The problem of feature selection has raised considerable interests in the past decade. Traditional unsupervised methods select the features which can faithfully preserve the intrinsic structures of data, where the intrinsic structures are estimated using all the input features of data. However, the estimated intrinsic structures are unreliable/inaccurate when the redundant and noisy features are not removed. Therefore, we face a dilemma here: one need the true structures of data to identify the informative features, and one need the informative features to accurately estimate the true structures of data. To address this, we propose a unified learning framework which performs structure learning and feature selection simultaneously. The structures are adaptively learned from the results of feature selection, and the informative features are reselected to preserve the refined structures of data. By leveraging the interactions between these two essential tasks, we are able to capture accurate structures and select more informative features. Experimental results on many benchmark data sets demonstrate that the proposed method outperforms many state of the art unsupervised feature selection methods.

Nonnegative matrix factorization (NMF) is a popular technique for learning parts-based representation and data clustering. It usually uses the squared residuals to quantify the quality of factorization, which is optimal specifically to zeromean, Gaussian noise and sensitive to outliers in general cases. In this paper, we propose a robust NMF method based on the correntropy induced metric, which is much more insensitive to outliers. A half-quadratic optimization algorithm is developed to solve the proposed problem efficiently. The proposed method is further extended to handle outlier rows by incorporating structural knowledge about the outliers. Experimental results on data sets with and without apparent outliers demonstrate the effectiveness of the proposed algorithms.

In this work we theoretically study, using Floquet-Bloch theory, the influence of circularly and linearly polarized light on two-dimensional band structures with Dirac and quadratic band touching points, and flat bands, taking the nearest neighbor hopping model on the kagome lattice as an example. We find circularly polarized light can invert the ordering of this three band model, while leaving the flat-band dispersionless. We find a small gap is also opened at the quadratic band touching point by 2-photon and higher order processes. By contrast, linearly polarized light splits the quadratic band touching point (into two Dirac points) by an amount that depends only on the amplitude and polarization direction of the light, independent of the frequency, and generally renders dispersion to the flat band. The splitting is perpendicular to the direction of the polarization of the light. We derive an effective low-energy theory that captures these key results. Finally, we compute the frequency dependence of the optical conductivity for this 3-band model and analyze the various interband contributions of the Floquet modes. Our results suggest strategies for optically controlling band structure and interaction strength in real systems.

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Abstract-As an effective method for copyright protection of digital products against illegal usage, watermarking in wavelet domain has recently received considerable attention due to the desirable multiresolution property of wavelet transform. In general, images can be represented with different resolutions by the wavelet decomposition, analogous to the human visual system (HVS). Usually, human eyes are insensitive to image singularities revealed by different high frequency subbands of wavelet decomposed images. Hence, adding watermarks into these singularities will improve the imperceptibility that is a desired property of a watermarking scheme. That is, the capability for revealing singularities of images plays a key role in designing wavelet-based watermarking algorithms. Unfortunately, the existing wavelets have a limited ability in revealing singularities in different directions. This motivates us to construct new wavelet filter banks that can reveal singularities in all directions. In this paper, we utilize special symmetric matrices to construct the new nontensor product wavelet filter banks, which can capture the singularities in all directions. Empirical studies will show their advantages of revealing singularities in comparison with the existing wavelets. Based upon these new wavelet filter banks, we, therefore, propose a modified significant difference watermarking algorithm. Experimental results show its promising results.Index Terms-Nontensor product wavelet filter, singularities, watermarking.

In this work we use Floquet-Bloch theory to study the influence of circularly and linearly polarized light on two-dimensional band structures with semi-Dirac band touching points, taking the anisotropic nearest neighbor hopping model on the honeycomb lattice as an example. We find circularly polarized light opens a gap and induces a band inversion to create a finite Chern number in the two-band model. By contrast, linearly polarized light can either open up a gap (polarized in the quadratically dispersing direction) or split the semi-Dirac band touching point into two Dirac points (polarized in the linearly dispersing direction) by an amount that depends on the amplitude of the light. Motivated by recent pump-probe experiments, we investigated the non-equilibrium spectral properties and momentum-dependent spin-texture of our model in the Floquet state following a quench in absence of phonons, and in the presence of phonon dissipation that leads to a steadystate independent of the pump protocol. Finally, we make connections to optical measurements by computing the frequency dependence of the longitudinal and transverse optical conductivity for this two-band model. We analyze the various contributions from inter-band transitions and different Floquet modes. Our results suggest strategies for optically controlling band structures and experimentally measuring topological Floquet systems.

Quantum impurity solvers have a broad range of applications in theoretical studies of strongly correlated electron systems. Especially, they play a key role in dynamical meanfield theory calculations of correlated lattice models and realistic materials. Therefore, the development and implementation of efficient quantum impurity solvers is an important task. In this paper, we present an open source interacting quantum impurity solver toolkit (dubbed iQIST). This package contains several highly optimized quantum impurity solvers which are based on the hybridization expansion continuous-time quantumMonte Carlo algorithm, as well as some essential pre-and post-processing tools. We first introduce the basic principle of continuous-time quantum Monte Carlo algorithm and then discuss the implementation details and optimization strategies. The software framework, major features, and installation procedure for iQIST are also explained. Finally, several simple tutorials are presented in order to demonstrate the usage and power of iQIST. External routines/libraries used: BLAS, LAPACK Nature of problem: Quantum impurity models were originally proposed to describe magnetic impurities in metallic hosts. In these models, the Coulomb interaction acts between electrons occupying the orbitals of the impurity atom. Electrons can hop between the impurity and the host, and in an action formulation, this hopping is described by a timedependent hybridization function. Nowadays quantum impurity model have a broad range of applications, from the description of heavy fermion systems, and Kondo insulators, to quantum dots in nano-science. They also play an important role as auxiliary problems in dynamical mean-field theory and its diagrammatic extensions [1][2][3], where an interacting lattice model is mapped onto a quantum impurity model in a self-consistent manner. Thus, the accurate and efficient solution of quantum impurity models becomes an essential task.Solution method: The quantum impurity model can be solved by the numerically exact continuous-time quantum Monte Carlo method, which is the most efficient and powerful impurity solver for finite temperature simulations. In the iQIST software package, we im-

In this paper, we consider the problem of unsupervised feature selection. Recently, spectral feature selection algorithms, which leverage both graph Laplacian and spectral regression, have received increasing attention. However, existing spectral feature selection algorithms suffer from two major problems: 1) since the graph Laplacian is constructed from the original feature space, noisy and irrelevant features may have adverse effect on the estimated graph Laplacian and hence degenerate the quality of the induced graph embedding; 2) since the cluster labels are discrete in natural, relaxing and approximating these labels into a continuous embedding can inevitably introduce noise into the estimated cluster labels. Without considering the noise in the cluster labels, the feature selection process may be misguided. In this paper, we propose a Robust Spectral learning framework for unsupervised Feature Selection (RSFS), which jointly improves the robustness of graph embedding and sparse spectral regression. Compared with existing methods which are sensitive to noisy features, our proposed method utilizes a robust local learning method to construct the graph Laplacian and a robust spectral regression method to handle the noise on the learned cluster labels. In order to solve the proposed optimization problem, an efficient iterative algorithm is proposed. We also show the close connection between the proposed robust spectral regression and robust Huber M-estimator. Experimental results on different datasets show the superiority of RSFS.