High-dimensional discriminant analysis and covariance matrix estimation

Statistical analysis in high-dimensional settings, where the data dimension p is close to or larger than the sample size n, has been an intriguing area of research. Applications include gene expression data analysis, financial economics, text mining, and many others. Estimating large covariance matrices is an essential part of high-dimensional data analysis because of the ubiquity of covariance matrices in statistical procedures. The estimation is also a challenging part, since the sample covariance matrix is no longer an accurate estimator of the population covariance matrix in high dimensions. In this thesis, a series of matrix structures, that facilitate the covariance matrix estimation, are studied. Firstly, we develop a set of innovative quadratic discriminant rules by applying the compound symmetry structure. For each class, we construct an estimator, by pooling the diagonal elements as well as the off-diagonal elements of the sample covariance matrix, and substitute the estimator for the covariance matrix in the normal quadratic discriminant rule. Furthermore, we develop a more general rule to deal with nonnormal data by incorporating an additional data transformation. Theoretically, as long as the population covariance matrices loosely conform to the compound symmetry structure, our specialized quadratic discriminant rules enjoy low asymptotic classification error. Computationally, they are easy to implement and do not require large-scale mathematical programming. Then, we generalize the compound symmetry structure by considering the assumption that the population covariance matrix (or equivalently its inverse, the precision matrix) can be decomposed into a diagonal component and a low-rank component. The rank of the low-rank component governs to what extent the decomposition can simplify the covariance/precision matrix and reduce the number of unknown parameters. In the estimation, this rank can either be pre-selected to be small or controlled by a penalty function. Under moderate conditions on the population covariance/precision matrix itself and on the penalty function, we prove some consistency results for our estimator. A blockwise coordinate descent algorithm, which iteratively updates the diagonal component and the low-rank component, is then proposed to obtain the estimator in practice. In the end, we consider jointly estimating large covariance matrices of multiple categories. In addition to the aforementioned diagonal and low-rank matrix decomposition, it is further assumed that there is some common matrix structure shared across the categories. We assume that the population precision matrix of category k can be decomposed into a diagonal matrix D, a shared low-rank matrix L, and a category-specific low-rank matrix Lk. The assumption can be understood under the framework of factor models --- some latent factors affect all categories alike while others are specific to only one of these categories. We propose a method that jointly estimates the precision matrices (therefore, the covariance matrices) --- D and L are estimated with the entire dataset whereas Lk is estimated solely with the data of category k. An AIC-type penalty is applied to encourage the decomposition, especially the shared component. Under certain conditions on the population covariance matrices, some consistency results are developed for the estimators. The performances in finite dimensions are shown through numerical experiments. Using simulated data, we demonstrate certain advantages of our methods over existing ones, in terms of classification error for the discriminant rules and Kullback--Leibler loss for the covariance matrix estimators. The proposed methods are also applied to real life datasets, including microarray data, stock return data and text data, to perform tasks, such as distinguishing normal from diseased tissues, portfolio selection and classifying webpages

Influencing Factors of Catering O2O Customer Experience: An Approach Integrating Big Data Analytics with Grounded Theory

In the era of digital economy, catering O2O is developing rapidly. Catering O2O (catering online to offline), namely catering takeout in the paper, means that customers place an order through online ordering platform, and delivery persons deliver the food provided by catering enterprises offline. Catering O2O conforms to the trend of the digital economy era, but exposes a variety of problems, such as lower feedback rate of the platform, lower timeliness of acceptance and handling, lower customer feedback satisfaction, and poorer customer experience. As China\u27s leading e-commerce platform for life services, Meituan won the rating of not recommending to place an order in the report of "2020 China E-commerce User Experience and Complaint Monitoring". In order to improve customer experience and service satisfaction of catering O2O, this paper takes Meituan takeout as an example, integrates big data analytics and grounded theory to explore influencing factors of catering O2O customer experience. With the big data analytics method, the main influencing factors are obtained from 54250 customer reviews, and then the grounded theory method is used to conduct in-depth analysis on negative reviews, and influencing factors of O2O customer experience are verified and confirmed. The results show that the main influencing factors of catering O2O customer experience are catering food quality and delivery service quality and after-sale service quality. Catering food quality and delivery service quality have a significant impact on customer experience. Finally, from perspectives of catering O2O platforms and enterprises, the paper obtains management implications as follows: Catering O2O platforms should attach great importance on the service of contact points in distribution link, strengthen the last-mile delivery service quality, and improve the supervision and feedback mechanism; catering O2O enterprises should ensure the quality, portion and package of catering food, so as to improve customer experience and win electronic word-of-mouth and customer satisfaction

Oligorotaxane radicals under orders

A strategy for creating foldameric oligorotaxanes composed of only positively charged components is reported. Threadlike components-namely oligoviologens-in which different numbers of 4,4'-bipyridinium (BIPY(2+)) subunits are linked by p-xylylene bridges, are shown to be capable of being threaded by cyclobis(paraquat-p-phenylene) (CBPQT(4+)) rings following the introduction of radical-pairing interactions under reducing conditions. UV/vis/NIR spectroscopic and electrochemical investigations suggest that the reduced oligopseudorotaxanes fold into highly ordered secondary structures as a result of the formation of BIPY(\u2022+) radical cation pairs. Furthermore, by installing bulky stoppers at each end of the oligopseudorotaxanes by means of Cu-free alkyne-azide cycloadditions, their analogous oligorotaxanes, which retain the same stoichiometries as their progenitors, can be prepared. Solution-state studies of the oligorotaxanes indicate that their mechanically interlocked structures lead to the enforced interactions between the dumbbell and ring components, allowing them to fold (contract) in their reduced states and unfold (expand) in their fully oxidized states as a result of Coulombic repulsions. This electrochemically controlled reversible folding and unfolding process, during which the oligorotaxanes experience length contractions and expansions, is reminiscent of the mechanisms of actuation associated with muscle fibers

Molecular rheometry: direct determination of viscosity in L-o and L-d lipid phases via fluorescence lifetime imaging

Understanding of cellular regulatory pathways that involve lipid membranes requires the detailed knowledge of their physical state and structure. However, mapping the viscosity and diffusion in the membranes of complex composition is currently a non-trivial technical challenge. We report fluorescence lifetime spectroscopy and imaging (FLIM) of a meso-substituted BODIPY molecular rotor localised in the leaflet of model membranes of various lipid compositions. We prepare large and giant unilamellar vesicles (LUVs and GUVs) containing phosphatidylcholine (PC) lipids and demonstrate that recording the fluorescence lifetime of the rotor allows us to directly detect the viscosity of the membrane leaflet and to monitor the influence of cholesterol on membrane viscosity in binary and ternary lipid mixtures. In phase-separated 1,2-dioleoyl-sn-glycero-3-phosphocholine-cholesterol–sphingomyelin GUVs we visualise individual liquid ordered (Lo) and liquid disordered (Ld) domains using FLIM and assign specific microscopic viscosities to each domain. Our study showcases the power of FLIM with molecular rotors to image microviscosity of heterogeneous microenvironments in complex biological systems, including membrane-localised lipid rafts

A Congruent‐Melting Mid‐Infrared Nonlinear Optical Vanadate Exhibiting Strong Second‐Harmonic Generation

Study of mid-infrared (mid-IR) nonlinear optical (NLO) materials is hindered by the competing requirements of optimized second-harmonic generation (SHG) coefficient dij and laser-induced damage threshold (LIDT) as well as the harsh synthetic conditions. Herein, we report facile hydrothermal synthesis of a polar NLO vanadate Cs4V8O22 (CVO) featuring a quasi-rigid honeycomb-layered structure with [VO4] and [VO5] polyhedra aligned parallel. CVO possesses a wide IR-transparent window, high LIDT, and congruent-melting behavior. It has very strong phase-matchable SHG intensities in metal vanadate family (12.0 × KDP @ 1064 nm and 2.2 × AGS @ 2100 nm). First-principles calculations suggest that the exceptional SHG responses of CVO largely originate from virtual electronic transitions within [V4O11]∞ layer; the excellent optical transmittance of CVO arises from the special characteristics of vibrational phonons resulting from the layered structure.This research was financially supported by the National Natural Science Foundation of China (Nos. 51432006 and 52002276), the Ministry of Education of China for the Changjiang Innovation Research Team (No. IRT14R23), the Ministry of Education and the State Administration of Foreign Experts Affairs for the 111 Project (No. B13025), and the Innovation Program of Shanghai Municipal Education Commission. M.G.H. thank the Australian Research Council for support (DP170100411). Author thanks G.Z. and B.X.L. at FJIRSM for the LIDT measurements

CogNLG: Cognitive Graph for KG-to-text Generation

Knowledge graph (KG) has been fully considered in natural language generation (NLG) tasks. A KG can help models generate controllable text and achieve better performance. However, most existing related approaches still lack explainability and scalability in large-scale knowledge reasoning. In this work, we propose a novel CogNLG framework for KG-to-text generation tasks. Our CogNLG is implemented based on the dual-process theory in cognitive science. It consists of two systems: one system acts as the analytic system for knowledge extraction, and another is the perceptual system for text generation by using existing knowledge. During text generation, CogNLG provides a visible and explainable reasoning path. Our framework shows excellent performance on all datasets and achieves a BLEU score of 36.7, which increases by 6.7 compared to the best competitor