211 research outputs found

    Blind restoration of images with penalty-based decision making : a consensus approach

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    In this thesis we show a relationship between fuzzy decision making and image processing . Various applications for image noise reduction with consensus methodology are introduced. A new approach is introduced to deal with non-stationary Gaussian noise and spatial non-stationary noise in MRI

    Insights and Characterization of l1-norm Based Sparsity Learning of a Lexicographically Encoded Capacity Vector for the Choquet Integral

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    This thesis aims to simultaneously minimize function error and model complexity for data fusion via the Choquet integral (CI). The CI is a generator function, i.e., it is parametric and yields a wealth of aggregation operators based on the specifics of the underlying fuzzy measure. It is often the case that we desire to learn a fusion from data and the goal is to have the smallest possible sum of squared error between the trained model and a set of labels. However, we also desire to learn as “simple’’ of solutions as possible. Herein, L1-norm regularization of a lexicographically encoded capacity vector relative to the CI is explored. The impact of regularization is explored in terms of what capacities and aggregation operators it induces under different common and extreme scenarios. Synthetic experiments are provided in order to illustrate the propositions and concepts put forth

    Efficient Data Driven Multi Source Fusion

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    Data/information fusion is an integral component of many existing and emerging applications; e.g., remote sensing, smart cars, Internet of Things (IoT), and Big Data, to name a few. While fusion aims to achieve better results than what any one individual input can provide, often the challenge is to determine the underlying mathematics for aggregation suitable for an application. In this dissertation, I focus on the following three aspects of aggregation: (i) efficient data-driven learning and optimization, (ii) extensions and new aggregation methods, and (iii) feature and decision level fusion for machine learning with applications to signal and image processing. The Choquet integral (ChI), a powerful nonlinear aggregation operator, is a parametric way (with respect to the fuzzy measure (FM)) to generate a wealth of aggregation operators. The FM has 2N variables and N(2N − 1) constraints for N inputs. As a result, learning the ChI parameters from data quickly becomes impractical for most applications. Herein, I propose a scalable learning procedure (which is linear with respect to training sample size) for the ChI that identifies and optimizes only data-supported variables. As such, the computational complexity of the learning algorithm is proportional to the complexity of the solver used. This method also includes an imputation framework to obtain scalar values for data-unsupported (aka missing) variables and a compression algorithm (lossy or losselss) of the learned variables. I also propose a genetic algorithm (GA) to optimize the ChI for non-convex, multi-modal, and/or analytical objective functions. This algorithm introduces two operators that automatically preserve the constraints; therefore there is no need to explicitly enforce the constraints as is required by traditional GA algorithms. In addition, this algorithm provides an efficient representation of the search space with the minimal set of vertices. Furthermore, I study different strategies for extending the fuzzy integral for missing data and I propose a GOAL programming framework to aggregate inputs from heterogeneous sources for the ChI learning. Last, my work in remote sensing involves visual clustering based band group selection and Lp-norm multiple kernel learning based feature level fusion in hyperspectral image processing to enhance pixel level classification

    A Behavioral Analysis of WOWA and SUOWA Operators

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    Producción CientíficaWeighted ordered weighted averaging (WOWA) and semiuninorm-based ordered weighted averaging (SUOWA) operators are two families of aggregation functions that simultaneously generalize weighted means and OWA operators. Both families can be obtained by using the Choquet integral with respect to normalized capacities. Therefore, they are continuous, monotonic, idempotent, compensative, and homogeneous of degree 1 functions. Although both families fulfill good properties, there are situations where their behavior is quite different. The aim of this paper is to analyze both families of functions regarding some simple cases of weighting vectors, the capacities from which they are building, the weights affecting the components of each vector, and the values they return.Ministerio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13

    Approximation to the theory of affinities to manage the problems of the groupping process

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    New economic and enterprise needs have increased the interest and utility of the methods of the grouping process based on the theory of uncertainty. A fuzzy grouping (clustering) process is a key phase of knowledge acquisition and reduction complexity regarding different groups of objects. Here, we considered some elements of the theory of affinities and uncertain pretopology that form a significant support tool for a fuzzy clustering process. A Galois lattice is introduced in order to provide a clearer vision of the results. We made an homogeneous grouping process of the economic regions of Russian Federation and Ukraine. The obtained results gave us a large panorama of a regional economic situation of two countries as well as the key guidelines for the decision-making. The mathematical method is very sensible to any changes the regional economy can have. We gave an alternative method of the grouping process under uncertainty

    Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making

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    The file attached is this record is the authors pre-print. The publishers version of record can be found by following the DOI link

    One image reduction algorithm for RGB color images

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    We investigate the problem of combining or aggregating several color values given in coding scheme RGB. For this reason, we study the problem of averaging values on lattices, and in particular on discrete product lattices. We study the arithemtic mean and the median on product lattices. We apply these aggregation functions in image reduction and we present a new algorithm based on the minimization of penalty functions on discrete product lattices
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