Accelerated Variance Reduced Stochastic ADMM

Recently, many variance reduced stochastic alternating direction method of multipliers (ADMM) methods (e.g.\ SAG-ADMM, SDCA-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rates for strongly convex problems. However, the best known convergence rate for general convex problems is O(1/T) as opposed to O(1/T^2) of accelerated batch algorithms, where $T$ is the number of iterations. Thus, there still remains a gap in convergence rates between existing stochastic ADMM and batch algorithms. To bridge this gap, we introduce the momentum acceleration trick for batch optimization into the stochastic variance reduced gradient based ADMM (SVRG-ADMM), which leads to an accelerated (ASVRG-ADMM) method. Then we design two different momentum term update rules for strongly convex and general convex cases. We prove that ASVRG-ADMM converges linearly for strongly convex problems. Besides having a low per-iteration complexity as existing stochastic ADMM methods, ASVRG-ADMM improves the convergence rate on general convex problems from O(1/T) to O(1/T^2). Our experimental results show the effectiveness of ASVRG-ADMM.Comment: 16 pages, 5 figures, Appears in Proceedings of the 31th AAAI Conference on Artificial Intelligence (AAAI), San Francisco, California, USA, pp. 2287--2293, 201

Scalable Algorithms for Tractable Schatten Quasi-Norm Minimization

The Schatten-p quasi-norm $(0<p<1)$ is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schatten-p quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may become very slow and impractical for large-scale problems. In this paper, we first define two tractable Schatten quasi-norms, i.e., the Frobenius/nuclear hybrid and bi-nuclear quasi-norms, and then prove that they are in essence the Schatten-2/3 and 1/2 quasi-norms, respectively, which lead to the design of very efficient algorithms that only need to update two much smaller factor matrices. We also design two efficient proximal alternating linearized minimization algorithms for solving representative matrix completion problems. Finally, we provide the global convergence and performance guarantees for our algorithms, which have better convergence properties than existing algorithms. Experimental results on synthetic and real-world data show that our algorithms are more accurate than the state-of-the-art methods, and are orders of magnitude faster.Comment: 16 pages, 5 figures, Appears in Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI), Phoenix, Arizona, USA, pp. 2016--2022, 201

Social Media and Online Public Deliberation: A Case Study of Climate Change Communication on Twitter

This thesis studies the deliberative potential of social media, focusing on climate change communication on Twitter. In particular, this study seeks to explore the online deliberation seen in users' interactions and user-generated content from the perspectives of social network analysis and framing. Three research questions will be answered by three case studies focusing on climate change and an emerging technological topic related to climate change (negative emissions, intentional human efforts to remove CO2 emissions from the atmosphere): how did the climate strikes impact the deliberative potential of climate change discussions online, how did users collectively frame climate change via hashtags, and how did different user groups on Twitter collectively frame negative emissions via tweets? Together, these three questions allow the construction of a picture on the overarching research question: what is the potential of online discussions for deliberation? The data was collected using Twitter's application programming interfaces, covering, for the general topic of climate change, the period 10 September 2018 to 10 September 2019 and, for the subtopic of negative emissions, the period 10 June 2019 to 10 September 2019. There are three main findings of this thesis. First, it shows the changes of deliberative potential of climate change discussions before and after climate strikes and provides evidence that climate strikes increased the potential for deliberation by increasing reciprocity and diversity within the discussion of climate change. However, discussion of climate change after the climate strikes appears to have had less deliberative equality. Second, the thesis reveals that users collectively frame climate change by selecting and associating different hashtags in tweets. In particular, users utilise different hashtags to serve different framing purposes. For example, they use hashtags about consequences, causes and solutions of climate change to spread meaning throughout the entire hashtag occurrence network. Users also tend to connect less popular hashtags with more popular hashtags and make the latter even more popular, and tend to connect hashtags in the same category together in general. The thesis also characterises how climate change is framed on Twitter. In particular, it shows evidence that users tend to frame climate change as a problem that we can solve, and highlights the need for further action. Third, the thesis provides insights into negative emissions as an emerging technological topic, perhaps not as studied from a communication and social impact perspective as is warranted. The frames identified by structural topic modelling show various concerns of different user groups, such as governments, the media and business, and give us clues to the current situation of the communication and acceptance of negative emissions. As it focuses on the politics of climate change in the English language, the findings can not be generalised to all situations. However, it provides a research framework based on social network analysis and framing to examine the deliberative potential of online discussions and contribute to the understanding of climate change communication practice. This thesis provides a basis for future research that is expected to measure online deliberation more comprehensively and thoroughly, and improve our understanding of how social media is used by publics to communally work through the issues of climate change

An FPGA Implementation of the Natural Logarithm Based on CORDIC Algorithm

Abstract: In digital signal and image processing, it&apos;s very common to calculate the value of certain transcendental functions, such as natural logarithmic function. This study introduces the basic principles of the mode of calculation of the hyperbolic systems by using the CORDIC algorithm, then analyses the Field-Programmable Gate Array (FPGA) CORDIC core processing unit in detail. The biggest advantage of the CORDIC algorithm is that its circuit structure is very simple, using only adder and shifter. It is very suitable for FPGA implementation. Based on the iterative algorithm, a FPGA implementation of the natural logarithmic function has been designed. The pipelined-FPGA architecture can achieve a high computational speed, for completing a computation only requires one clock cycle. The relative error values are below 10 -4 , which can satisfy the accuracy requirements