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An affine combination of two adaptive filters (AFs) based control is developed for a three-phase single stage grid tied photo voltaic (PV) array and ultra-capacitor (UC) charging electric vehicle spot (CEVS) of a charging station (CS). This algorithm is a combination of low complexity normalized least mean square (NLMS) and improved sparse channel identification reweighted zero attracting-NLMS (RZA-NLMS) filters. This combination offers the variable sparsity identification and improves the power quality of the CS. This CS is capable of grid to vehicle (G2V), PV source to vehicle (S2V), PV source to grid (S2G) and PV source to home (S2H). This CS also incorporates the vehicle to grid (V2G) and vehicle to home (V2H) functions when solar generation is reduced due to cloud crossing or in night time and state of charge (SOC) of the battery is sufficient to discharge battery. The DC link voltage is regulated through a bidirectional converter (BDC) using a cascaded PI controller. To improve the stability of the BDC, the loop shaping method is used. The loop shaping method is incorporated using k-factor approach. The efficacy of CS is demonstrated through the simulated results using MATLAB Simulink Library.

Spectra from a single intimate (nonlinear) mixture can be modeled as data points drawn from a smooth manifold. Spectral data sets containing hyperspectral observations of multiple intimate mixtures with some constituent materials in common can, therefore, be modeled as data clouds, in which each point is drawn from a union of manifolds that share a boundary. Two important steps in the processing of such data are to: 1) identify the different mixture manifolds present in the data and 2) invert the nonlinear mixing function by mapping each mixture manifold into some low-dimensional Euclidean space (manifold embedding). The present state-of-the-art algorithms for joint manifold clustering and embedding perform poorly for hyperspectral data, particularly in the embedding task. We propose a novel reconstruction-based algorithm for the improved clustering and the embedding of mixture manifolds. The algorithm attempts to reconstruct each target point as an affine combination of its nearest neighbors with an additional rank penalty on the neighborhood to ensure that only the neighbors on the same manifold as the target point are used in the reconstruction. The reconstruction matrix generated by this technique is both block diagonal and neighborhood-based, leading to improved clustering and embedding. The improved performance of the algorithm against its competitors is exhibited on a variety of simulated and real mixture data sets.

Adaptive filters are at the core of many signal processing applications, ranging from acoustic noise supression to echo cancelation, array beamforming, channel equalization, to more recent sensor network applications in surveillance, target localization, and tracking. A trending approach in this direction is to recur to in-network distributed processing in which individual nodes implement adaptation rules and diffuse their estimation to the network. When the a priori knowledge about the filtering scenario is limited or imprecise, selecting the most adequate filter structure and adjusting its parameters becomes a challenging task, and erroneous choices can lead to inadequate performance. To address this difficulty, one useful approach is to rely on combinations of adaptive structures. The combination of adaptive filters exploits to some extent the same divide and conquer principle that has also been successfully exploited by the machine-learning community (e.g., in bagging or boosting). In particular, the problem of combining the outputs of several learning algorithms (mixture of experts) has been studied in the computational learning field under a different perspective: rather than studying the expected performance of the mixture, deterministic bounds are derived that apply to individual sequences and, therefore, reflect worst-case scenarios. These bounds require assumptions different from the ones typically used in adaptive filtering, which is the emphasis of this overview article. We review the key ideas and principles behind these combination schemes, with emphasis on design rules. We also illustrate their performance with a variety of examples.

The filtered-x least mean square algorithm is extensively employed for active control, which exhibits a trade-off between convergence speed and the steady-state control performance. In this paper, an affine combination strategy of the filtered-x least mean square and fourth algorithms is proposed, which can be regarded as a generalized convex combination. Unlike the convex combination, the combining parameter in this linear combination is not constrained to lie in a specific interval and plays a vital role in deciding the overall system performance. An adaptation rule is developed for updating the combining parameter. The proposed affine combination strategy is used to control white noise and multitone noise. The simulation results demonstrate that the proposed algorithm provides faster convergence and improved steady-state control performance. Furthermore, the proposed affine combination is also robust with an imperfect secondary path model.

Chapter 11 has taught us that the pignistic transform is just a member of what we have called the ‘affine’ group of probability transforms, characterised by their commutativity with affine combination (a property called ‘linearity’ in the TBM).

Prediction interval modelling has been proposed in the literature to characterize uncertain phenomena and provide useful information from a decision-making point of view. In most of the reported studies, assumptions about the data distribution are made and/or the models are trained at one step ahead, which can decrease the quality of the interval in terms of the information about the uncertainty modelled for a higher prediction horizon. In this paper, a new prediction interval modelling methodology based on fuzzy numbers is proposed to solve the abovementioned drawbacks. Fuzzy and neural network prediction interval models are developed based on this proposed methodology by minimizing a novel criterion that includes the coverage probability and normalized average width. The fuzzy number concept is considered because the affine combination of fuzzy numbers generates, by definition, prediction intervals that can handle uncertainty without requiring assumptions about the data distribution. The developed models are compared with a covariance-based prediction interval method, and high-quality intervals are obtained, as determined by the narrower interval width of the proposed method. Additionally, the proposed prediction intervals are tested by forecasting up to two days ahead of the load of the Huatacondo microgrid in the north of Chile and the consumption of the residential dwellings in the town of Loughborough, UK. The results show that the proposed models are suitable alternatives to electrical consumption forecasting because they obtain the minimum interval widths that characterize the uncertainty of this type of stochastic process. Furthermore, the information provided by the obtained prediction interval could be used to develop robust energy management systems that, for example, consider the worst-case scenario.

Mixed Oblique Extension Principles (MOEP) provide an important method to construct affine dual frames from refinable functions. This paper addresses MOEP under the setting of reducing subspaces of L 2 ( R d ) . We obtain an MOEP for (non)homogeneous affine dual frames and (non)homogeneous affine Parseval frames.

For a number of years we have been investigating the geometric and algebraic properties of a family of discrete sets of points in Euclidean space generated by a simple binary operation: pairwise affine combination by a xed parameter, which we call xed-parameter extrapolation. By varying the parameter and the set of initial points, a large variety of point sets emerge. To our surprise, many of these sets display aperiodic order and share properties of so-called \quasicrystals" or \quasilattices." Such sets display some ordered crystal-like properties (e.g., generation by a regular set of local rules, such as a nite set of tiles, and possessing a kind of repetitivity), but are \aperiodic" in the sense that they have no translational symmetry. The most famous of such systems are Penrose's aperiodic tilings of the plane [16]. Mathematically, a widely accepted way of capturing the idea of aperiodic order is via the notion of Meyer sets, which we de ne later. Our goal is to classify the sets generated by xed-parameter extrapolation in terms of a number of these properties, including but not limited to aperiodicity, uniform discreteness, and relative density. We also seek to determine exactly which parameter values lead to which types of sets.

Motivated to apply sustainable supply chain principles to air-pollution control systems, this paper presents a dynamic inventory-management approach where substitution is possible to maintain these systems’ equipment. An air-pollution control system’s subsequent reliability depends on the replacement equipment selected. The corresponding problem is formulated as a stochastic dynamic program. Because the state and action space are prohibitively large, the approximate policy iteration algorithm is adapted to generate high-quality solutions. Therefore, this work replaces the value function with an affine combination of nonlinear basis functions and shows that a relaxation of the policy improvement step requires the solving of a mixed integer linear program. This approach helps in the designing of an algorithm that improves the quality of the approximation by solving a convex optimization problem. To assess the quality of resulting solutions, a lower bound is developed by considering a relaxation of the problem. In addition, two classes of heuristics are proposed based on a rolling-horizon two-stage stochastic programming formulation of the problem and a standard base-stock ordering policy. The performance of proposed policies is tested on a variety of settings, and results show that the approximate dynamic programming policies are near-optimal in the settings of interest and significantly outperform available benchmarks. The following analysis reveals that the proposed inventory replenishment policies resemble a base-stock policy with occasional deviations, and assignment and substitution decisions are determined by balancing the reliability with ordering, holding, and shortage costs. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0794 .

The goal of our paper is to semantically edit parts of an image matching a given text that describes desired attributes (e.g., texture, colour, and background), while preserving other contents that are irrelevant to the text. To achieve this, we propose a novel generative adversarial network (ManiGAN), which contains two key components: text-image affine combination module (ACM) and detail correction module (DCM). The ACM selects image regions relevant to the given text and then correlates the regions with corresponding semantic words for effective manipulation. Meanwhile, it encodes original image features to help reconstruct text-irrelevant contents. The DCM rectifies mismatched attributes and completes missing contents of the synthetic image. Finally, we suggest a new metric for evaluating image manipulation results, in terms of both the generation of new attributes and the reconstruction of text-irrelevant contents. Extensive experiments on the CUB and COCO datasets demonstrate the superior performance of the proposed method. Code is available at https://github.com/mrlibw/ManiGAN., Comment: CVPR 2020

In hyperspectral image classification, small number of labeled samples versus high dimensional data is one of major challenges. Semi-supervised learning has shown potential to relieve the dilemma. Compared with its supervised learning counterpart, semi-supervised learning exploits both intrinsic structure of labeled and unlabeled samples. In this work, we proposed a graph-fusion based semi-supervised learning method for hyperspectral image classification. More specially, two graphs are constructed from spectral-spatial Gabor features and original spectral signatures, respectively, and then are integrated using an affine combination. Experimental results from an AVIRIS hyperspectral dataset verify the excellent classification performance of our method.

Diffusion adaptation is a powerful strategy for distributed estimation and learning over networks. Motivated by the concept of combining adaptive filters, this work proposes a combination framework that aggregates the operation of multiple diffusion strategies for enhanced performance. By assigning a combination coefficient to each node, and using an adaptation mechanism to minimize the network error, we obtain a combined diffusion strategy that benefits from the best characteristics of all component strategies simultaneously in terms of excess-mean-square error (EMSE). Analyses of the universality are provided to show the superior performance of affine combination scheme and to characterize its behavior in the mean and mean-square sense. Simulation results are presented to demonstrate the effectiveness of the proposed strategies, as well as the accuracy of theoretical findings., 31 pages

We describe invariants of centers of ellipse-inscribed triangle families with two vertices fixed to the ellipse boundary and a third one which sweeps it. We prove that: (i) if a triangle center is a fixed affine combination of barycenter and orthocenter, its locus is an ellipse; (ii) and that over the family of said affine combinations, the centers of said loci sweep a line; (iii) over the family of parallel fixed vertices, said loci rigidly translate along a second line. Additionally, we study invariants of the envelope of elliptic loci over combinations of two fixed vertices on the ellipse., Comment: 17 pages, 10 figures, 3 tables, 6 video links

Combining diffusion strategies with complementary properties enables enhanced performance when they can be run simultaneously. In this article, we first propose two schemes for the convex combination of two diffusion strategies, namely, the power-normalized scheme and the sign-regressor scheme. Then, we conduct theoretical analysis for one of the schemes, i.e., the power-normalized one. An analysis of universality shows that it cannot perform worse than any of its component strategies in terms of the excess mean-square-error (EMSE) at steady state, and sometimes even better. An analysis of stability also reveals that it is more stable than affine combination schemes already proposed by the authors in the literature. Next, several adjustments are proposed to further improve the performance of convex combination schemes. A discussion about the computational and communication complexity is provided, as well as a comparison between convex and affine combination schemes. Finally, simulation results are shown to demonstrate their effectiveness, the accuracy of the theoretical results, and the improved stability of the convex power-normalized scheme over the affine one.

We present an algorithmic and visual grouping of participants and eye-tracking metrics derived from recorded eye-tracking data. Our method utilizes two well-established visualization concepts. First, parallel coordinates are used to provide an overview of the used metrics, their interactions, and similarities, which helps select suitable metrics that describe characteristics of the eye-tracking data. Furthermore, parallel coordinates plots enable an analyst to test the effects of creating a combination of a subset of metrics resulting in a newly derived eye-tracking metric. Second, a similarity matrix visualization is used to visually represent the affine combination of metrics utilizing an algorithmic grouping of subjects that leads to distinct visual groups of similar behavior. To keep the diagrams of the matrix visualization simple and understandable, we visually encode our eye-tracking data into the cells of a similarity matrix of participants. The algorithmic grouping is performed with a clustering based on the affine combination of metrics, which is also the basis for the similarity value computation of the similarity matrix. To illustrate the usefulness of our visualization, we applied it to an eye-tracking data set involving the reading behavior of metro maps of up to 40 participants. Finally, we discuss limitations and scalability issues of the approach focusing on visual and perceptual issues., 17 pages, 15 figures

In this paper, we introduce a Bayesian framework to perform model selection for nonlinear acoustic echo cancellation. This is especially important for scenarios where the functional form of the underlying nonlinear distortion is time-varying and/or is unknown, e.g., nonlinear distortions that vary with the volume level of the loudspeakers. To this end, the proposed method evaluates the model probabilities, or what is known as the evidence density, in a Bayesian manner. Thus, unlike convex and affine combination schemes of adaptive filters, the proposed method optimizes both the model complexity as well as the model performance by a single criterion. Moreover, by using the significance-aware principle, the proposed framework is realized in a computationally efficient way. The method is validated by three experiments using synthesized time-invariant nonlinearities, synthesized time-varying nonlinearities, and using real recorded nonlinearities.

This work presents a data driven control strategy able to track a set point without steady state error. The control sequence is computed as an affine combination of past control signals, which belong to a set of past closed loop trajectories stored in a process historian database. This affine combination is computed so that the variance of the tracking error is minimized. It is shown that offset free control (zero mean tracking error) is achieved under the assumption that the underlying dynamics are linear and the closed loop trajectories of the database are in turn offset free. That is, the proposed strategy inherits the offset free tracking capability of the stored past closed loop trajectories. No prior or subsequent knowledge about the process dynamics is required. The procedure to build the database is to store only the best trajectories that meet a design criteria, chosen from a series of iteratively tuned controllers. In this way the proposed controller will learn how to obtain a well tuned control in spite of the different operating conditions.

Subspace clustering is an important problem in machine learning with many applications in computer vision and pattern recognition. Prior work has studied this problem using algebraic, iterative, statistical, low-rank and sparse representation techniques. While these methods have been applied to both linear and affine subspaces, theoretical results have only been established in the case of linear subspaces. For example, algebraic subspace clustering (ASC) is guaranteed to provide the correct clustering when the data points are in general position and the union of subspaces is transversal . In this paper we study in a rigorous fashion the properties of ASC in the case of affine subspaces. Using notions from algebraic geometry, we prove that the homogenization trick , which embeds points in a union of affine subspaces into points in a union of linear subspaces, preserves the general position of the points and the transversality of the union of subspaces in the embedded space, thus establishing the correctness of ASC for affine subspaces.

We study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial point. Without assuming any condition on singular minimizers, we prove that the value function is continuous on an open and dense subset of the interior of the attainable set. As a byproduct we obtain that it is actually smooth on a possibly smaller set, still open and dense.

This paper presents a fast and accurate affine canonicalization method for planar shapes. This method improves on previous ones based on iterative optimization that produce multiple canonical versions. Canonicalization provides a common reference frame for shape comparison without the loss of discrimination ability often caused by invariant features. It also gives for free the alignment transformation between any pair of shapes. The proposed method is based on the properties of the joint angular distribution of marginal skewness and kurtosis, the so-called SK signature, which can be efficiently computed in closed form from the raw image moments. The experiments demonstrate that the method is robust to the non-affine distortions caused by natural perspective image conditions. Thus, it can be used as an automatic preprocessing step to add affine invariance in statistical pattern recognition applications.

We introduce the two-parameter quantum affine algebra U r , s ( gl ˆ n ) via the RTT realization. The Drinfeld realization is given and the type A quantum affine algebra is proved to be a special subalgebra of our extended algebra.

In this paper, we introduce an affine scaling cubic regularization algorithm for solving optimization problem without available derivatives subject to bound constraints employing a polynomial interpolation approach to handle the unavailable derivatives of the original objective function. We first define an affine scaling cubic model of the approximate objective function which is obtained by the polynomial interpolation approach with an affine scaling method. At each iteration a candidate search direction is determined by solving the affine scaling cubic regularization subproblem and the new iteration is strictly feasible by way of an interior backtracking technique. The global convergence and local superlinear convergence of the proposed algorithm are established under some mild conditions. Preliminary numerical results are reported to show the effectiveness of the proposed algorithm.

Cryptographic properties of permutations viz non-linearity, affine equivalence, and mode transform have been studied in the literature, treating them as bijections on ℤn. In this article, the autho...

In this paper, the classical density classification problem is considered in the context of affine continuous cellular automata. It has been shown earlier that there exists no general solution to this problem that is valid for any number of cells. Here, we consider this problem in the case of a fixed number of cells. Necessary conditions for solving the problem are formulated. Based on this knowledge, a specific class of affine continuous cellular automata is evaluated experimentally for 23 cells. A rich solution set is analysed and visualised.

For refinable function-based affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame (WNABF). Under the setting of reducing subspaces of L 2(R d ), we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.

In this paper, we introduce the notion of partial affine system that is a subset of an affine system. It has potential applications in signal analysis. A general affine system has been extensively studied; however, the partial one has not. The main focus of this paper is on partial affine system–based frames and dual frames. We obtain a necessary condition and a sufficient condition for a partial affine system to be a frame and present a characterization of partial affine system–based dual frames. Some examples are also provided.

We prove that generically, for a self-affine set in $\mathbb{R}^d$, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question., Comment: arXiv admin note: text overlap with arXiv:1609.07360