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

Smoothed Analysis of Tensor Decompositions

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results. Efficient decomposition in the overcomplete case (where rank exceeds dimension) is particularly challenging. We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension). In this setting, we show that our algorithm is robust to inverse polynomial error -- a crucial property for applications in learning since we are only allowed a polynomial number of samples. While algorithms are known for exact tensor decomposition in some overcomplete settings, our main contribution is in analyzing their stability in the framework of smoothed analysis. Our main technical contribution is to show that tensor products of perturbed vectors are linearly independent in a robust sense (i.e. the associated matrix has singular values that are at least an inverse polynomial). This key result paves the way for applying tensor methods to learning problems in the smoothed setting. In particular, we use it to obtain results for learning multi-view models and mixtures of axis-aligned Gaussians where there are many more "components" than dimensions. The assumption here is that the model is not adversarially chosen, formalized by a perturbation of model parameters. We believe this an appealing way to analyze realistic instances of learning problems, since this framework allows us to overcome many of the usual limitations of using tensor methods.Comment: 32 pages (including appendix

Triggering information by context

With the increased availability of personal computers with attached sensors to capture their environment, there is a big opportunity for context-aware applications; these automatically provide information and/or take actions according to the user's present context, as detected by sensors. When wel l designed, these applications provide an opportunity to tailor the provision of information closely to the user's current needs. A sub-set of context-a ware applications are discrete applications, where discrete pieces of i nformation are attached to individual contexts, to be triggered when the user enters those contexts. The advantage of discrete applications is that authori ng them can be solely a creative process rather than a programming process: it can be a task akin to creating simple web pages. This paper looks at a general system that can be used in any discrete context- aware application. It propounds a general triggering rule, and investigates how this rule applies in practical applications

Diffusion methods for wind power ramp detection

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-38679-4_9Proceedings of 12th International Work-Conference on Artificial Neural Networks, IWANN 2013, Puerto de la Cruz, Tenerife, Spain, June 12-14, 2013, Part IThe prediction and management of wind power ramps is currently receiving large attention as it is a crucial issue for both system operators and wind farm managers. However, this is still an issue far from being solved and in this work we will address it as a classification problem working with delay vectors of the wind power time series and applying local Mahalanobis K-NN search with metrics derived from Anisotropic Diffusion methods. The resulting procedures clearly outperform a random baseline method and yield good sensitivity but more work is needed to improve on specificity and, hence, precision.With partial support from Spain's grant TIN2010-21575- C02-01 and the UAM-ADIC Chair for Machine Learning. The rst author is also supported by an FPI-UAM grant and kindly thanks the Applied Mathematics Department of Yale University for receiving her during her visits. The second author is supported by the FPU-MEC grant AP2008-00167

Non-Redundant Spectral Dimensionality Reduction

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known as the "repeated Eigen-directions" phenomenon. That is, many of the embedding coordinates they produce typically capture the same direction along the data manifold. This leads to redundant and inefficient representations that do not reveal the true intrinsic dimensionality of the data. In this paper, we propose a general method for avoiding redundancy in spectral algorithms. Our approach relies on replacing the orthogonality constraints underlying those methods by unpredictability constraints. Specifically, we require that each embedding coordinate be unpredictable (in the statistical sense) from all previous ones. We prove that these constraints necessarily prevent redundancy, and provide a simple technique to incorporate them into existing methods. As we illustrate on challenging high-dimensional scenarios, our approach produces significantly more informative and compact representations, which improve visualization and classification tasks

Considerations about multistep community detection

The problem and implications of community detection in networks have raised a huge attention, for its important applications in both natural and social sciences. A number of algorithms has been developed to solve this problem, addressing either speed optimization or the quality of the partitions calculated. In this paper we propose a multi-step procedure bridging the fastest, but less accurate algorithms (coarse clustering), with the slowest, most effective ones (refinement). By adopting heuristic ranking of the nodes, and classifying a fraction of them as `critical', a refinement step can be restricted to this subset of the network, thus saving computational time. Preliminary numerical results are discussed, showing improvement of the final partition.Comment: 12 page

User interfaces for information systems

This paper presents descriptions of four information-system interface projects in progress at ESRIN, each demonstrating a somewhat different approach to interface design, but ali sharing the commonality of responding to user goals, tasks and characteristics. It is suggested that next-generation scientific information systems will have to be designed for direct access by end users to a large variety of information sources, through a commom interface. Design of such systems, including their interfaces, should be based on a multi-level analysis of user goals, tasks and domain views.Se describen cuatro proyectos de interfaces de sistemas de información que se están desarrollando en ESRIN (establecimiento de la Agencia Espacial Europea, en Frascati). Cada uno de ellos muestra un enfoque diferente del diseño de interfaces, pero todos tienen en común el responder a los objetivos, tareas y características de los usuarios. Se sugiere que la próxima generación de sistemas de información científica se tendrá que diseñar para permitir el acceso directo de los usuarios finales a una gran variedad de fuentes de información a través de una interfaz común. El diseño de tales sistemas y de sus interfaces debería basarse en un análisis multinivel de objetivos, tareas y puntos de vista propios de la materia de trabajo de cada usuario

Personalisation and recommender systems in digital libraries

Widespread use of the Internet has resulted in digital libraries that are increasingly used by diverse communities of users for diverse purposes and in which sharing and collaboration have become important social elements. As such libraries become commonplace, as their contents and services become more varied, and as their patrons become more experienced with computer technology, users will expect more sophisticated services from these libraries. A simple search function, normally an integral part of any digital library, increasingly leads to user frustration as user needs become more complex and as the volume of managed information increases. Proactive digital libraries, where the library evolves from being passive and untailored, are seen as offering great potential for addressing and overcoming these issues and include techniques such as personalisation and recommender systems. In this paper, following on from the DELOS/NSF Working Group on Personalisation and Recommender Systems for Digital Libraries, which met and reported during 2003, we present some background material on the scope of personalisation and recommender systems in digital libraries. We then outline the working group’s vision for the evolution of digital libraries and the role that personalisation and recommender systems will play, and we present a series of research challenges and specific recommendations and research priorities for the field

Modelling the response of phytoplankton in a shallow lake (Loch Leven, UK) to changes in lake retention time and water temperature.

The phytoplankton community of Loch Leven in 2005 was modelled and subjected to a combination of different flushing rates and water temperatures in order to assess the lake’s sensitivity to these two climatic drivers. Whilst the simulated annual mean total chlorophyll a proved relatively insensitive to these changes, at the species level marked changes were recorded. Some species responded positively to increased temperature (e.g. Aulacoseira), some negatively (e.g. Asterionella), whilst others were negatively affected by increased flow (e.g. Aphanocapsa) and others enhanced (e.g. Stephanodiscus). However, this relationship with flow was season dependent with, for example, a simulated increase in summer inflows actually benefiting some species through increased nutrient supply, whereas an equivalent increase in flow in wetter seasons would have negatively affected those species (i.e. through flushing loss). Overall, the simulations showed that the range of species types simulated in the community was sufficient for one species to always benefit from the changing niches created by the multiple climatic drivers applied in this study. The level of exploitation by such a species was only constrained by the nutrient carrying capacity of the system, which led to the overall dampened response in the total chlorophyll a measure, both at the annual and season scale. Thus, whilst overall biomass showed relatively little reaction to the two climatic drivers tested, the phytoplankton community composition responded markedly

Widely tunable thermo-optic plasmonic bandpass filter

We report thermally tunable optical bandpass filters based on long-range surface plasmon polariton waveguides. A thin gold stripe in the waveguide core is surrounded by dielectric layers with dissimilar refractive index dispersions and dissimilar thermo-optic coefficients. High filter transmission is achieved for a wavelength at which the refractive indices of the upper and lower cladding layers are identical, and this spectral point may be changed by varying the filter temperature. Experimentally, over 220 nm of bandpass tuning is achieved around 1550 nm wavelength by varying the device temperature from 19 to 27 degrees C. (C) 2013 AIP Publishing LLC.close3