Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 6

regularization Related Abstracts

6 Sum Capacity with Regularized Channel Inversion in Multi-Antenna Downlink Systems under Equal Power Constraint

Authors: Attaullah Khawaja, Amna Shabbir


Channel inversion is one of the simplest techniques for multiuser downlink systems with single-antenna users. In this paper regularized channel inversion under equal power constraint in the multiuser multiple input multiple output (MU-MIMO) broadcast channels has been considered. Sum capacity with plain channel inversion also known as Zero Forcing Beam Forming (ZFBF) and optimum sum capacity using Dirty Paper Coding (DPC) has also been investigated. Analysis and simulations show that regularization enhances the system performance and empower linear growth in Sum Capacity and specially work well at low signal to noise ratio (SNRs) regime.

Keywords: broadcast channel, channel inversion, multiple antenna multiple-user wireless, multiple-input multiple-output (MIMO), regularization, dirty paper coding (DPC), sum capacity

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5 Analysis of the Significance of Multimedia Channels Using Sparse PCA and Regularized SVD

Authors: Kourosh Modarresi


The abundance of media channels and devices has given users a variety of options to extract, discover, and explore information in the digital world. Since, often, there is a long and complicated path that a typical user may venture before taking any (significant) action (such as purchasing goods and services), it is critical to know how each node (media channel) in the path of user has contributed to the final action. In this work, the significance of each media channel is computed using statistical analysis and machine learning techniques. More specifically, “Regularized Singular Value Decomposition”, and “Sparse Principal Component” has been used to compute the significance of each channel toward the final action. The results of this work are a considerable improvement compared to the present approaches.

Keywords: Linear Systems, Machine Learning, regularization, singular value decomposition, multimedia attribution, sparse principal component, feature significance, variable shrinkage

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4 Training a Neural Network Using Input Dropout with Aggressive Reweighting (IDAR) on Datasets with Many Useless Features

Authors: Stylianos Kampakis


This paper presents a new algorithm for neural networks called “Input Dropout with Aggressive Re-weighting” (IDAR) aimed specifically at datasets with many useless features. IDAR combines two techniques (dropout of input neurons and aggressive re weighting) in order to eliminate the influence of noisy features. The technique can be seen as a generalization of dropout. The algorithm is tested on two different benchmark data sets: a noisy version of the iris dataset and the MADELON data set. Its performance is compared against three other popular techniques for dealing with useless features: L2 regularization, LASSO and random forests. The results demonstrate that IDAR can be an effective technique for handling data sets with many useless features.

Keywords: Neural Networks, Feature selection, regularization, aggressive reweighting

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3 Regularizing Software for Aerosol Particles

Authors: Christine Böckmann, Julia Rosemann


We present an inversion algorithm that is used in the European Aerosol Lidar Network for the inversion of data collected with multi-wavelength Raman lidar. These instruments measure backscatter coefficients at 355, 532, and 1064 nm, and extinction coefficients at 355 and 532 nm. The algorithm is based on manually controlled inversion of optical data which allows for detailed sensitivity studies and thus provides us with comparably high quality of the derived data products. The algorithm allows us to derive particle effective radius, volume, surface-area concentration with comparably high confidence. The retrieval of the real and imaginary parts of the complex refractive index still is a challenge in view of the accuracy required for these parameters in climate change studies in which light-absorption needs to be known with high accuracy. Single-scattering albedo (SSA) can be computed from the retrieve microphysical parameters and allows us to categorize aerosols into high and low absorbing aerosols. From mathematical point of view the algorithm is based on the concept of using truncated singular value decomposition as regularization method. This method was adapted to work for the retrieval of the particle size distribution function (PSD) and is called hybrid regularization technique since it is using a triple of regularization parameters. The inversion of an ill-posed problem, such as the retrieval of the PSD, is always a challenging task because very small measurement errors will be amplified most often hugely during the solution process unless an appropriate regularization method is used. Even using a regularization method is difficult since appropriate regularization parameters have to be determined. Therefore, in a next stage of our work we decided to use two regularization techniques in parallel for comparison purpose. The second method is an iterative regularization method based on Pade iteration. Here, the number of iteration steps serves as the regularization parameter. We successfully developed a semi-automated software for spherical particles which is able to run even on a parallel processor machine. From a mathematical point of view, it is also very important (as selection criteria for an appropriate regularization method) to investigate the degree of ill-posedness of the problem which we found is a moderate ill-posedness. We computed the optical data from mono-modal logarithmic PSD and investigated particles of spherical shape in our simulations. We considered particle radii as large as 6 nm which does not only cover the size range of particles in the fine-mode fraction of naturally occurring PSD but also covers a part of the coarse-mode fraction of PSD. We considered errors of 15% in the simulation studies. For the SSA, 100% of all cases achieve relative errors below 12%. In more detail, 87% of all cases for 355 nm and 88% of all cases for 532 nm are well below 6%. With respect to the absolute error for non- and weak-absorbing particles with real parts 1.5 and 1.6 in all modes the accuracy limit +/- 0.03 is achieved. In sum, 70% of all cases stay below +/-0.03 which is sufficient for climate change studies.

Keywords: Inverse problem, regularization, aerosol particles, microphysical particle properties

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2 Parameters Identification and Sensitivity Study for Abrasive WaterJet Milling Model

Authors: Didier Auroux, Vladimir Groza


This work is part of STEEP Marie-Curie ITN project, and it focuses on the identification of unknown parameters of the proposed generic Abrasive WaterJet Milling (AWJM) PDE model, that appears as an ill-posed inverse problem. The necessity of studying this problem comes from the industrial milling applications where the possibility to predict and model the final surface with high accuracy is one of the primary tasks in the absence of any knowledge of the model parameters that should be used. In this framework, we propose the identification of model parameters by minimizing a cost function, measuring the difference between experimental and numerical solutions. The adjoint approach based on corresponding Lagrangian gives the opportunity to find out the unknowns of the AWJM model and their optimal values that could be used to reproduce the required trench profile. Due to the complexity of the nonlinear problem and a large number of model parameters, we use an automatic differentiation software tool (TAPENADE) for the adjoint computations. By adding noise to the artificial data, we show that in fact the parameter identification problem is highly unstable and strictly depends on input measurements. Regularization terms could be effectively used to deal with the presence of data noise and to improve the identification correctness. Based on this approach we present results in 2D and 3D of the identification of the model parameters and of the surface prediction both with self-generated data and measurements obtained from the real production. Considering different types of model and measurement errors allows us to obtain acceptable results for manufacturing and to expect the proper identification of unknowns. This approach also gives us the ability to distribute the research on more complex cases and consider different types of model and measurement errors as well as 3D time-dependent model with variations of the jet feed speed.

Keywords: Inverse problem, regularization, Abrasive Waterjet Milling, model parameters identification

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1 A Relative Entropy Regularization Approach for Fuzzy C-Means Clustering Problem

Authors: Ouafa Amira, Jiangshe Zhang


Clustering is an unsupervised machine learning technique; its aim is to extract the data structures, in which similar data objects are grouped in the same cluster, whereas dissimilar objects are grouped in different clusters. Clustering methods are widely utilized in different fields, such as: image processing, computer vision , and pattern recognition, etc. Fuzzy c-means clustering (fcm) is one of the most well known fuzzy clustering methods. It is based on solving an optimization problem, in which a minimization of a given cost function has been studied. This minimization aims to decrease the dissimilarity inside clusters, where the dissimilarity here is measured by the distances between data objects and cluster centers. The degree of belonging of a data point in a cluster is measured by a membership function which is included in the interval [0, 1]. In fcm clustering, the membership degree is constrained with the condition that the sum of a data object’s memberships in all clusters must be equal to one. This constraint can cause several problems, specially when our data objects are included in a noisy space. Regularization approach took a part in fuzzy c-means clustering technique. This process introduces an additional information in order to solve an ill-posed optimization problem. In this study, we focus on regularization by relative entropy approach, where in our optimization problem we aim to minimize the dissimilarity inside clusters. Finding an appropriate membership degree to each data object is our objective, because an appropriate membership degree leads to an accurate clustering result. Our clustering results in synthetic data sets, gaussian based data sets, and real world data sets show that our proposed model achieves a good accuracy.

Keywords: Clustering, fuzzy c-means, regularization, Relative Entropy

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