On the conditions for valid objective functions in blind separation of independent and dependent sources

It is well known that independent sources can be blindly detected and separated, one by one, from linear mixtures by identifying local extrema of certain objective functions (contrasts), like negentropy, Non-Gaussianity measures, kurtosis, etc. It was also suggested in [1], and verified in practice in [2,4], that some of these measures remain useful for particular cases with dependent sources, but not much work has been done in this respect and a rigorous theoretical ground still lacks. In this paper, it is shown that, if a specific type of pairwise dependence among sources exists, called Linear Conditional Expectation (LCE) law, then a family of objective functions are valid for their separation. Interestingly, this particular type of dependence arises in modeling material abundances in the spectral unmixing problem of remote sensed images. In this work, a theoretical novel approach is used to analyze Shannon entropy (SE), Non-Gaussianity (NG) measure and absolute moments of arbitrarily order, i.e. Generic Absolute (GA) moments for the separation of sources allowing them to be dependent. We provide theoretical results that show the conditions under which sources are isolated by searching for a maximum or a minimum. Also, simple and efficient algorithms based on Parzen windows estimations of probability density functions (pdfs) and Newton-Raphson iterations are proposed for the separation of dependent or independent sources. A set of simulation results on synthetic data and an application to the blind spectral unmixing problem are provided in order to validate our theoretical results and compare these algorithms against FastICA and a very recently proposed algorithm for dependent sources, the Bounded Component Analysis algorithm (BCA). It is shown that, for dependent sources verifying the LCE law, the NG measure provides the best separation results.Fil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentin

Decomposition Methods for Machine Learning with Small, Incomplete or Noisy Datasets

In many machine learning applications, measurements are sometimes incomplete or noisy resulting in missing features. In other cases, and for different reasons, the datasets are originally small, and therefore, more data samples are required to derive useful supervised or unsupervised classification methods. Correct handling of incomplete, noisy or small datasets in machine learning is a fundamental and classic challenge. In this article, we provide a unified review of recently proposed methods based on signal decomposition for missing features imputation (data completion), classification of noisy samples and artificial generation of new data samples (data augmentation). We illustrate the application of these signal decomposition methods in diverse selected practical machine learning examples including: brain computer interface, epileptic intracranial electroencephalogram signals classification, face recognition/verification and water networks data analysis. We show that a signal decomposition approach can provide valuable tools to improve machine learning performance with low quality datasets.Instituto Argentino de Radioastronomí

Complex network representation of multiagent systems with cooperative and competitive interactions

The dynamic behavior of Multi-Agent Systems (MAS) is analyzed in the context of a modified Lotka-Volterra model. The interaction strength is determined by the difference of agent sizes: as the difference increases, the interaction is weaker. Competitive and cooperative scenarios are analyzed, showing clusters of agents in the stationary state. However, meantime in the competitive scenario the agent sizes are constrained to be non greater than the capacity value (β = 1), in the cooperative scenario, they are allowed to exceed such capacity making clear the advantages of cooperation. The complex network representation is introduced in order to enhance the role of agent sizes and their one-on-one interactions in the dynamic behavior of the system.Fil: Caram, Leonidas Facundo. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Computación. Laboratorio de Sistemas Complejos; ArgentinaFil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto Argentino de Radioastronomia (i); ArgentinaFil: Proto, Araceli Noemi. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Computación. Laboratorio de Sistemas Complejos; Argentin

A new Catalogue of HI supershells in gthe outer part of the Milky Way

A New catalogue of H I supershell candidates (GSc) was developed in the outer part  of the Galaxy. The search was carried out using a combination of two techniques: one based on a visual inspection plus an automatic algorithm. A statistical study of the main properties of the detected structure was also carried out.Fil: Suad, Laura Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); ArgentinaFil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Arnal, Edmundo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Cichowoslki, Silvina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio(i); Argentin

Large HI shells catalogue in the second galactic quadrant

Presentamos los resultados de un catálogo de supercáscaras (GS, por sus siglas en inglés) de hidrógeno neutro (HI) localizadas en la parte externa de la Galaxia en una zona delimitada por las logitudes galácticas 88◦ ≤ l ≤ 165◦ y las latitudes galácticas −50◦ ≤ b ≤ +50◦. Dicho catálogo se realizó mediante una combinación de la tradicional técnica de identificación visual y de un algoritmo automático de búsqueda, resultando en la identificación de 382 estructuras. Debido a que nuestro algoritmo permite la detección de estructuras incompletas, hemos incrementado el número de cáscaras catalogadas por otros autores en esta misma región del cielo. Aproximadamente el 80 % de las estructuras (consideradas de máxima confiabilidad por otros autores) han sido identificadas en nuestra búsqueda. El radio efectivo de las estructuras crece linealmente con la altura sobre el plano galáctico.We present the results of a neutral hydrogen shell (GS) catalogue located in the outer part of the Galaxy in a region delimited by the galactic longitudes 88◦ ≤ l ≤ 165◦ and galactic latitudes −50◦ ≤ b ≤ +50◦ . This catalogue was made using a combination of the traditional technique of visual identification and of an automatic search, resulting in the identification of 382 structures. Due to that our algorithm is able to detect incomplete structures, we have incremented the number of shells catalogued by other authors. About 80 % of the structures (considered as maximum confidence by other authors) have been identified in our search. The effective radius of the shells increments linearly with respect to the galactic plane height.Fil: Suad, Laura Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); ArgentinaFil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Arnal, Edmundo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Cichowolski, Silvina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio(i); Argentin

Large HI shells catalogue in the second galactic quadrant

Presentamos los resultados de un catálogo de supercáscaras (GS, por sus siglas en inglés) de hidrógeno neutro (HI) localizadas en la parte externa de la Galaxia en una zona delimitada por las logitudes galácticas 88° ≤ l ≤ 165° y las latitudes galácticas −50° ≤ b ≤ +50°. Dicho catálogo se realizó mediante una combinación de la tradicional técnica de identificación visual y de un algoritmo automático de búsqueda, resultando en la identificación de 382 estructuras. Debido a que nuestro algoritmo permite la detección de estructuras incompletas, hemos incrementado el número de cáscaras catalogadas por otros autores en esta misma región del cielo. Aproximadamente el 80 % de las estructuras (consideradas de máxima confiabilidad por otros autores) han sido identificadas en nuestra búsqueda. El radio efectivo de las estructuras crece linealmente con la altura sobre el plano galáctico.We present the results of a neutral hydrogen shell (GS) catalogue located in the outer part of the Galaxy in a region delimited by the galactic longitudes 88° ≤ l ≤ 165° and galactic latitudes −50° ≤ b ≤ +50°. This catalogue was made using a combination of the traditional technique of visual identification and of an automatic search, resulting in the identification of 382 structures. Due to that our algorithm is able to detect incomplete structures, we have incremented the number of shells catalogued by other authors. About 80 % of the structures (considered as maximum confidence by other authors) have been identified in our search. The effective radius of the shells increments linearly with respect to the galactic plane height.Instituto Argentino de RadioastronomíaFacultad de Ciencias Astronómicas y Geofísica

Higher-Order Partial Least Squares (HOPLS) : a generalized multi-linear regression method

A new generalized multilinear regression model, termed the Higher-Order Partial Least Squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) Y from a tensor X through projecting the data onto the latent space and performing regression on the corresponding latent variables. HOPLS differs substantially from other regression models in that it explains the data by a sum of orthogonal Tucker tensors, while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting. The low dimensional latent space is optimized sequentially via a deflation operation, yielding the best joint subspace approximation for both X and Y. Instead of decomposing X and Y individually, higher order singular value decomposition on a newly defined generalized cross-covariance tensor is employed to optimize the orthogonal loadings. A systematic comparison on both synthetic data and real-world decoding of 3D movement trajectories from electrocorticogram (ECoG) signals demonstrate the advantages of HOPLS over the existing methods in terms of better predictive ability, suitability to handle small sample sizes, and robustness to noise.Fil: Zhao, Qibin . RIKEN Brain Science Institute; JapónFil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto Argentino de Radioastronomia (i); ArgentinaFil: Mandic, Danilo P. . Imperial College Of Science And Technology; Reino UnidoFil: Chao, Zenas C. . RIKEN Brain Science Institute; JapónFil: Nagasaka, Yasuo . RIKEN Brain Science Institute; JapónFil: Fujii, Naotaka. RIKEN Brain Science Institute; JapónFil: Zhang, Liqing. Shanghai Jiao Tong University; ChinaFil: Cichocki, Andrzej. RIKEN Brain Science Institute; Japó

Cross Tensor Approximation Methods for Compression and Dimensionality Reduction

Cross Tensor Approximation (CTA) is a generalization of Cross/skeleton matrix and CUR Matrix Approximation (CMA) and is a suitable tool for fast low-rank tensor approximation. It facilitates interpreting the underlying data tensors and decomposing/compressing tensors so that their structures, such as nonnegativity, smoothness, or sparsity, can be potentially preserved. This paper reviews and extends state-of-the-art deterministic and randomized algorithms for CTA with intuitive graphical illustrations. We discuss several possible generalizations of the CMA to tensors, including CTAs: based on fiber selection, slice-tube selection, and lateral-horizontal slice selection. The main focus is on the CTA algorithms using Tucker and tubal SVD (t-SVD) models while we provide references to other decompositions such as Tensor Train (TT), Hierarchical Tucker (HT), and Canonical Polyadic (CP) decompositions. We evaluate the performance of the CTA algorithms by extensive computer simulations to compress color and medical images and compare their performance.Instituto Argentino de Radioastronomí

Multidimensional compressed sensing and their applications

Compressed Sensing (CS) comprises a set of relatively new techniques that exploit the underlying structure of data sets allowing their reconstruction from compressed versions or incomplete information. CS reconstruction algorithms are essentially non-linear, demanding heavy computation load and large storage memory, especially in the case of multidimensional signals. Excellent review papers discussing CS state-of-the-art theory and algorithms already exist in the literature which mostly consider data sets in vector forms. In this article, we give an overview of existing techniques with special focus on the treatment of multidimensional signals (tensors). We discuss recent trends that exploit the natural multidimensional structure of signals (tensors) achieving simple and efficient CS algorithms. The Kronecker structure of dictionaries is emphasized and its equivalence to the Tucker tensor decomposition is exploited allowing us to use tensor tools and models for CS. Several examples based on real world multidimensional signals are presented illustrating common problems in signal processing such as: the recovery of signals from compressed measurements for MRI signals or for hyper-spectral imaging, and the tensor completion problem (multidimensional inpainting).Fil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto Argentino de Radioastronomia (i); Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Cichocki, Andrzej . Laboratory for Advanced Brain Signal Processing; Polonia. Research Systems Institute; Poloni