EcoICA: Skewness-based ICA via Eigenvectors of Cumulant Operator

Independent component analysis (ICA) is an important unsupervised learning method. Most popular ICA methods use kurtosis as a metric of non-Gaussianity to maximize, such as FastICA and JADE. However, their assumption of kurtosic sources may not always be satisfied in practice. For weak-kurtosic but skewed sources, kurtosis-based methods could fail while skewness-based methods seem more promising, where skewness is another non-Gaussianity metric measuring the nonsymmetry of signals. Partly due to the common assumption of signal symmetry, skewness-based ICA has not been systematically studied in spite of some existing works. In this paper, we take a systematic approach to develop EcoICA, a new skewness-based ICA method for weak-kurtosic but skewed sources. Specifically, we design a new cumulant operator, define its eigenvalues and eigenvectors, reveal their connections with the ICA model to formulate the EcoICA problem, and use Jacobi method to solve it. Experiments on both synthetic and real data show the superior performance of EcoICA over existing kurtosis-based and skewness-based methods for skewed sources. In particular, EcoICA is less sensitive to sample size, noise, and outlier than other methods. Studies on face recognition further confirm the usefulness of EcoICA in classification. Keywords: Independent Component Analysis, Cumulant Operator, Skewness, Eigenvector

Ecosystem Monitoring and Port Surveillance Systems

International audienceIn this project, we should build up a novel system able to perform a sustainable and long term monitoring coastal marine ecosystems and enhance port surveillance capability. The outcomes will be based on the analysis, classification and the fusion of a variety of heterogeneous data collected using different sensors (hydrophones, sonars, various camera types, etc). This manuscript introduces the identified approaches and the system structure. In addition, it focuses on developed techniques and concepts to deal with several problems related to our project. The new system will address the shortcomings of traditional approaches based on measuring environmental parameters which are expensive and fail to provide adequate large-scale monitoring. More efficient monitoring will also enable improved analysis of climate change, and provide knowledge informing the civil authority's economic relationship with its coastal marine ecosystems

Hybrid solutions to instantaneous MIMO blind separation and decoding: narrowband, QAM and square cases

Future wireless communication systems are desired to support high data rates and high quality transmission when considering the growing multimedia applications. Increasing the channel throughput leads to the multiple input and multiple output and blind equalization techniques in recent years. Thereby blind MIMO equalization has attracted a great interest.Both system performance and computational complexities play important roles in real time communications. Reducing the computational load and providing accurate performances are the main challenges in present systems. In this thesis, a hybrid method which can provide an affordable complexity with good performance for Blind Equalization in large constellation MIMO systems is proposed first. Saving computational cost happens both in the signal sep- aration part and in signal detection part. First, based on Quadrature amplitude modulation signal characteristics, an efficient and simple nonlinear function for the Independent Compo- nent Analysis is introduced. Second, using the idea of the sphere decoding, we choose the soft information of channels in a sphere, and overcome the so- called curse of dimensionality of the Expectation Maximization (EM) algorithm and enhance the final results simultaneously. Mathematically, we demonstrate in the digital communication cases, the EM algorithm shows Newton -like convergence.Despite the widespread use of forward -error coding (FEC), most multiple input multiple output (MIMO) blind channel estimation techniques ignore its presence, and instead make the sim- plifying assumption that the transmitted symbols are uncoded. However, FEC induces code structure in the transmitted sequence that can be exploited to improve blind MIMO channel estimates. In final part of this work, we exploit the iterative channel estimation and decoding performance for blind MIMO equalization. Experiments show the improvements achievable by exploiting the existence of coding structures and that it can access the performance of a BCJR equalizer with perfect channel information in a reasonable SNR range. All results are confirmed experimentally for the example of blind equalization in block fading MIMO systems

Fourier PCA and Robust Tensor Decomposition

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-$1$ decompositions. Our main application is the first provably polynomial-time algorithm for underdetermined ICA, i.e., learning an $n \times m$ matrix $A$ from observations $y=Ax$ where $x$ is drawn from an unknown product distribution with arbitrary non-Gaussian components. The number of component distributions $m$ can be arbitrarily higher than the dimension $n$ and the columns of $A$ only need to satisfy a natural and efficiently verifiable nondegeneracy condition. As a second application, we give an alternative algorithm for learning mixtures of spherical Gaussians with linearly independent means. These results also hold in the presence of Gaussian noise.Comment: Extensively revised; details added; minor errors corrected; exposition improve