亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Although many techniques have been applied to matrix factorization (MF), they may not fully exploit the feature structure. In this paper, we incorporate the grouping effect into MF and propose a novel method called Robust Matrix Factorization with Grouping effect (GRMF). The grouping effect is a generalization of the sparsity effect, which conducts denoising by clustering similar values around multiple centers instead of just around 0. Compared with existing algorithms, the proposed GRMF can automatically learn the grouping structure and sparsity in MF without prior knowledge, by introducing a naturally adjustable non-convex regularization to achieve simultaneous sparsity and grouping effect. Specifically, GRMF uses an efficient alternating minimization framework to perform MF, in which the original non-convex problem is first converted into a convex problem through Difference-of-Convex (DC) programming, and then solved by Alternating Direction Method of Multipliers (ADMM). In addition, GRMF can be easily extended to the Non-negative Matrix Factorization (NMF) settings. Extensive experiments have been conducted using real-world data sets with outliers and contaminated noise, where the experimental results show that GRMF has promoted performance and robustness, compared to five benchmark algorithms.

Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis. However, as the number of parameters scales quadratically with the dimension p, computation becomes very challenging when p is large. In this paper, we propose an adaptive sieving reduction algorithm to generate a solution path for the estimation of precision matrices under the $\ell_1$ penalized D-trace loss, with each subproblem being solved by a second-order algorithm. In each iteration of our algorithm, we are able to greatly reduce the number of variables in the problem based on the Karush-Kuhn-Tucker (KKT) conditions and the sparse structure of the estimated precision matrix in the previous iteration. As a result, our algorithm is capable of handling datasets with very high dimensions that may go beyond the capacity of the existing methods. Moreover, for the sub-problem in each iteration, other than solving the primal problem directly, we develop a semismooth Newton augmented Lagrangian algorithm with global linear convergence on the dual problem to improve the efficiency. Theoretical properties of our proposed algorithm have been established. In particular, we show that the convergence rate of our algorithm is asymptotically superlinear. The high efficiency and promising performance of our algorithm are illustrated via extensive simulation studies and real data applications, with comparison to several state-of-the-art solvers.

Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.

In this paper a methodology is described to estimate multigroup neutron source distributions which must be added into a subcritical system to drive it to a steady state prescribed power distribution. This work has been motivated by the principle of operation of the ADS (Accelerator Driven System) reactors, which have subcritical cores stabilized by the action of external sources. We use the energy multigroup two-dimensional neutron transport equation in the discrete ordinates formulation (SN) and the equation which is adjoint to it, whose solution is interpreted here as a distribution measuring the importance of the angular flux of neutrons to a linear functional. These equations are correlated through a reciprocity relation, leading to a relationship between the interior sources of neutrons and the power produced by unit length of height of the domain. A coarse-mesh numerical method of the spectral nodal class, referred to as adjoint response matrix constant-nodal method, is applied to numerically solve the adjoint SN equations. Numerical experiments are performed to analyze the accuracy of the present methodology so as to illustrate its potential practical applications.

We prove that Strings-and-Coins -- the combinatorial two-player game generalizing the dual of Dots-and-Boxes -- is strongly PSPACE-complete on multigraphs. This result improves the best previous result, NP-hardness, argued in Winning Ways. Our result also applies to the Nimstring variant, where the winner is determined by normal play; indeed, one step in our reduction is the standard reduction (also from Winning Ways) from Nimstring to Strings-and-Coins.

Shapley values has established itself as one of the most appropriate and theoretically sound frameworks for explaining predictions from complex machine learning models. The popularity of Shapley values in the explanation setting is probably due to its unique theoretical properties. The main drawback with Shapley values, however, is that its computational complexity grows exponentially in the number of input features, making it unfeasible in many real world situations where there could be hundreds or thousands of features. Furthermore, with many (dependent) features, presenting/visualizing and interpreting the computed Shapley values also becomes challenging. The present paper introduces groupShapley: a conceptually simple approach for dealing with the aforementioned bottlenecks. The idea is to group the features, for example by type or dependence, and then compute and present Shapley values for these groups instead of for all individual features. Reducing hundreds or thousands of features to half a dozen or so, makes precise computations practically feasible and the presentation and knowledge extraction greatly simplified. We prove that under certain conditions, groupShapley is equivalent to summing the feature-wise Shapley values within each feature group. Moreover, we provide a simulation study exemplifying the differences when these conditions are not met. We illustrate the usability of the approach in a real world car insurance example, where groupShapley is used to provide simple and intuitive explanations.

Image reconstruction is likely the most predominant auxiliary task for image classification. In this paper, we investigate "approximating the Fourier Transform of the input image" as a potential alternative, in the hope that it may further boost the performances on the primary task or introduce novel constraints not well covered by image reconstruction. We experimented with five popular classification architectures on the CIFAR-10 dataset, and the empirical results indicated that our proposed auxiliary task generally improves the classification accuracy. More notably, the results showed that in certain cases our proposed auxiliary task may enhance the classifiers' resistance to adversarial attacks generated using the fast gradient sign method.

Multispectral imaging is an important technique for improving the readability of written or printed text where the letters have faded, either due to deliberate erasing or simply due to the ravages of time. Often the text can be read simply by looking at individual wavelengths, but in some cases the images need further enhancement to maximise the chances of reading the text. There are many possible enhancement techniques and this paper assesses and compares an extended set of dimensionality reduction methods for image processing. We assess 15 dimensionality reduction methods in two different manuscripts. This assessment was performed both subjectively by asking the opinions of scholars who were experts in the languages used in the manuscripts which of the techniques they preferred and also by using the Davies-Bouldin and Dunn indexes for assessing the quality of the resulted image clusters. We found that the Canonical Variates Analysis (CVA) method which was using a Matlab implementation and we have used previously to enhance multispectral images, it was indeed superior to all the other tested methods. However it is very likely that other approaches will be more suitable in specific circumstance so we would still recommend that a range of these techniques are tried. In particular, CVA is a supervised clustering technique so it requires considerably more user time and effort than a non-supervised technique such as the much more commonly used Principle Component Analysis Approach (PCA). If the results from PCA are adequate to allow a text to be read then the added effort required for CVA may not be justified. For the purposes of comparing the computational times and the image results, a CVA method is also implemented in C programming language and using the GNU (GNUs Not Unix) Scientific Library (GSL) and the OpenCV (OPEN source Computer Vision) computer vision programming library.

Although Recommender Systems have been comprehensively studied in the past decade both in industry and academia, most of current recommender systems suffer from the fol- lowing issues: 1) The data sparsity of the user-item matrix seriously affect the recommender system quality. As a result, most of traditional recommender system approaches are not able to deal with the users who have rated few items, which is known as cold start problem in recommender system. 2) Traditional recommender systems assume that users are in- dependently and identically distributed and ignore the social relation between users. However, in real life scenario, due to the exponential growth of social networking service, such as facebook and Twitter, social connections between different users play an significant role for recommender system task. In this work, aiming at providing a better recommender sys- tems by incorporating user social network information, we propose a matrix factorization framework with user social connection constraints. Experimental results on the real-life dataset shows that the proposed method performs signifi- cantly better than the state-of-the-art approaches in terms of MAE and RMSE, especially for the cold start users.

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple, accurate, numerically stable, and provably correct. Moreover, each method is accompanied by an informative error bound that allows users to select parameters a priori to achieve a given approximation quality. These claims are supported by numerical experiments with real and synthetic data.