Joint Tensor Factorization and Outlying Slab Suppression with Applications

We consider factoring low-rank tensors in the presence of outlying slabs. This problem is important in practice, because data collected in many real-world applications, such as speech, fluorescence, and some social network data, fit this paradigm. Prior work tackles this problem by iteratively selecting a fixed number of slabs and fitting, a procedure which may not converge. We formulate this problem from a group-sparsity promoting point of view, and propose an alternating optimization framework to handle the corresponding $\ell_p$ ($0<p\leq 1$) minimization-based low-rank tensor factorization problem. The proposed algorithm features a similar per-iteration complexity as the plain trilinear alternating least squares (TALS) algorithm. Convergence of the proposed algorithm is also easy to analyze under the framework of alternating optimization and its variants. In addition, regularization and constraints can be easily incorporated to make use of \emph{a priori} information on the latent loading factors. Simulations and real data experiments on blind speech separation, fluorescence data analysis, and social network mining are used to showcase the effectiveness of the proposed algorithm

CDMF: A Deep Learning Model based on Convolutional and Dense-layer Matrix Factorization for Context-Aware Recommendation

We proposes a novel deep neural network based recommendation model named Convolutional and Dense-layer Matrix Factorization (CDMF) for Context-aware recommendation, which is to combine multi-source information from item description and tag information. CDMF adopts a convolution neural network to extract hidden feature from item description as document and then fuses it with tag information via a full connection layer, thus generates a comprehensive feature vector. Based on the matrix factorization method, CDMF makes rating prediction based on the fused information of both users and items. Experiments on a real dataset show that the proposed deep learning model obviously outperforms the state-of-art recommendation methods

Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications

Nonnegative matrix factorization (NMF) has become a workhorse for signal and data analytics, triggered by its model parsimony and interpretability. Perhaps a bit surprisingly, the understanding to its model identifiability---the major reason behind the interpretability in many applications such as topic mining and hyperspectral imaging---had been rather limited until recent years. Beginning from the 2010s, the identifiability research of NMF has progressed considerably: Many interesting and important results have been discovered by the signal processing (SP) and machine learning (ML) communities. NMF identifiability has a great impact on many aspects in practice, such as ill-posed formulation avoidance and performance-guaranteed algorithm design. On the other hand, there is no tutorial paper that introduces NMF from an identifiability viewpoint. In this paper, we aim at filling this gap by offering a comprehensive and deep tutorial on model identifiability of NMF as well as the connections to algorithms and applications. This tutorial will help researchers and graduate students grasp the essence and insights of NMF, thereby avoiding typical `pitfalls' that are often times due to unidentifiable NMF formulations. This paper will also help practitioners pick/design suitable factorization tools for their own problems.Comment: accepted version, IEEE Signal Processing Magazine; supplementary materials added. Some minor revisions implemente

Capacity Matching Based Model for Protected Left Turn Phases Design of Adjacent Signalized Intersections Along Arterial Roads

A protected left turn phase is often used at intersections with heavy left turns. This may induce a capacity gap between adjacent intersections along the arterial road among which only parts of intersection are with protected left turn phase. A model for integrated optimization of protected left turn phases for adjacent intersections along the arterial road is developed to solve this problem. Two objectives are considered: capacity gap minimization and capacity maximization. The problems are formulated as Binary-Integer-Linear-Programs, which are solvable by standard branch-and-bound routine. A set of constraints have been set up to ensure the feasibility of the resulting optimal left turn phase type and signal settings. A field intersections group of the Wei-er Road of Ji’nan city is used to test the proposed model. The results show that the method can decrease the capacity gap between adjacent intersections, reduce the delay as well as increase the capacity in comparison with the field signal plan and signal plan optimized by Synchro. The sensitivity analysis has further demonstrated the potential of the proposed approach to be applied in coordinated design of left turn phases between adjacent intersections along the arterial road under different traffic demandpatterns

Design monolayer iodinenes based on halogen bond and tiling theory

Xenes, two-dimensional (2D) monolayers composed of a single element, with graphene as a typical representative, have attracted widespread attention. Most of the previous Xenes, X from group-IIIA to group-VIA elements have bonding characteristics of covalent bonds. In this work, we for the first time unveil the pivotal role of a halogen bond, which is a distinctive type of bonding with interaction strength between that of a covalent bond and a van der Waals interaction, in 2D group-VIIA monolayers. Combing the ingenious non-edge-to-edge tiling theory and state-of-art ab initio method with refined local density functional M06-L, we provide a precise and effective bottom-up construction of 2D iodine monolayer sheets, iodinenes, primarily governed by halogen bonds, and successfully design a category of stable iodinenes, encompassing herringbone, Pythagorean, gyrated truncated hexagonal, i.e. diatomic-kagome, and gyrated hexagonal tiling pattern. These iodinene structures exhibit a wealth of properties, such as flat bands, nontrivial topology, and fascinating optical characteristics, offering valuable insights and guidance for future experimental investigations. Our work not only unveils the unexplored halogen bonding mechanism in 2D materials but also opens a new avenue for designing other non-covalent bonding 2D materials.Comment: 6 pages, 4 figure

Early Cretaceous high-Ti and low-Ti mafic magmatism in Southeastern Tibet: Insights into magmatic evolution of the Comei Large Igneous Province

The Dala diabase intrusion, at the southeastern margin of the Yardoi gneiss dome, is located within the outcrop area of the ~ 132 Ma Comei Large Igneous Province (LIP), the result of initial activity of the Kerguelen plume. We present new zircon U-Pb geochronology results to show that the Dala diabase was emplaced at ~ 132 Ma and geochemical data (whole-rock element and Sr-Nd isotope ratios, zircon Hf isotopes and Fe-Ti oxide mineral chemistry) to confirm that the Dala diabase intrusion is part of the Comei LIP. The Dala diabase can be divided into a high-Mg/low-Ti series and a low-Mg/high-Ti series. The high-Mg/low-Ti series represents more primitive mafic magma compositions that we demonstrate are parental to the low-Mg/high-Ti series. Fractionation of olivine and clinopyroxene, followed by plagioclase within the low-Mg series, lead to systematic changes in concentrations of mantle compatible elements (Cr, Co, Ni, and V), REEs, HFSEs, and major elements such as Ti and P. Some Dala samples from the low-Mg/high-Ti series contain large ilmenite clusters and show extreme enrichment of Ti with elevated Ti/Y ratios, likely due to settling and accumulation of ilmenite during the magma chamber evolution. However, most samples from throughout the Comei LIP follow the Ti-evolution trend of the typical liquid line of descent (LLD) of primary OIB compositions, showing strong evidence of control of Ti contents by differentiation processes. In many other localities, however, primitive magmas are absent and observed Ti contents of evolved magmas cannot be quantitatively related to source processes. Careful examination of the petrogenetic relationship between co-existing low-Ti and high-Ti mafic rocks is essential to using observed rock chemistry to infer source composition, location, and degree of melting