Structured Low-Rank Algorithms: Theory, MR Applications, and Links to Machine Learning

arXiv.org Machine Learning

In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few nonuniform (multichannel) measurements using structured low-rank matrix completion formulation. This framework is centered on the fundamental duality between the compactness (e.g., sparsity) of the continuous signal and the rank of a structured matrix, whose entries are functions of the signal. This property enables the reformulation of the signal recovery as a low-rank structured matrix completion, which comes with performance guarantees. We will also review fast algorithms that are comparable in complexity to current compressed sensing methods, which enables the application of the framework to large-scale magnetic resonance (MR) recovery problems. The remarkable flexibility of the formulation can be used to exploit signal properties that are difficult to capture by current sparse and low-rank optimization strategies. We demonstrate the utility of the framework in a wide range of MR imaging (MRI) applications, including highly accelerated imaging, calibration-free acquisition, MR artifact correction, and ungated dynamic MRI. The slow nature of signal acquisition in magnetic resonance imaging (MRI), where the image is formed from a sequence of Fourier samples, often restricts the achievable spatial and temporal resolution in multidimensional static and dynamic imaging applications. Discrete compressed sensing (CS) methods provided a major breakthrough to accelerate the magnetic resonance (MR) signal acquisition by reducing the sampling burden. As described in an introductory article in this special issue [1] these algorithms exploited the sparsity of the discrete signal in a transform domain to recover the images from a few measurements. In this paper, we review a continuous domain extension of CS using a structured low-rank (SLR) framework for the recovery of an image or a series of images from a few measurements using various compactness assumptions [2]-[22]. The general strategy of the SLR framework starts with defining a lifting operation to construct a structured matrix, whose entries are functions of the signal samples. The SLR algorithms exploit the dual relationships between the signal compactness properties (e.g. This dual relationship allows recovery of the signal from a few samples in the measurement domain as an SLR optimization problem. MJ and MM are with the University of Iowa, Iowa City, IA 52242 (emails: mathews-jacob@uiowa.edu,merry-mani@uiowa.edu). JCY is with the Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea (email: jong.ye@kaist.ac.kr).


A high-bias, low-variance introduction to Machine Learning for physicists

arXiv.org Machine Learning

Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, and generalization before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists maybe able to contribute. (Notebooks are available at https://physics.bu.edu/~pankajm/MLnotebooks.html )


The Livehoods Project: Utilizing Social Media to Understand the Dynamics of a City

AAAI Conferences

Studying the social dynamics of a city on a large scale has tra- ditionally been a challenging endeavor, requiring long hours of observation and interviews, usually resulting in only a par- tial depiction of reality. At the same time, the boundaries of municipal organizational units, such as neighborhoods and districts, are largely statically defined by the city government and do not always reflect the character of life in these ar- eas. To address both difficulties, we introduce a clustering model and research methodology for studying the structure and composition of a city based on the social media its res- idents generate. We use data from approximately 18 million check-ins collected from users of a location-based online so- cial network. The resulting clusters, which we call Livehoods, are representations of the dynamic urban areas that comprise the city. We take an interdisciplinary approach to validating these clusters, interviewing 27 residents of Pittsburgh, PA, to see how their perceptions of the city project onto our findings there. Our results provide strong support for the discovered clusters, showing how Livehoods reveal the distinctly charac- terized areas of the city and the forces that shape them.


Top 10 Predictions For The Digital Future

#artificialintelligence

This article is part of CMO.com's March/April series about emerging technology. Adobe Summit is in full swing in Las Vegas. And for the fourth year in a row, Constellation Research founder Ray Wang and Adobe Experience Index principal analyst Tamara Gaffney took to the stage to talk about the top trends experience makers can expect over the next year. Their predictions are based on a survey of 1,000 people in the United States. Prediction 1: Marketing budgets will get windfall as a result of extra tax-plan cash flow.


Reddit raises $200 million, valued at $1.8 billion

USATODAY - Tech Top Stories

NEW YORK, NY - MAY 06: Co-Founder and Executive Chair of Reddit, and Partner at Y Combinator, Alexis Ohanian (L) and co-editor at TechCrunch, Alexia Tsotsis appear onstage during TechCrunch Disrupt NY. (Photo: Noam Galai, Getty Images for TechCrunch) SAN FRANCISCO -- Reddit has raised $200 million in a new round of funding, which will be used for a website redesign and a focus on user-uploaded video, tech news outlet Recode reported Monday. The influx of capital is courtesy of the some of the biggest Silicon Valley venture capital firms, including Andreessen Horowitz and Sequoia Capital. The company's valuation is now at $1.8 billion. Reddit is structured like a message board, allowing users to directly upload links and text posts, which are then discussed in communities, or subreddits. In an interview with Recode, CEO Steve Huffman said the social news and entertainment website will not be seeking an IPO anytime soon.