Compressive PCA for Low-Rank Matrices on Graphs

We introduce a novel framework for an approxi- mate recovery of data matrices which are low-rank on graphs, from sampled measurements. The rows and columns of such matrices belong to the span of the first few eigenvectors of the graphs constructed between their rows and columns. We leverage this property to recover the non-linear low-rank structures efficiently from sampled data measurements, with a low cost (linear in n). First, a Resrtricted Isometry Property (RIP) condition is introduced for efficient uniform sampling of the rows and columns of such matrices based on the cumulative coherence of graph eigenvectors. Secondly, a state-of-the-art fast low-rank recovery method is suggested for the sampled data. Finally, several efficient, parallel and parameter-free decoders are presented along with their theoretical analysis for decoding the low-rank and cluster indicators for the full data matrix. Thus, we overcome the computational limitations of the standard linear low-rank recovery methods for big datasets. Our method can also be seen as a major step towards efficient recovery of non- linear low-rank structures. For a matrix of size n X p, on a single core machine, our method gains a speed up of $p^2/k$ over Robust Principal Component Analysis (RPCA), where k << p is the subspace dimension. Numerically, we can recover a low-rank matrix of size 10304 X 1000, 100 times faster than Robust PCA

Thirty Years of Machine Learning: The Road to Pareto-Optimal Wireless Networks

Future wireless networks have a substantial potential in terms of supporting a broad range of complex compelling applications both in military and civilian fields, where the users are able to enjoy high-rate, low-latency, low-cost and reliable information services. Achieving this ambitious goal requires new radio techniques for adaptive learning and intelligent decision making because of the complex heterogeneous nature of the network structures and wireless services. Machine learning (ML) algorithms have great success in supporting big data analytics, efficient parameter estimation and interactive decision making. Hence, in this article, we review the thirty-year history of ML by elaborating on supervised learning, unsupervised learning, reinforcement learning and deep learning. Furthermore, we investigate their employment in the compelling applications of wireless networks, including heterogeneous networks (HetNets), cognitive radios (CR), Internet of things (IoT), machine to machine networks (M2M), and so on. This article aims for assisting the readers in clarifying the motivation and methodology of the various ML algorithms, so as to invoke them for hitherto unexplored services as well as scenarios of future wireless networks.Comment: 46 pages, 22 fig

Deep Learning in Cardiology

The medical field is creating large amount of data that physicians are unable to decipher and use efficiently. Moreover, rule-based expert systems are inefficient in solving complicated medical tasks or for creating insights using big data. Deep learning has emerged as a more accurate and effective technology in a wide range of medical problems such as diagnosis, prediction and intervention. Deep learning is a representation learning method that consists of layers that transform the data non-linearly, thus, revealing hierarchical relationships and structures. In this review we survey deep learning application papers that use structured data, signal and imaging modalities from cardiology. We discuss the advantages and limitations of applying deep learning in cardiology that also apply in medicine in general, while proposing certain directions as the most viable for clinical use.Comment: 27 pages, 2 figures, 10 table

Random projection to preserve patient privacy

With the availability of accessible and widely used cloud services, it is natural that large components of healthcare systems migrate to them; for example, patient databases can be stored and processed in the cloud. Such cloud services provide enhanced flexibility and additional gains, such as availability, ease of data share, and so on. This trend poses serious threats regarding the privacy of the patients and the trust that an individual must put into the healthcare system itself. Thus, there is a strong need of privacy preservation, achieved through a variety of different approaches. In this paper, we study the application of a random projection-based approach to patient data as a means to achieve two goals: (1) provably mask the identity of users under some adversarial-attack settings, (2) preserve enough information to allow for aggregate data analysis and application of machine-learning techniques. As far as we know, such approaches have not been applied and tested on medical data. We analyze the tradeoff between the loss of accuracy on the outcome of machine-learning algorithms and the resilience against an adversary. We show that random projections proved to be strong against known input/output attacks while offering high quality data, as long as the projected space is smaller than the original space, and as long as the amount of leaked data available to the adversary is limited