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

This work characterizes the nature of the limit point of distributed strategies for adaptation and learning over networks in the general case when the combination policy is not necessarily doubly stochastic and when the individual risks do not necessarily share a common minimizer. It is shown that, for sufficiently small step-sizes, the limiting behavior of the network is mainly influenced by the right-eigenvector of the combination policy corresponding to the single eigenvalue at one. It is also shown that the limit point of the network is the unique solution to a certain fixed-point equation determined by the entries of this eigenvector. The arguments show further that even when only partial information is available to the agents, cooperation over a connected network enables the agents to attain the same level of performance as a centralized solution.

On the benefits of diffusion cooperation for distributed optimization and learning

One of the most crucial stages of the Mars exploration missions is the entry, descent, and landing (EDL) phase. During EDL, maintaining reliable communication from the spacecraft to Earth is extremely important for the success of future missions, especially in case of mission failure. EDL is characterized by very deep accelerations, caused by friction, parachute deployment and rocket firing among others. These dynamics cause a severe Doppler shift on the carrier communications link to Earth. Methods have been proposed to estimate the Doppler shift based on Maximum Likelihood. So far these methods have proved successful, but it is expected that the next Mars mission, known as the Mars Science Laboratory, will suffer from higher dynamics and lower SNR. Thus, improving the existing estimation methods becomes a necessity. We propose a Maximum Likelihood approach that takes into account the power in the data tones to enhance carrier recovery, and improve the estimation performance by up to 3 dB. Simulations are performed using real data obtained during the EDL stage of the Mars Exploration Rover B (MERB) mission.

Carrier Recovery Enhancement for Maximum-Likelihood Doppler Shift Estimation in Mars Exploration Missions

The scope of the IEEE Signal Processing Theory and Methods (SPTM) Technical Committee has a broad span, ranging from digital filtering and adaptive signal processing to statistical signal analysis, estimation, and detection. There have also been significant advances in the estimation of sparse systems. These areas continue to play a key role in classical and timely applications. This paper discusses about solving estimation and tracking problems over cognitive networks that requires optimizing certain global cost functions in a distributed manner.

Signal Processing Theory and Methods [In the Spotlight]

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.

Network Classifiers Based on Social Learning

Reference EPFL-CHAPTER-233299 URL: http://iracema.icsl.ucla.edu/publications/book_chapters/kalman_2009.pdf Record created on 2017-12-19, modified on 2018-01-16

Ali H. Sayed

Papers

On the benefits of diffusion cooperation for distributed optimization and learning

Carrier Recovery Enhancement for Maximum-Likelihood Doppler Shift Estimation in Mars Exploration Missions

Signal Processing Theory and Methods [In the Spotlight]

Network Classifiers Based on Social Learning

Energy conservation in adaptive filtering