While uniform sampling has been widely studied in the matrix completion literature, CUR sampling approximates a low-rank matrix via row and column samples. Unfortunately, both sampling models lack flexibility for various circumstances in real-world applications. In this work, we propose a novel and easy-to-implement sampling strategy, coined Cross-Concentrated Sampling (CCS). By bridging uniform sampling and CUR sampling, CCS provides extra flexibility that can potentially save sampling costs in applications. In addition, we also provide a sufficient condition for CCS-based matrix completion. Moreover, we propose a highly efficient non-convex algorithm, termed Iterative CUR Completion (ICURC), for the proposed CCS model. Numerical experiments verify the empirical advantages of CCS and ICURC against uniform sampling and its baseline algorithms, on both synthetic and real-world datasets.

Classification and topic modeling are popular techniques in machine learning that extract information from large-scale datasets. By incorporating a priori information such as labels or important features, methods have been developed to perform classification and topic modeling tasks; however, most methods that can perform both do not allow for guidance of the topics or features. In this paper, we propose a novel method, namely Guided Semi-Supervised Non-negative Matrix Factorization (GSSNMF), that performs both classification and topic modeling by incorporating supervision from both pre-assigned document class labels and user-designed seed words. We test the performance of this method on legal documents provided by the California Innocence Project and the 20 Newsgroups dataset. Our results show that the proposed method improves both classification accuracy and topic coherence in comparison to past methods such as Semi-Supervised Non-negative Matrix Factorization (SSNMF), Guided Non-negative Matrix Factorization (Guided NMF), and Topic Supervised NMF.

This work proposes a deep learning (DL)-based framework, namely Sim2Real, for spectral signal reconstruction in reconstructive spectroscopy, focusing on efficient data sampling and fast inference time. The work focuses on the challenge of reconstructing real-world spectral signals in an extreme setting where only device-informed simulated data are available for training. Such device-informed simulated data are much easier to collect than real-world data but exhibit large distribution shifts from their real-world counterparts. To leverage such simulated data effectively, a hierarchical data augmentation strategy is introduced to mitigate the adverse effects of this domain shift, and a corresponding neural network for the spectral signal reconstruction with our augmented data is designed. Experiments using a real dataset measured from our spectrometer device demonstrate that Sim2Real achieves significant speed-up during the inference while attaining on-par performance with the state-of-the-art optimization-based methods.

Visual communication has an important impact on revitalizing rural culture, but its implementation still lacks empirical research support. Based on the grounded theory, this study conducted a coding analysis of the data collected in Shuikou Town, Yunyang County, by research method of field investigation. Relevant research shows that: Shuikou Town, Yunyang County, has a positive role in promoting cultural revitalization in terms of content consciousness, villager consciousness, media consciousness, subject environment, and object environment of visual communication. The analysis of the influence mechanism of visual communication on the “consciousness-environment” of rural cultural revitalization from an empirical perspective can also provide a closer look at the current status of rural cultural revitalization to provide a reference for visual communication to promote rural cultural revitalization.

The California Innocence Project (CIP), a clinical law school program aiming to free wrongfully convicted prisoners, evaluates thousands of mails containing new requests for assistance and corresponding case files. Processing and interpreting this large amount of information presents a significant challenge for CIP officials, which can be successfully aided by topic modeling techniques.In this paper, we apply Non-negative Matrix Factorization (NMF) method and implement various offshoots of it to the important and previously unstudied data set compiled by CIP. We identify underlying topics of existing case files and classify request files by crime type and case status (decision type). The results uncover the semantic structure of current case files and can provide CIP officials with a general understanding of newly received case files before further examinations. We also provide an exposition of popular variants of NMF with their experimental results and discuss the benefits and drawbacks of each variant through the real-world application.

Classification and topic modeling are popular techniques in machine learning that extract information from large-scale datasets. By incorporating a priori information such as labels or important features, methods have been developed to perform classification and topic modeling tasks; however, most methods that can perform both do not allow for guidance of the topics or features. In this paper, we propose a method, namely Guided Semi-Supervised Non-negative Matrix Factorization (GSSNMF), that performs both classification and topic modeling by incorporating supervision from both pre-assigned document class labels and user-designed seed words. We test the performance of this method through its application to legal documents provided by the California Innocence Project, a nonprofit that works to free innocent convicted persons and reform the justice system. The results show that our proposed method improves both classification accuracy and topic coherence in comparison to past methods like Semi-Supervised Non-negative Matrix Factorization (SSNMF) and Guided Non-negative Matrix Factorization (Guided NMF).