It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic data reconstruction, we consider the matrix completion problem when entries of the matrix of interest are observed gradually. Precisely, we place ourselves in the situation where the predictive rule should be refined incrementally, rather than recomputed from scratch each time the sample of observed entries increases. The extension of existing matrix completion methods to the sequential prediction context is indeed a major issue in the Big Data era, and yet little addressed in the literature. The algorithm promoted in this article builds upon the Soft Impute approach introduced in Mazumder et al. (2010). The major novelty essentially arises from the use of a randomised technique for both computing and updating the Singular Value Decomposition (SVD) involved in the algorithm. Though of disarming simplicity, the method proposed turns out to be very efficient, while requiring reduced computations. Several numerical experiments based on real datasets illustrating its performance are displayed, together with preliminary results giving it a theoretical basis.

The least absolute shrinkage and selection operator (lasso) and ridge regression produce usually different estimates although input, loss function and parameterization of the penalty are identical. In this paper we look for ridge and lasso models with identical solution set. It turns out, that the lasso model with shrink vector $\lambda$ and a quadratic penalized model with shrink matrix as outer product of $\lambda$ with itself are equivalent, in the sense that they have equal solutions. To achieve this, we have to restrict the estimates to be positive. This doesn't limit the area of application since we can easily decompose every estimate in a positive and negative part. The resulting problem can be solved with a non negative least square algorithm. Beside this quadratic penalized model, an augmented regression model with positive bounded estimates is developed which is also equivalent to the lasso model, but is probably faster to solve.

A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$ corresponds to the coefficients of a wavelet or block-DCT representation of data. The method we consider in detail, and for which numerical results are presented, is based on increments of a gamma process. However, we demonstrate that the general framework is appropriate for many other types of shrinkage priors, all within the L\'{e}vy process family, with the gamma process a special case. Bayesian inference is carried out by approximating the posterior with samples from an MCMC algorithm, as well as by constructing a heuristic variational approximation to the posterior. We also consider expectation-maximization (EM) for a MAP (point) solution. State-of-the-art results are manifested for compressive sensing and denoising applications, the latter with spiky (non-Gaussian) noise.

In this paper we formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other unknown static parameters. We also propose a sequential Monte Carlo approximation of our online EM algorithm. We show the performance of the proposed method with two numerical examples.

A recently proposed methodology called the Horizontal Visibility Graph (HVG) [Luque {\it et al.}, Phys. Rev. E., 80, 046103 (2009)] that constitutes a geometrical simplification of the well known Visibility Graph algorithm [Lacasa {\it et al.\/}, Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to study the distinction between deterministic and stochastic components in time series [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)]. Specifically, the authors propose that the node degree distribution of these processes follows an exponential functional of the form $P(\kappa)\sim \exp(-\lambda~\kappa)$, in which $\kappa$ is the node degree and $\lambda$ is a positive parameter able to distinguish between deterministic (chaotic) and stochastic (uncorrelated and correlated) dynamics. In this work, we investigate the characteristics of the node degree distributions constructed by using HVG, for time series corresponding to $28$ chaotic maps and $3$ different stochastic processes. We thoroughly study the methodology proposed by Lacasa and Toral finding several cases for which their hypothesis is not valid. We propose a methodology that uses the HVG together with Information Theory quantifiers. An extensive and careful analysis of the node degree distributions obtained by applying HVG allow us to conclude that the Fisher-Shannon information plane is a remarkable tool able to graphically represent the different nature, deterministic or stochastic, of the systems under study.

Addressing the issue of SVMs parameters optimization, this study proposes an efficient memetic algorithm based on Particle Swarm Optimization algorithm (PSO) and Pattern Search (PS). In the proposed memetic algorithm, PSO is responsible for exploration of the search space and the detection of the potential regions with optimum solutions, while pattern search (PS) is used to produce an effective exploitation on the potential regions obtained by PSO. Moreover, a novel probabilistic selection strategy is proposed to select the appropriate individuals among the current population to undergo local refinement, keeping a well balance between exploration and exploitation. Experimental results confirm that the local refinement with PS and our proposed selection strategy are effective, and finally demonstrate effectiveness and robustness of the proposed PSO-PS based MA for SVMs parameters optimization.

This paper provides a new unimodality test with application in hierarchical clustering methods. The proposed method denoted by signature test (Sigtest), transforms the data based on its statistics. The transformed data has much smaller variation compared to the original data and can be evaluated in a simple proposed unimodality test. Compared with the existing unimodality tests, Sigtest is more accurate in detecting the overlapped clusters and has a much less computational complexity. Simulation results demonstrate the efficiency of this statistic test for both real and synthetic data sets.

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming (LP) algorithm of [9] by introducing a reduced set of constraints for exact NMF. In contrast to the previous approaches, the proposed algorithm does not require the knowledge of factorization rank (extreme rays [3] or topics [7]). Furthermore, motivated by a similar problem arising in the context of metabolic network analysis [13], we consider an entirely different regime where the number of extreme rays or topics can be much larger than the dimension of the data vectors. The performance of the algorithm for different synthetic data sets are provided.

Recent work on learning multilingual word representations usually relies on the use of word-level alignements (e.g. infered with the help of GIZA++) between translated sentences, in order to align the word embeddings in different languages. In this workshop paper, we investigate an autoencoder model for learning multilingual word representations that does without such word-level alignements. The autoencoder is trained to reconstruct the bag-of-word representation of given sentence from an encoded representation extracted from its translation. We evaluate our approach on a multilingual document classification task, where labeled data is available only for one language (e.g. English) while classification must be performed in a different language (e.g. French). In our experiments, we observe that our method compares favorably with a previously proposed method that exploits word-level alignments to learn word representations.

These notes describe how the "SP theory of intelligence", and its embodiment in the "SP machine", may help to realise cognitive computing, as described in the book "Smart Machines". In the SP system, information compression and a concept of "multiple alignment" are centre stage. The system is designed to integrate such things as unsupervised learning, pattern recognition, probabilistic reasoning, and more. It may help to overcome the problem of variety in big data, it may serve in pattern recognition and in the unsupervised learning of structure in data, and it may facilitate the management and transmission of big data. There is potential, via information compression, for substantial gains in computational efficiency, especially in the use of energy. The SP system may help to realise data-centric computing, perhaps via a development of Hebb's concept of a "cell assembly", or via the use of light or DNA for the processing of information. It has potential in the management of errors and uncertainty in data, in medical diagnosis, in processing streams of data, and in promoting adaptability in robots.