SNIG PROPERTY OF MATRIX LOW-RANK FACTORIZATION MODEL

Recently, the matrix factorization model attracts increasing attentions in handling large-scale rank minimization problems, which is essentially a nonconvex minimization problem. Specifically, it is a quadratic least squares problem and consequently a quartic polynomial optimization problem. In this paper, we introduce a concept of the SNIG （＂Second-order Necessary optimality Implies Global optimality＂） condition which stands for the property that any second-order stationary point of the matrix factorization model must be a global minimizer. Some scenarios under which the SNIG condition holds are presented. Furthermore, we illustrate by an example when the SNIG condition may fail.

Importance Ranking of Accident Factors of Construction Tower Crane by AHP Technique

In Korea construction industry, the increase of tower crane’s usage continuously and the accidents of tower crane are increasing simultaneously. But research on tower crane is insufficient for reducing the tower crane accident. This study aims to derive the importance ranking of accident factors of cab-control tower crane by AHP analysis. AHP survey was conducted on experts such as construction engineer, construction manager, safety engineer, and tower crane operator, who have more than 10-year career. The results of AHP analysis reveal that top ranking factor of cab-control tower crane’s accident is erection work. Therefore, the derived factors should be managed, and the priority measures taken for reducing the tower crane accidents according to the ranking of accident factors.

Coal reservoir characteristics and their controlling factors in the eastern Ordos basin in China

In the eastern Ordos basin, due to the diversity of the tectonic setting, coal rank, gas content and permeability, coal reservoirs have differing characteristics. In this paper, based on coal reservoir geometry, gas content, adsorption capacity, pores and fissures developments and permeability data, the coalbed methane(CBM) reservoir characteristics and their controlling factors in the eastern Ordos basin is discussed. The results show that, due to undergoing different paleo-temperatures in the geological history,coal rank has a higher trend from the north part to the south and from the shallow part to the inward basin, which determines CBM distribution and recoverability. In the north, although having large coal thickness and high permeability, Zhungeer-Xingxian coal rank is low, and gas content is small. In the central part, with medium rank, higher gas content and relatively high permeability, and the Wubao-Liulin area is the most favorable area in the eastern Ordos basin. In the southern part, medium and high metamorphism coal occurs, and although having the highest gas content, the permeability in the Hancheng area is low due to the development of sheared coal.

Recommender systems based on ranking performance optimization

The rapid development of online services and information overload has inspired the fast development of recommender systems, among which collaborative filtering algorithms and model-based recommendation approaches are wildly exploited. For instance, matrix factorization （MF） demonstrated successful achievements and advantages in assisting internet users in finding interested information. These existing models focus on the prediction of the users＇ ratings on unknown items. The performance is usually evaluated by the metric root mean square error （RMSE）. However, achieving good performance in terms of RMSE does not always guarantee a good ranking performance. Therefore, in this paper, we advocate to treat the recommendation as a ranking problem. Normalized discounted cumulative gain （NDCG） is chosen as the optimization target when evaluating the ranking accuracy. Specifically, we present three ranking-oriented recommender algorithms, NSME AdaMF and AdaNSME NSMF builds a NDCG approximated loss function for Matrix Factorization. AdaMF is based on an algorithm by adaptively combining component MF recommenders with boosting method. To combine the advantages of both algorithms, we propose AdaNSME which is a hybird of NSMF and AdaME and show the superiority in both ranking accuracy and model generalization. In addition, we compare our proposed approaches with the state-of-the-art recommendation algorithms. The comparison studies confirm the advantage of our proposed approaches.

Completely Positive Matrices Having Cyclic Graphs

We prove that a CP matrix A having cyclic graph has exactly two minimal rank 1 factorization if det M(A) > 0 and has exactly one minimal rank 1 factorization if detM(A) = 0.