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Zernike circular polynomials (ZCP) play a significant role in optics engineering. The symbolic expressions for ZCP are valuable for theoretic analysis and engineering designs. However, there are still two problems which remain open: firstly, there is a lack of sufficient mathematical formulas of the ZCP for optics designers; secondly the formulas for inter-conversion of Noll’s single index and Born-Wolf’s double indices of ZCP are neither uniquely determinate nor satisfactory. An automatic method for generating symbolic expressions for ZCP is proposed based on five essential factors: the new theorems for converting the single/double indices of the ZCP, the robust and effective numeric algorithms for computing key parameters of ZCP, the symbolic algorithms for generating mathematical expressions of ZCP, and meta-programming & LATEX programming for generating the table of ZCP. The theorems, method, algorithms and system architecture proposed are beneficial to both optics design process, optics software, computer-output typesetting in publishing industry as well as STEM education.

Multiview subspace clustering (MVSC) leverages the complementary information among different views of multiview data and seeks a consensus subspace clustering result better than that using any individual view. Though proved effective in some cases, existing MVSC methods often obtain unsatisfactory results since they perform subspace analysis with raw features that are often of high dimensions and contain noises. To remedy this, we propose a self-guided deep multiview subspace clustering (SDMSC) model that performs joint deep feature embedding and subspace analysis. SDMSC comprehensively explores multiview data and strives to obtain a consensus data affinity relationship agreed by features from not only all views but also all intermediate embedding spaces. With more constraints being cast, the desirable data affinity relationship is supposed to be more reliably recovered. Besides, to secure effective deep feature embedding without label supervision, we propose to use the data affinity relationship obtained with raw features as the supervision signals to self-guide the embedding process. With this strategy, the risk that our deep clustering model being trapped in bad local minima is reduced, bringing us satisfactory clustering results in a higher possibility. The experiments on seven widely used datasets show the proposed method significantly outperforms the state-of-the-art clustering methods. Our code is available at https://github.com/kailigo/dmvsc.git. [ABSTRACT FROM AUTHOR]

Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS2C) problem, that is, partitioning million data points with a millon dimensions. To address this, we explore an independent distributed and parallel framework by dividing big data/variable matrices and regularization by both columns and rows. Specifically, LS2C is independently decomposed into many subproblems by distributing those matrices into different machines by columns since the regularization of the code matrix is equal to a sum of that of its submatrices (e.g., square-of-Frobenius/ $\ell _{1}$ -norm). Consensus optimization is designed to solve these subproblems in a parallel way for saving communication costs. Moreover, we provide theoretical guarantees that LS2C can recover consensus subspace representations of high-dimensional data points under broad conditions. Compared with the state-of-the-art LS2C methods, our approach achieves better clustering results in public datasets, including a million images and videos. [ABSTRACT FROM AUTHOR]

Kinship recognition is a challenging problem with many practical applications. With much progress and milestones having been reached after ten years, we are now able to survey the research and create new milestones. We review the public resources and data challenges that enabled and inspired many to hone-in on the views of automatic kinship recognition in the visual domain. The different tasks are described in technical terms and syntax consistent across the problem domain and the practical value of each discussed and measured. State-of-the-art methods for visual kinship recognition problems, whether to discriminate between or generate from, are examined. As part of such, we review systems proposed as part of a recent data challenge held in conjunction with the 2020 IEEE Conference on Automatic Face and Gesture Recognition. We establish a stronghold for the state of progress for the different problems in a consistent manner. This survey will serve as the central resource for the work of the next decade to build upon. For the tenth anniversary, the demo code is provided for the various kin-based tasks. Detecting relatives with visual recognition and classifying the relationship is an area with high potential for impact in research and practice. [ABSTRACT FROM AUTHOR]

Semi-supervised domain adaptation (SSDA) is quite a challenging problem requiring methods to overcome both 1) overfitting towards poorly annotated data and 2) distribution shift across domains. Unfortunately, a simple combination of domain adaptation (DA) and semi-supervised learning (SSL) methods often fail to address such two objects because of training data bias towards labeled samples. In this paper, we introduce an adaptive structure learning method to regularize the cooperation of SSL and DA. Inspired by the multi-views learning, our proposed framework is composed of a shared feature encoder network and two classifier networks, trained for contradictory purposes. Among them, one of the classifiers is applied to group target features to improve intra-class density, enlarging the gap of categorical clusters for robust representation learning. Meanwhile, the other classifier, serviced as a regularizer, attempts to scatter the source features to enhance the smoothness of the decision boundary. The iterations of target clustering and source expansion make the target features being well-enclosed inside the dilated boundary of the corresponding source points. For the joint address of cross-domain features alignment and partially labeled data learning, we apply the maximum mean discrepancy (MMD) distance minimization and self-training (ST) to project the contradictory structures into a shared view to make the reliable final decision. The experimental results over the standard SSDA benchmarks, including DomainNet and Office-home, demonstrate both the accuracy and robustness of our method over the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]