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

https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

Independent component models have gained increasing interest in various fields of applications in recent years. The basic independent component model is a semiparametric model assuming that a p-variate observed random vector is a linear transformation of an unobserved vector of p independent latent variables. This linear transformation is given by an unknown mixing matrix, and one of the main objectives of independent component analysis (ICA) is to estimate an unmixing matrix by means of which the latent variables can be recovered. In this article, we discuss the basic independent component model in detail, define the concepts and analysis tools carefully, and consider two families of ICA estimates. The statistical properties (consistency, asymptotic normality, efficiency, robustness) of the estimates can be analyzed and compared via the so called gain matrices. Some extensions of the basic independent component model, such as models with additive noise or models with dependent observations, are briefly discussed. The article ends with a short example.


Keywords:

blind source separation;
fastICA;
independent component model;
independent subspace analysis;
mixing matrix;
overcomplete ICA;
undercomplete ICA;
unmixing matrix

Independent Component Analysis

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.

http://www.eeci-institute.eu/GSC2011/Photos-EECI/EECI-GSC-2011-M5/book_AMS.pdf

Optimization Algorithms on Matrix Manifolds

Independent Component Analysis.

We consider a zero padding OFDM system to which we apply channel shortening to cope with channel responses larger than the guard interval (GI) redundancy. In this article, we propose a blind channel shortening algorithm based on the restoration of zero padding (ZP) redundancy. A main contribution consists in the introduction of a new optimization constraint that allows us to control the target impulse response (TIR) quality and to improve significantly the system performance. Finally, we present a performance comparison between this new technique and similar existing techniques from the literature: MERRY and FRODO algorithms.

Blind channel shortening in ZP-OFDM systems with controlled TIR

Beaconless geo-routing protocols have been traditionally analyzed assuming equal communication ranges for the data and control packets. This is not true in reality, since the communication range is in practice function of the packet length. As a consequence, a substantial discrepancy may exist between analytical and empirical results offered in beaconless geo-routing literature. Furthermore, performance of beaconless geo-routing protocols has typically considered using single-hop metrics only. End-to-end performance is considered in literature only occasionally and mainly in terms of simulation only. In this paper, we re-examine this class of protocols. We first incorporate practical packet detection models in order to capture the dependency of the communication range on the packet's length. We then develop a detailed analytical framework for the end-to-end delay and energy performance of beaconless geo-routing protocols. Finally, we present two different application scenarios and study various tradeoffs in light of the framework developed.

/pdf/a-novel-insight-into-beaconless-geo-routing-2tei53c2t4.pdf

A novel insight into beaconless geo-routing

Blind Source Separation (BSS) is a vast field of research where a large number of BSS algorithms have already been proposed. However, derivation of adaptive BSS solutions with good trade-off between the computational cost and the convergence rate is still a challenging problem. In this work we consider low-cost adaptive BSS methods using statistical independence criteria. We introduce new algorithms using fast data whitening followed by source separation via Givens rotations. These algorithms are compared to other existing techniques and shown to present faster convergence rate and better separation performance.

New algorithms for adaptive BSS

Big data streaming analytics has recently attracted much attention in the signal and information processing communities due to the fact that massive streaming datasets have been collected over the years. Among them, many modern data streams are represented as multidimensional arrays (aka tensors), and thus, streaming tensor decomposition or tensor tracking has become a promising tool to analyze such streaming data. In this paper, we propose a novel online algorithm called ROTDL for the problem of robust tensor tracking under the Tucker format. ROTDL is not only capable of tracking the underlying Tucker dictionary of multidimensional data streams over time, but also robust to sparse outliers. The proposed algorithm is specifically designed by using the alternating direction method of multipliers, block-coordinate descent, and recursive least-squares filtering techniques. Several experiments demonstrate the effectiveness of ROTDL for robust tensor tracking.

Robust Online Tucker Dictionary Learning from Multidimensional Data Streams

This paper introduces a new blind time domain equalization (TEQ) technique for downlink MC-CDMA systems operating in multipath fading channels. This equalization exploits the guard interval redundancy (GI) together with the excess codes (EC). Indeed, since in CDMA based wireless systems, the number of users per cell is significantly less than the spreading factor, a base station can set apart a subset of the codes, the excess codes that will not be used for spreading. A main advantage of this method is its simplicity compared to subspace based techniques and its relative efficiency illustrated by simulation results.

Karim Abed-Meraim

Papers

Blind channel shortening in ZP-OFDM systems with controlled TIR

A novel insight into beaconless geo-routing

New algorithms for adaptive BSS

Robust Online Tucker Dictionary Learning from Multidimensional Data Streams

Blind Channel Equalization in Downlink MC-CDMA Systems Exploiting Guard Interval Redundancy and Excess Codes