An Accelerated Block Proximal Framework with Adaptive Momentum for Nonconvex and Nonsmooth Optimization

We propose an accelerated block proximal linear framework with adaptive momentum (ABPL$^+$) for nonconvex and nonsmooth optimization. We analyze the potential causes of the extrapolation step failing in some algorithms, and resolve this issue by enhancing the comparison process that evaluates the trade-off between the proximal gradient step and the linear extrapolation step in our algorithm. Furthermore, we extends our algorithm to any scenario involving updating block variables with positive integers, allowing each cycle to randomly shuffle the update order of the variable blocks. Additionally, under mild assumptions, we prove that ABPL$^+$ can monotonically decrease the function value without strictly restricting the extrapolation parameters and step size, demonstrates the viability and effectiveness of updating these blocks in a random order, and we also more obviously and intuitively demonstrate that the derivative set of the sequence generated by our algorithm is a critical point set. Moreover, we demonstrate the global convergence as well as the linear and sublinear convergence rates of our algorithm by utilizing the Kurdyka-Lojasiewicz (K{\L}) condition. To enhance the effectiveness and flexibility of our algorithm, we also expand the study to the imprecise version of our algorithm and construct an adaptive extrapolation parameter strategy, which improving its overall performance. We apply our algorithm to multiple non-negative matrix factorization with the $\ell_0$ norm, nonnegative tensor decomposition with the $\ell_0$ norm, and perform extensive numerical experiments to validate its effectiveness and efficiency

Globally Convergent Accelerated Algorithms for Multilinear Sparse Logistic Regression with ℓ0\ell_0-constraints

Tensor data represents a multidimensional array. Regression methods based on low-rank tensor decomposition leverage structural information to reduce the parameter count. Multilinear logistic regression serves as a powerful tool for the analysis of multidimensional data. To improve its efficacy and interpretability, we present a Multilinear Sparse Logistic Regression model with $\ell_0$-constraints ($\ell_0$-MLSR). In contrast to the $\ell_1$-norm and $\ell_2$-norm, the $\ell_0$-norm constraint is better suited for feature selection. However, due to its nonconvex and nonsmooth properties, solving it is challenging and convergence guarantees are lacking. Additionally, the multilinear operation in $\ell_0$-MLSR also brings non-convexity. To tackle these challenges, we propose an Accelerated Proximal Alternating Linearized Minimization with Adaptive Momentum (APALM$^+$) method to solve the $\ell_0$-MLSR model. We provide a proof that APALM$^+$ can ensure the convergence of the objective function of $\ell_0$-MLSR. We also demonstrate that APALM$^+$ is globally convergent to a first-order critical point as well as establish convergence rate by using the Kurdyka-Lojasiewicz property. Empirical results obtained from synthetic and real-world datasets validate the superior performance of our algorithm in terms of both accuracy and speed compared to other state-of-the-art methods.Comment: arXiv admin note: text overlap with arXiv:2308.1212

Weighted Sparse Partial Least Squares for Joint Sample and Feature Selection

Sparse Partial Least Squares (sPLS) is a common dimensionality reduction technique for data fusion, which projects data samples from two views by seeking linear combinations with a small number of variables with the maximum variance. However, sPLS extracts the combinations between two data sets with all data samples so that it cannot detect latent subsets of samples. To extend the application of sPLS by identifying a specific subset of samples and remove outliers, we propose an $\ell_\infty/\ell_0$-norm constrained weighted sparse PLS ($\ell_\infty/\ell_0$-wsPLS) method for joint sample and feature selection, where the $\ell_\infty/\ell_0$-norm constrains are used to select a subset of samples. We prove that the $\ell_\infty/\ell_0$-norm constrains have the Kurdyka-\L{ojasiewicz}~property so that a globally convergent algorithm is developed to solve it. Moreover, multi-view data with a same set of samples can be available in various real problems. To this end, we extend the $\ell_\infty/\ell_0$-wsPLS model and propose two multi-view wsPLS models for multi-view data fusion. We develop an efficient iterative algorithm for each multi-view wsPLS model and show its convergence property. As well as numerical and biomedical data experiments demonstrate the efficiency of the proposed methods

Orthodontic mini-implants: A systematic review.

 AbstractPurposeTo compile and analyze the literature regarding orthodontic mini-implants (MIs) placement, clinical applications, success rate, adverse effects and patients’ pain experience in clinical practice.MethodologyPublications about orthodontic MIs variables were systematically searched from PubMed, Science Direct, and Google Scholar Beta electronic data bases using “orthodontic in conjunction with implant, microimplant, screw, miniscrew, screw implant, mini-implant, and temporary anchorage” as keywords. Data from selected articles were extracted and compiled to produce a summarized report. ResultsSeveral areas are suitable for MI placement. However; the region between second premolar and first molar is the safest. The MI success rate ranges from 77.7% to 93.43%. The pain associated with MIs is far less than tooth extraction and significantly lower than patients’ expectation. Root resorption is among the adverse effects and gonial angle pattern influences the MI success rate. ConclusionMIs offer a wide range of clinical anchorage application due to their minimal anatomical location limitation. The success rate of MI is reliably high. The pain caused by orthodontics MI is significantly lower than patients’ expectation. &nbsp

Precise Facial Landmark Detection by Reference Heatmap Transformer

Most facial landmark detection methods predict landmarks by mapping the input facial appearance features to landmark heatmaps and have achieved promising results. However, when the face image is suffering from large poses, heavy occlusions and complicated illuminations, they cannot learn discriminative feature representations and effective facial shape constraints, nor can they accurately predict the value of each element in the landmark heatmap, limiting their detection accuracy. To address this problem, we propose a novel Reference Heatmap Transformer (RHT) by introducing reference heatmap information for more precise facial landmark detection. The proposed RHT consists of a Soft Transformation Module (STM) and a Hard Transformation Module (HTM), which can cooperate with each other to encourage the accurate transformation of the reference heatmap information and facial shape constraints. Then, a Multi-Scale Feature Fusion Module (MSFFM) is proposed to fuse the transformed heatmap features and the semantic features learned from the original face images to enhance feature representations for producing more accurate target heatmaps. To the best of our knowledge, this is the first study to explore how to enhance facial landmark detection by transforming the reference heatmap information. The experimental results from challenging benchmark datasets demonstrate that our proposed method outperforms the state-of-the-art methods in the literature.Comment: Accepted by IEEE Transactions on Image Processing, March 202

SDSS J013127.34−-032100.1: A newly discovered radio-loud quasar at z=5.18z=5.18 with extremely high luminosity

Only very few z>5 quasars discovered to date are radio-loud, with a radio-to-optical flux ratio (radio-loudness parameter) higher than 10. Here we report the discovery of an optically luminous radio-loud quasar, SDSS J013127.34-032100.1 (J0131-0321 in short), at z=5.18+-0.01 using the Lijiang 2.4m and Magellan telescopes. J0131-0321 has a spectral energy distribution consistent with that of radio-loud quasars. With an i-band magnitude of 18.47 and radio flux density of 33 mJy, its radio-loudness parameter is ~100. The optical and near-infrared spectra taken by Magellan enable us to estimate its bolometric luminosity to be L_bol ~ 1.1E48 erg/s, approximately 4.5 times greater than that of the most distant quasar known to date. The black hole mass of J0131-0321 is estimated to be 2.7E9 solar masses, with an uncertainty up to 0.4 dex. Detailed physical properties of this high-redshift, radio-loud, potentially super-Eddington quasar can be probed in the future with more dedicated and intensive follow-up observations using multi-wavelength facilities.Comment: 5 pages, 3 figures, accepted to ApJ