Collaborative Filtering Algorithms Based on Kendall Correlation in Recommender Systems

In this work, Kendall correlation based collaborative filtering algorithms for the recommender systems are proposed. The Kendall correlation method is used to measure the correlation amongst users by means of considering the relative order of the users＇ ratings. Kendall based algorithm is based upon a more general model and thus could be more widely applied in e-commerce. Another discovery of this work is that the consideration of only positive correlated neighbors in prediction, in both Pearson and Kendall algorithms, achieves higher accuracy than the consideration of all neighbors, with only a small loss of coverage.

Factorial analysis on forest canopy density restoration in the burned area of northern Great Xing＇an Mountains, China

The restoration of forest landscape has drawn much attention since thecatastrophic fire took place on the northern slope of Great Xing'an Mountains in 1987. Forest canopydensity, which has close relation to forest productivity, was selected as a key factor to find howmuch the forest quality was changed 13 years after fire, and how fire severity, regeneration way andterrain factors influenced the restoration of forest canopy density, based on forest inventory datain China, and using Kendall Bivariate Correlation Analysis, and Distances Correlation Analysis. Theresults showed that fire severity which was inversely correlated with forest canopy density gradewas an initial factor among all that selected. Regeneration way which did not remarkably affectforest canopy density restoration in short period, may shorten the cycle of forest succession andpromote the forest productivity of conophorium in the future. Among the three terrain factors, theeffect of slope was the strongest, the position on slope was the second and the aspect was the last.

Uncertainty analysis of correlated non-normal geotechnical parameters using Gaussian copula

Determining the joint probability distribution of correlated non-normal geotechnical parameters based on incomplete statistical data is a challenging problem.This paper proposes a Gaussian copula-based method for modelling the joint probability distribution of bivariate uncertain data.First,the concepts of Pearson and Kendall correlation coefficients are presented,and the copula theory is briefly introduced.Thereafter,a Pearson method and a Kendall method are developed to determine the copula parameter underlying Gaussian copula.Second,these two methods are compared in computational efficiency,applicability,and capability of fitting data.Finally,four load-test datasets of load-displacement curves of piles are used to illustrate the proposed method.The results indicate that the proposed Gaussian copula-based method can not only characterize the correlation between geotechnical parameters,but also construct the joint probability distribution function of correlated non-normal geotechnical parameters in a more general way.It can serve as a general tool to construct the joint probability distribution of correlated geotechnical parameters based on incomplete data.The Gaussian copula using the Kendall method is superior to that using the Pearson method,which should be recommended for modelling and simulating the joint probability distribution of correlated geotechnical parameters.There exists a strong negative correlation between the two parameters underlying load-displacement curves.Neglecting such correlation will not capture the scatter in the measured load-displacement curves.These results substantially extend the application of the copula theory to multivariate simulation in geotechnical engineering.

Inter-annual variations in vegetation and their response to climatic factors in the upper catchments of the Yellow River from 2000 to 2010

To understand the variations in vegetation and their correlation with climate factors in the upper catchments of the Yellow River, China, Normalized Difference Vegetation Index（NDVI） time series data from 2000 to 2010 were collected based on the MOD13Q1 product. The coefficient of variation, Theil–Sen median trend analysis and the Mann–Kendall test were combined to investigate the volatility characteristic and trend characteristic of the vegetation. Climate data sets were then used to analyze the correlation between variations in vegetation and climate change. In terms of the temporal variations, the vegetation in this study area improved slightly from 2000 to 2010, although the volatility characteristic was larger in 2000–2005 than in 2006–2010. In terms of the spatial variation, vegetation which is relatively stable and has a significantly increasing trend accounts for the largest part of the study area. Its spatial distribution is highly correlated with altitude, which ranges from about 2000 to 3000 m in this area. Highly fluctuating vegetation and vegetation which showed a significantly decreasing trend were mostly distributed around the reservoirs and in the reaches of the river with hydropower developments. Vegetation with a relatively stable and significantly decreasing trend and vegetation with a highly fluctuating and significantly increasing trend are widely dispersed. With respect to the response of vegetation to climate change, about 20–30% of the vegetation has a significant correlation with climatic factors and the correlations in most areas are positive： regions with precipitation as the key influencing factor account for more than 10% of the area; regions with temperature as the key influencing factor account for less than 10% of the area; and regions with precipitation and temperature as the key influencing factors together account for about 5% of the total area. More than 70% of the vegetation has an insignificant correlation with climatic factors.