Higher-order tensor canonical polyadic decomposition (CPD) with one or more of the latent factor matrices being columnwisely orthonormal has been well studied in recent years. However, most existing ...models penalize the noises, if occurring, by employing the least squares loss, which may be sensitive to non-Gaussian noise or outliers, leading to bias estimates of the latent factors. In this paper, we derive a robust orthogonal tensor CPD model with Cauchy loss, which is resistant to heavy-tailed noise such as the Cauchy noise, or outliers. By exploring the half-quadratic property of the model, we develop the so-called half-quadratic alternating direction method of multipliers (HQ-ADMM) to solve the model. Each subproblem involved in HQ-ADMM admits a closed-form solution. Thanks to some nice properties of the Cauchy loss, we show that the whole sequence generated by the algorithm globally converges to a stationary point of the problem under consideration. Numerical experiments on synthetic and real data demonstrate the effectiveness of the proposed model and algorithm.
A novel phosphorus‐containing porous polymer is efficiently prepared from tris(4‐vinylphenyl)phosphane by radical polymerization, and it can be easily ionized to form an ionic porous polymer after ...treatment with hydrogen iodide. Upon ionic exchange, transition‐metal‐containing anions, such as tetrathiomolybdate (MoS4
2−) and hexacyanoferrate (Fe(CN)6
3−), are successfully loaded into the framework of the porous polymer to replace the original iodide anions, resulting in a polymer framework containing complex anions (termed HT‐Met, where Met = Mo or Fe). After pyrolysis under a hydrogen atmosphere, the HT‐Met materials are efficiently converted at a large scale to metal‐phosphide‐containing porous carbons (denoted as MetP@PC, where again Met = Mo or Fe). This approach provides a convenient pathway to the controlled preparation of metal‐phosphide‐loaded porous carbon composites. The MetP@PC composites exhibit superior electrocatalytic activity for the hydrogen evolution reaction (HER) under acidic conditions. In particular, MoP@PC with a low loading of 0.24 mg cm−2 (on a glass carbon electrode) affords an iR‐corrected (where i is current and R is resistance) current density of up to 10 mA cm−2 at 51 mV versus the reversible hydrogen electrode and a very low Tafel slope of 45 mV dec−1, in rotating disk measurements under saturated N2 conditions.
Metal‐phosphide‐loaded porous carbons (MetP@PCs) are prepared from a phosphorous‐containing ionic‐polymer framework. Unlike previously reported transition‐metal‐based electrocatalysts, the metal source for MetP@PCs are complex ions, rather than metal salts. Their performance in the electrochemical catalysis of the hydrogen evolution reaction is very promising, and the performance of the PC loaded with molybdenum phosphide is comparable with that of the commercial Pt/C catalyst.
This paper addresses the robust low-rank tensor recovery problems. Tensor recovery aims at reconstructing a low-rank tensor from some linear measurements, which finds applications in image ...processing, pattern recognition, multitask learning, and so on. In real-world applications, data might be contaminated by sparse gross errors. However, the existing approaches may not be very robust to outliers. To resolve this problem, this paper proposes approaches based on the regularized redescending M-estimators, which have been introduced in robust statistics. The robustness of the proposed approaches is achieved by the regularized redescending M-estimators. However, the nonconvexity also leads to a computational difficulty. To handle this problem, we develop algorithms based on proximal and linearized block coordinate descent methods. By explicitly deriving the Lipschitz constant of the gradient of the data-fitting risk, the descent property of the algorithms is present. Moreover, we verify that the objective functions of the proposed approaches satisfy the Kurdyka-Łojasiewicz property, which establishes the global convergence of the algorithms. The numerical experiments on synthetic data as well as real data verify that our approaches are robust in the presence of outliers and still effective in the absence of outliers.
Design and synthesis of robust porous lanthanide-based metal–organic frameworks (Ln-MOFs) from flexible organic ligands is currently a formidable task to chemists. In this work, a porous Ln-MOF based ...on a flexible cyclotriphosphazene-functionalized organic ligand, hexakis(4-carboxylatephenoxy) cyclotriphosphazene, has been solvothermally synthesized. Single-crystal X-ray diffraction analyses show that the compound exhibits a three-dimensional structure built from rod-shaped secondary building units which are linked to each other through the organic ligands to form open frameworks with rectangular channels along the crystallographic a direction. Remarkably, although the flexible ligand was used, the Ln-MOF material after desolvation exhibited permanent porosity which has been established by various gas adsorption isotherms, displaying selective adsorption of C 2 hydrocarbons over CH 4 at room temperature. This work presents a rare example of a permanently porous Ln-MOF based on a flexible ligand exhibiting selective gas adsorption behaviours.
In this letter, we propose a rank-one tensor updating algorithm for solving tensor completion problems. Unlike the existing methods which penalize the tensor by using the sum of nuclear norms of ...unfolding matrices, our optimization model directly employs the tensor nuclear norm which is studied recently. Under the framework of the conditional gradient method, we show that at each iteration, solving the proposed model amounts to computing the tensor spectral norm and the related rank-one tensor. Because the problem of finding the related rank-one tensor is NP-hard, we propose a subroutine to solve it approximately, which is of low computational complexity. Experimental results on real datasets show that our algorithm is efficient and effective.
Bright crescent areas were obviously apparent at the bottom of melt pools of Inconel 718 samples prepared by selective laser melting (SLM). Their microstructure, composition, spatial morphology, and ...mechanical behaviors were systematically investigated. These areas consisted of finer columnar dendrites with underdeveloped secondary arms, which resulted in a bright color under optical field and dark color under SEM. Both growth and crystal orientations were consistent with those of the grains in the melt pool of the former layer. Enrichment of elements Nb and Ti occurred among the dendrites in these areas, leading to the formation of Laves phases. The crescent areas underwent great deformation together with the melt pools during tensile testing, which showed that they were of great plasticity and no gaps or cracks were found around these areas. In addition, the bright crescent areas possessed higher hardness than that of the surrounding regions. Furthermore, the simulated temperature field results showed that the incomplete re-melting of the formed dendrites and a large number of nucleated dendrites among them are the main reasons for the formation of the bright crescent areas.
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•A kind of bright crescent-shaped areas was obviously found at the bottom of melt pools.•The bright areas were composed of finer columnar dendrites with orientation consistent with the former melt pools.•The bright crescent areas had higher hardness.•The incomplete remelting of the former layer led to the formation of the bright crescent areas.
The selective laser melting of tin bronze (CuSn10) powder was performed with a laser energy density intensity level at 210, 220, and 230 J/mm2. The composition was homogeneous with almost all tin ...dissolved into the matrix. The grain size of the obtained alpha copper phase was around 5 μm. The best properties were achieved at 220 J/mm2 laser energy density with a density of 8.82 g/cm3, hardness of 78.2 HRB (Rockwell Hardness measured on the B scale), yield strength of 399 MPa, tensile strength of 490 MPa, and an elongation that reached 19%. “Balling effect” appeared and resulted into a decrease of properties when the laser energy density increased to 230 J/mm2.
Registration of retinal images is significant for clinical diagnosis. Numerous methods have been proposed to evaluate registration performance. The available evaluation methods can work well in ...normal image pairs, but fair evaluation cannot be obtained for image pairs with anatomical changes. We propose an automatic method to quantitatively assess the registration of retinal images based on the extraction of similar vessel structures and modified Hausdorff distance. Firstly, vessel detection and skeletonization are performed to detect the vascular centerline. Secondly, the vessel segments having similar structures in the image pair are selected for assessment of registration. The bifurcation and terminal points are determined from the vascular centerline. Then, the Hungarian matching algorithm with a pruning process is employed to match the bifurcation and terminal points to detect similar vessel segments. Finally, a modified Hausdorff distance is employed to evaluate the performance of registration. Our experimental results show that the Pearson product–moment correlation coefficient can reach 0.76 and 0.63 in test set of normal image pairs and image pairs with anomalies respectively, which outperforms other methods. An accurate evaluation can not only compare the performance of different registration methods but also can facilitate the clinical diagnosis by screening out the inaccurate registration.
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Stemming from information-theoretic learning, the correntropy criterion and its applications to machine learning tasks have been extensively studied and explored. Its application to regression ...problems leads to the robustness-enhanced regression paradigm: correntropy-based regression. Having drawn a great variety of successful real-world applications, its theoretical properties have also been investigated recently in a series of studies from a statistical learning viewpoint. The resulting big picture is that correntropy-based regression regresses toward the conditional mode function or the conditional mean function robustly under certain conditions. Continuing this trend and going further, in this study, we report some new insights into this problem. First, we show that under the additive noise regression model, such a regression paradigm can be deduced from minimum distance estimation, implying that the resulting estimator is essentially a minimum distance estimator and thus possesses robustness properties. Second, we show that the regression paradigm in fact provides a unified approach to regression problems in that it approaches the conditional mean, the conditional mode, and the conditional median functions under certain conditions. Third, we present some new results when it is used to learn the conditional mean function by developing its error bounds and exponential convergence rates under conditional (
)-moment assumptions. The saturation effect on the established convergence rates, which was observed under (
)-moment assumptions, still occurs, indicating the inherent bias of the regression estimator. These novel insights deepen our understanding of correntropy-based regression, help cement the theoretic correntropy framework, and enable us to investigate learning schemes induced by general bounded nonconvex loss functions.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Kernelized elastic net regularization (KENReg) is a kernelization of the well-known elastic net regularization (Zou & Hastie,
). The kernel in KENReg is not required to be a Mercer kernel since it ...learns from a kernelized dictionary in the coefficient space. Feng, Yang, Zhao, Lv, and Suykens (
) showed that KENReg has some nice properties including stability, sparseness, and generalization. In this letter, we continue our study on KENReg by conducting a refined learning theory analysis. This letter makes the following three main contributions. First, we present refined error analysis on the generalization performance of KENReg. The main difficulty of analyzing the generalization error of KENReg lies in characterizing the population version of its empirical target function. We overcome this by introducing a weighted Banach space associated with the elastic net regularization. We are then able to conduct elaborated learning theory analysis and obtain fast convergence rates under proper complexity and regularity assumptions. Second, we study the sparse recovery problem in KENReg with fixed design and show that the kernelization may improve the sparse recovery ability compared to the classical elastic net regularization. Finally, we discuss the interplay among different properties of KENReg that include sparseness, stability, and generalization. We show that the stability of KENReg leads to generalization, and its sparseness confidence can be derived from generalization. Moreover, KENReg is stable and can be simultaneously sparse, which makes it attractive theoretically and practically.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
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