Structured Matrix Completion with Applications to Genomic Data Integration

Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.Comment: Accepted for publication in Journal of the American Statistical Associatio

Impacts of WeChat on Millennials’ Perceptions and Consumption Behaviors in the Hotel Industry

Social media, known as interactive Web 2.0 Internet-based applications, has deeply changed and reformed interpersonal communication and business operation with the wide spread of Internet and the development of technology. In the past few years, since mobile apps are becoming more and more popular, the access of social media is not limited to tablet computers only, but is also available for almost all kinds of smart phone devices, such as iPhone, Android, Symbian and so on. The function of social media is not confined to real- time message transmission or information sharing any more. It has expanded to a widely range of features, such as online purchase and payment, e-commerce business, and service for different types of social events. Social media plays an increasingly important role in daily personal life as well as in business activities. People are not merely considered as social media users, but also the component of social media itself. As a result, it is very crucial for people to realize the importance and impacts of social media, especially for those business operators. WeChat (Weixin in Chinses, literally “micro message”) is a cross-platform instant text and voice messaging communication service for multiple mobile devices, developed by Tecent in China, first released in the January of 2011. It is claimed to provide “the new way to connect” and create “a way of life”. It is free to download, install and register, and support all kinds of smart phone platforms with multiple language versions, such as Chinese, English, Japanese, French, and Spanish. WeChat provides its users different ways to communicate and interact with friends innovatively through instant text messaging, hold-to-talk voice messaging, group messaging, lively video sharing, location sharing, money transferring, and contact information sharing. Among all the WeChat users, Millennials is the majority. With the growing-up of Millennials, they are becoming more and more powerful and important to the society and will be the next target segmentation for most of the industries in the very near future. Especially for the hotel industry, the industry that urges to attract Millennials patrons for further substantial development, how to attract Millennials is becoming a critical issue for those hotel operators

Knowledge reduction of dynamic covering decision information systems with varying attribute values

Knowledge reduction of dynamic covering information systems involves with the time in practical situations. In this paper, we provide incremental approaches to computing the type-1 and type-2 characteristic matrices of dynamic coverings because of varying attribute values. Then we present incremental algorithms of constructing the second and sixth approximations of sets by using characteristic matrices. We employ experimental results to illustrate that the incremental approaches are effective to calculate approximations of sets in dynamic covering information systems. Finally, we perform knowledge reduction of dynamic covering information systems with the incremental approaches