an optimization problem over a certain Lie group. In order to simplify the model and to reduce the dimension of parameter space, the translation part of geometric transformation is eliminated by calibrating the centers of two data sets under registration. As a result, a fast algorithm by solving an iterative linear system is designed for the optimization problem on Lie groups. Moreover, PCA and ICA methods are jointly applied to estimate the initial registration to achieve the global minimum. Finally, several illustrations and comparison experiments are presented to test the performance of the proposed algorithm.

SUMMARY Weighted graph matching is computationally challenging due to the combinatorial nature of the set of permutations. In this paper, a new relaxation approach to weighted graph matching is proposed, by which a new matching algorithm, named alternate iteration algorithm, is designed. It is proved that the algorithm proposed is locally convergent. Experiments are presented to show the effectiveness of the proposed algorithm. eration algorithm.

Recently, group wise registration has been investigated for simultaneous alignment of all images without selecting any individual image as the template, thus avoiding the potential bias in image registration. However, none of current group wise registration method fully utilizes the image distribution to guide the registration. Thus, the registration performance usually suffers from large inter-subject variations across individual images. To solve this issue, we propose a novel group wise registration algorithm for large population dataset, guided by the image distribution on the manifold. Specifically, we first use a graph to model the distribution of all image data sitting on the image manifold, with each node representing an image and each edge representing the geodesic pathway between two nodes (or images). Then, the procedure of warping all images to their population center turns to the dynamic shrinking of the graph nodes along their graph edges until all graph nodes become close to each other. Thus, the topology of image distribution on the image manifold is always preserved during the group wise registration. More importantly, by modeling the distribution of all images via a graph, we can potentially reduce registration error since every time each image is warped only according to its nearby images with similar structures in the graph. We have evaluated our proposed group wise registration method on both synthetic and real datasets, with comparison to the two state-of-the-art group wise registration methods. All experimental results show that our proposed method achieves the best performance in terms of registration accuracy and robustness.

In this paper, we propose a novel inter-group image registration method to register different groups of images (e.g., young and elderly brains) simultaneously. Specifically, we use a hierarchical two-level graph to model the distribution of entire images on the manifold, with intra-graph representing the image distribution in each group and the inter-graph describing the relationship between two groups. Then the procedure of inter-group registration is formulated as a dynamic evolution of graph shrinkage. The advantage of our method is that the topology of entire image distribution is explored to guide the image registration. In this way, each image coordinates with its neighboring images on the manifold to deform towards the population center, by following the deformation pathway simultaneously optimized within the graph. Our proposed method has been also compared with other state-of-the-art inter-group registration methods, where our method achieves better registration results in terms of registration accuracy and robustness.