There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

/pdf/tensor-decompositions-and-applications-46vl2ih5gn.pdf

Tensor Decompositions and Applications

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Statistics for Spatial Data.

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Table Of Integrals Series And Products

In this paper, we design cooperative beamforming weights for source, relay and destination nodes based on a minimum means-quare-error (MMSE) formulation under network power constraints. We also propose a mode selection procedure based on the instantaneous system throughput. Simulation results indicate that the MMSE cooperative beamforming method with mode selection achieves better performance compared to other beamforming methods: direct beamforming, relay beamforming, and cooperative beamforming without mode selection.

Distributed beamforming and mode selection based on instantaneous system throughput

We present a receiver design for joint interference suppression and equalization of asynchronous multi-user space-time block coded (STBC) systems. We describe the design of front end prefilters to synchronize the received blocks from all users. Simulation results show significant performance improvement for asynchronous transmissions.

Interference suppression of asynchronous multi-user space-time block coded transmissions

Block and Subband Adaptive Filters

The problem of learning simultaneously several related tasks has received considerable attention in several domains, especially in machine learning with the so-called multitask learning problem or learning to learn problem [1], [2]. Multitask learning is an approach to inductive transfer learning (using what is learned for one problem to assist in another problem) and helps improve generalization performance relative to learning each task separately by using the domain information contained in the training signals of related tasks as an inductive bias. Several strategies have been derived within this community under the assumption that all data are available beforehand at a fusion center. However, recent years have witnessed an increasing ability to collect data in a distributed and streaming manner. This requires the design of new strategies for learning jointly multiple tasks from streaming data over distributed (or networked) systems. This article provides an overview of multitask strategies for learning and adaptation over networks. The working hypothesis for these strategies is that agents are allowed to cooperate with each other in order to learn distinct, though related tasks. The article shows how cooperation steers the network limiting point and how different cooperation rules allow to promote different task relatedness models. It also explains how and when cooperation over multitask networks outperforms non-cooperative strategies.

Multitask learning over graphs: An Approach for Distributed, Streaming Machine Learning.

This work proposes a new way of combining independently trained classifiers over space and time. Combination over space means that the outputs of spatially distributed classifiers are aggregated. Combination over time means that the classifiers respond to streaming data during testing and continue to improve their performance even during this phase. By doing so, the proposed architecture is able to improve prediction performance over time with unlabeled data. Inspired by social learning algorithms, which require prior knowledge of the observations distribution, we propose a Social Machine Learning (SML) paradigm that is able to exploit the imperfect models generated during the learning phase. We show that this strategy results in consistent learning with high probability, and it yields a robust structure against poorly trained classifiers. Simulations with an ensemble of feedforward neural networks are provided to illustrate the theoretical results.

Ali H. Sayed

Papers

Distributed beamforming and mode selection based on instantaneous system throughput

Interference suppression of asynchronous multi-user space-time block coded transmissions

Block and Subband Adaptive Filters

Multitask learning over graphs: An Approach for Distributed, Streaming Machine Learning.

Network Classifiers Based on Social Learning