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Yanguang Chen

Publications and source records attributed to Yanguang Chen.

At least 19 recordsLinked to original sources
arXiv2025

From Events to Trending: A Multi-Stage Hotspots Detection Method Based on Generative Query Indexing

LLM-based conversational systems have become a popular gateway for information access, yet most existing chatbots struggle to handle news-related trending queries effectively. To improve user experience, an effective trending query detection method is urgently needed to enable differentiated processing of such target traffic. However, current research on trending detection tailored to the dialogue system scenario remains largely unexplored, and methods designed for traditional search engines often underperform in conversational contexts due to radically distinct query distributions and expression patterns. To fill this gap, we propose a multi-stage framework for trending detection, which achieves systematic optimization from both offline generation and online identification perspectives. Specifically, our framework first exploits selected hot events to generate index queries, establishing a key bridge between static events and dynamic user queries. It then employs a retrieval matching mechanism for real-time online detection of trending queries, where we introduce a cascaded recall and ranking architecture to balance detection efficiency and accuracy. Furthermore, to better adapt to the practical application scenario, our framework adopts a single-recall module as a cold-start strategy to collect online data for fine-tuning the reranker. Extensive experiments demonstrate that our framework significantly outperforms baseline methods in both offline evaluations and online A/B tests, and user satisfaction is relatively improved by 27\% in terms of positive-negative feedback ratio.

cs.IR↗
arXiv2025

A Study on the Curves of Scaling Behavior of Fractal Cities

The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching a set of basic problems of the scaling behavior curves in urban studies by using mathematical reasoning and empirical analysis. The main findings are as follows. First, the formula of scaling behavior curves is derived from a fractal model based on hierarchical structure of urban systems. Second, the relationships between the formula of scaling behavior curves and similarity dimension are revealed. Third, according to the fractal dimension measurement methods, the scaling behavior curves are divided into two different types. Fourth, empirically, 1-dimensional spatial autocorrelation function of scaling behavior curves can be employed to reveal the basic property of scaling behavior curves. The scaling behavior curves can be utilized to evaluate fractal development extent of urban systems and identify scaling ranges of fractal cities. In positive studies, the curves may be used to help distinguish the boundaries between urban areas and rural areas and self-affine fractal structure behind the dynamical process of spatial correlation.

physics.soc-ph↗
arXiv2025

Structural Decomposition of Moran's Index by Getis-Ord's Indices

Moran's index and Getis-Ord,s indices are important statistical measures of spatial autocorrelation analysis. Each of them has its own function and scope of application. However, the association of Moran index with Getis-Ord index is not clear. This paper is devoted to deriving and verify the relationships between Moran's index and Getis-Ord's indices using mathematical reasoning and empirical analysis. Getis-Ord's indices are employed to decompose Moran's index. The results show that there is a strict nonlinear relationship between Moran's index and Getis-Ord's indices. Moran's index consists of four components: global Getis-Ord's index, sum of local Getis-Ord's indices, number of elements, and size correlation function. Thus the mathematical structure of Moran's index is revealed. A theoretical discovery is that the characteristics of spatial autocorrelation depends on the relationship between the global Getis-Ord's index and the sum of local Getis-Ord's indices, as well as the number of spatial elements. Local Getis-Ord's indices proved to be equivalent to the potential indices based on gravity model. A conclusion can be drawn that Moran's index is related to gravity model, and thus spatial autocorrelation is associated with spatial interaction. This indicates that weak spatial interaction leads to not significant spatial autocorrelation. The conclusion is supported by observational data. This study not only helps to better understand the basic statistics of spatial analysis, but also contributes to the further development of spatial autocorrelation theory.

physics.soc-ph↗
arXiv2025

An Approach to Estimating Quadratic Logistic Model Parameters of Fractal Dimension Curves

The fractal dimension curves of urban form and growth fall into two categories: One can be described by common logistic function, and the other can be described with quadratic logistic function. The approach to estimating the parameter of the ordinary logistic model has been developed. However, how to estimate the parameter of quadratic logistic model is still a problem. This paper is devoted to finding a nonlinear regressive approach for estimating parameter values of quadratic logistic model of fractal dimension curves. The process can be summarized as below. First, differentiating quadratic logistic function in theory with respect to time yields a growth rate equation of fractal dimension. Second, discretizing the growth rate equation yields a nonlinear regressive model of fractal dimension curve. Third, applying the least squares method to the nonlinear regressive equation yields the capacity parameter value of the quadratic logistic model. Fourth, substituting the capacity parameter value into the quadratic logistic model and changing it into a quasilinear form, we can estimate the other parameter values by ordinary linear regression analysis. In this way, a practical quadratic logistic model of fractal dimension curves can be gained. The approach is applied to multifractal dimension curves of Beijing city to show its effectiveness. The method can be extended to estimate the parameter values of quadratic logistic models in many fields besides urban science.

physics.soc-ph↗
arXiv2025

Data-driven Mixed Integer Optimization through Probabilistic Multi-variable Branching

In this paper, we propose a Pre-trained Mixed Integer Optimization framework (PreMIO) that accelerates online mixed integer program (MIP) solving with offline datasets and machine learning models. Our method is based on a data-driven multi-variable cardinality branching procedure that splits the MIP feasible region using hyperplanes chosen by the concentration inequalities. Unlike most previous ML+MIP approaches that either require complicated implementation or suffer from a lack of theoretical justification, our method is simple, flexible, provable, and explainable. Numerical experiments on both classical OR benchmark datasets and real-life instances validate the efficiency of our proposed method.

math.OC↗
arXiv2025

On measure problems in allometric analysis of cities -- How to correctly understand the law of allometric growth

The law of allometric growth originated from biology has been widely used in urban research for a long time. Some conditional research conclusions based on biological phenomena have been erroneously transmitted in the field of urban geography, leading to some misunderstandings. One of the misunderstandings is that allometric analysis must be based on average measure. The aim of this paper is at explaining how to correctly understand the law of urban allometric growth by means of the methods of literature analysis and mathematical analysis. The results show the average measures cannot be applied to all types of allometric relationships, and the allometric relationships based on average measures cannot be derived from a general principle. Whether it is an empirical model or a theoretical model of allometric growth, its generation and derivation are independent of the average measures. Conclusions can be reached that the essence of allometric growth lies in that the ratio of two related general relative growth rates is a constant, and this constant represents the allometric scaling exponent and fractal dimension ratio. The average measures are helpful to estimate the allometric scaling exponent value which accords with certain theoretical expectations more effectively.

physics.soc-ph↗
arXiv2023

Multifractal scaling analyses of the spatial diffusion pattern of COVID-19 pandemic in Chinese mainland

Revealing spatiotemporal evolution regularity in the spatial diffusion of epidemics is helpful for preventing and controlling the spread of epidemics. Based on the real-time COVID-19 datasets by prefecture-level cities, this paper is devoted to exploring the multifractal scaling in spatial diffusion pattern of COVID-19 pandemic and its evolution characteristics in Chinese mainland. The ArcGIS technology and box-counting method are employed to extract spatial data and the least square regression based on rescaling probability (miu-weight method) is used to calculate fractal parameters. The results show multifractal distribution of COVID-19 pandemic in China. The generalized correlation dimension spectrums are inverse S-shaped curves, but the fractal dimension values significantly exceed the Euclidean dimension of embedding space when moment order q<<0. The local singularity spectrums are asymmetric unimodal curves, which slant to right. The fractal dimension growth curves are shown as quasi S-shaped curves. From these spectrums and growth curves, the main conclusions can be drawn as follows: First, self-similar patterns developed in the process of COVID-19 pandemic, which seem be dominated by multifractal scaling law. Second, the spatial pattern of COVID-19 across China can be characterized by global clustering with local disordered diffusion. Third, the spatial diffusion process of COVID-19 in China experienced four stages, i.e., initial stage, the rapid diffusion stage, the hierarchical diffusion stage, and finally the contraction stage. This study suggests that multifractal theory can be utilized to characterize spatio-temporal diffusion of COVID-19 pandemic, and the case analyses may be instructive for further exploring natural laws of spatial diffusion.

physics.soc-ph↗
arXiv2023

Scaling invariance of spatial autocorrelation in urban built-up area

City is proved to be a scale-free phenomenon, and spatial autocorrelation is often employed to analyze spatial redundancy of cities. Unfortunately, spatial analysis results deviated practical requirement in many cases due to fractal nature of cities. This paper is devoted to revealing the internal relationship between the scale dependence of Moran's I and fractal scaling. Mathematical reasoning and empirical analysis are employed to derive and test the model on the scale dependence of spatial autocorrelation. The data extraction way for fractal dimension estimation is box-counting method, and parameter estimation relies on the least squares regression. In light of the locality postulate of spatial correlation and the idea of multifractals, a power law model on Moran's I changing with measurement scale is derived from the principle of recursive subdivision of space. The power exponent is proved to be a function of fractal dimension. This suggests that the numerical relationship between Moran's I and fractal dimension can be established through the scaling process of granularity. An empirical analysis is made to testify the theoretical model. It can be concluded that spatial autocorrelation of urban built-up area has no characteristic scale in many cases, and urban spatial analysis need new thinking.

physics.soc-ph↗
arXiv2023

Geographical space based on urban allometry and fractal dimension

The conventional concept of geographical space is mainly referred to actual space based on landscape, maps, and remote sensing images. However, this notion of space is not enough to interpret different types of fractal dimension of cities. The fractal dimensions derived from Zipf's law and time series analysis do not belong to the traditional geographical space. Based on the nature of the datasets, the urban allometry can be divided into three types: longitudinal allometry indicating time, transversal allometry indicating hierarchy, and isoline allometry indicating space. According to the principle of dimension consistency, an allometric scaling exponent must be a ratio of one fractal dimension to another. From abovementioned three allometric models, we can derive three sets of fractal dimension. In light of the three sets of fractal dimension and the principle of dimension uniqueness, urban geographical space falls into three categories, including the real space based on isoline allometry and spatial distribution, the phase space based on longitudinal allometry and time series, and order space based on transversal allometry and rank-size distribution. The generalized space not only helps to explain various fractal dimensions of cities, but also can be used to develop new theory and methods of geospatial analysis.

physics.soc-ph↗
arXiv2023

Logistic Regression Modeling Based on Fractal Dimension Curves of Urban Growth

Fractal dimension is an effective scaling exponent of characterizing scale-free phenomena such as cities. Urban growth can be described with time series of fractal dimension of urban form. However, how to explain the factors behind fractal dimension sequences that affect fractal urban growth remains a problem. This paper is devoted to developing a method of logistic regression modeling, which can be employed to find the influencing factors of urban growth and rank them in terms of importance. The logistic regression model comprises three components. The first is a linear function indicating the relationship between time dummy and influencing variables. The second is a logistic function linking fractal dimension and time dummy. The third is a ratio function representing normalized fractal dimension. The core composition is the logistic function that implies the dynamics of spatial replacement. The logistic regression modeling can be extended to other spatial replacement phenomena such as urbanization, traffic network development, and technology innovation diffusion. This study contributes to the development of quantitative analysis tools based on the combination of fractal geometry and conventional mathematical methods.

physics.soc-ph↗
arXiv2023

Nonlinear Autoregressive Approach to Estimating Logistic Model Parameters of Urban Fractal Dimension Curves

A time series of fractal dimension values of urban form can form a fractal dimension curve and reflects urban growth. In many cases, the fractal dimension curves of cities can be modeled with logistic function, which in turn can be used to make prediction analysis and stage division studies of urban evolution. Although there is more than one method available, it is difficult for many scholars to estimate the capacity parameter value in a logistic model. This paper shows a nonlinear autoregressive approach to estimating parameter values of logistic growth model of fractal dimension curves. The process is as follows. First, differentiating logistic function in theory with respect to time yields a growth rate equation of fractal dimension. Second, discretizing the growth rate equation yields a nonlinear autoregressive equation of fractal dimension. Third, applying the least square calculation to the nonlinear autoregressive equation yields partial parameter values of the logistic model. Fourth, substituting the preliminarily estimated results into the logistic models and changing it into a linear form, we can estimate the other parameter values by linear regression analysis. Finally, a practical logistic model of fractal dimension curves is obtained. The approach is applied the Baltimore's and Shenzhen's fractal dimension curves to demonstrate how to make use of it. This study provides a simple and effective method for estimating logistic model parameters, and it can be extended to the logistic models in other fields.

physics.soc-ph↗
arXiv2023

Multivariable-based correlation dimension analysis for generalized space

Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been reported. An abstract space can be defined by multivariable distance metrics, which is frequently met in scientific research. Based on the ideas from fractals, this paper is devoted to developing correlation dimension analysis method for generalized geographical space by means of mathematical derivation and empirical analysis. Defining a mathematical distance or statistical distance, we can construct a generalized correlation function. If the relationship between correlation function and correlation lengths follows a power law, the power exponent can be demonstrated to associate with correlation dimension. Thus fractal dimension can be employed to analyze the structure and nature of generalized geographical space. This suggests that fractal geometry can be generalized to explore scale-free abstract geographical space. The theoretical model was proved mathematically, and the analytical method was illustrated by using observational data. This research is helpful to expand the application of fractal theory in geographical analysis, and the results and conclusions can be extended to other scientific fields.

physics.soc-ph↗
arXiv2023

An Integrated Framework of Spatial Autocorrelation Analysis Based on Gravity Model

Spatial interaction and spatial autocorrelation are two different fields of geo-spatial analysis, revealing the internal relationship between the two fields will help to develop the theory and method of geographical analysis. This paper is devoted to deducing a system of spatial correlation analysis models from the gravity model by mathematical derivation. The main results are as follows. First, a set of potential energy measurements are derived from the gravity model. Second, a pair of correlation equations, including an inner product equation and an outer product equation, are constructed based on the quadratic form of potential energy formula. Third, a series of spatial autocorrelation statistics, including Moran's index and Getis-Ord's index are derived from the potential energy formula. Fourth, the concept of fractal dimension is introduced into spatial weight matrix. The observational data of urban systems are employed to make an empirical analysis, demonstrating the application procedure of newly derived models. A conclusion can be drawn that spatial autocorrelation is actually rooted in spatial interaction process, and an improved methodology of spatial analysis can be developed by integrating spatial autocorrelation models and gravity model into the same framework.

physics.soc-ph↗
arXiv2023

Exploring the relationship between urbanization and Ikization

The phenomenon of Iks was first found by anthropologists and biologists, but it is actually a problem of human geography. However, it has not yet drawn extensive attention of geographers. In this paper, a hypothesis of ikization is presented that sudden and violent change of geographical environments results in dismantling of traditional culture, which then result in collective depravity of a nationality. By quantitative analysis and mathematical modeling, the causality between urbanization and ikization is discussed, and the theory of replacement dynamics is employed to interpret the process of ikization. Urbanization is in essence a nonlinear process of population replacement. Urbanization may result in ikization because that the migration of population from rural regions to urban regions always give rise to abrupt changes of geographical environments and traditional culture. It is necessary to protect the geographical environment against disruption, and to inherit and develop traditional culture in order to avoid ikization of a nation. The approach to solving the problems caused by fast urbanization is to reconstruct geographical environment so that rural culture will be naturally replaced by urban culture.

physics.soc-ph↗
arXiv2023

Spatial autocorrelation equation based on Moran's index

Based on standardized vector and globally normalized weight matrix, Moran's index of spatial autocorrelation analysis has been expressed as a formula of quadratic form. Further, based on this formula, an inner product equation and outer product equation of the standardized vector can be constructed for Moran's index. However, the theoretical foundations and application direction of these equations are not yet clear. This paper is devoted to exploring the inner and outer product equations of Moran's index. The methods include mathematical derivation and empirical analysis. The results are as follows. First, based on the inner product equation, two spatial autocorrelation models can be constructed. One bears constant terms, and the other bear no constant term. The spatial autocorrelation models can be employed to calculate Moran's index by regression analysis. Second, the inner and outer product equations can be used to improve Moran's scatterplot. The normalized Moran's scatterplot can show more geospatial information than the conventional Moran's scatterplot. A conclusion can be reached that the spatial autocorrelation models are useful spatial analysis tools, complementing the uses of spatial autocorrelation coefficient and spatial autoregressive models. These models are helpful for understanding the boundary values of Moran's index and spatial autoregressive modeling process.

stat.ME↗
arXiv2023

Deriving two sets of bounds of Moran's index by conditional extremum method

Moran's index is a basic measure of spatial autocorrelation, which has been applied to varied fields of both natural and social sciences. A good measure should have clear boundary values or critical value. However, for Moran's index, both boundary values and critical value are controversial. In this paper, a novel method is proposed to derive the boundary values of Moran's index. The key lies in finding conditional extremum based on quadratic form of defining Moran's index. As a result, two sets of boundary values are derived naturally for Moran's index. One is determined by the eigenvalues of spatial weight matrix, and the other is determined by the quadratic form of spatial autocorrelation coefficient (-1<Moran's I<1). The intersection of these two sets of boundary values gives four possible numerical ranges of Moran's index. A conclusion can be reached that the bounds of Moran's index is determined by size vector and spatial weight matrix, and the basic boundary values are -1 and 1. The eigenvalues of spatial weight matrix represent the maximum extension length of the eigenvector axes of n geographical elements at different directions. This work solves one of the fundamental problems of spatial autocorrelation analysis.

physics.soc-ph↗
arXiv2022

Derivation of an Inverse Spatial Autoregressive Model for Estimating Moran's Index

Spatial autocorrelation measures such as Moran's index can be expressed as a pair of equations based on a standardized size variable and a globally normalized weight matrix. One is based on inner product, and the other is based on outer product of the size variable. The inner product equation is actually a spatial autocorrelation model. However, the theoretical basis of the inner product equation for Moran's index is not clear. This paper is devoted to revealing the antecedents and consequences of the inner product equation of Moran's index. The method is mathematical derivation and empirical analysis. The main results are as follows. First, the inner product equation is derived from a simple spatial autoregressive model, and thus the relation between Moran's index and spatial autoregressive coefficient is clarified. Second, the least squares regression is proved to be one of effective approaches for estimating spatial autoregressive coefficient. Third, the value ranges of the spatial autoregressive coefficient can be identified from three angles of view. A conclusion can be drawn that a spatial autocorrelation model is actually an inverse spatial autoregressive model, and Moran's index and spatial autoregressive models can be integrated into the same framework through inner product and outer product equations. This work may be helpful for understanding the connections and differences between spatial autocorrelation measurements and spatial autoregressive modeling.

stat.ME↗
arXiv2022

Coefficient Decomposition of Spatial Regressive Models Based on Standardized Variables

Spatial autocorrelation analysis is the basis for spatial autoregressive modeling. However, the relationships between spatial correlation coefficients and spatial regression models are not yet well clarified. The paper is devoted to explore the deep structure of spatial regression coefficients. By means of mathematical reasoning, a pair of formulae of canonical spatial regression coefficients are derived from a general spatial regression model based on standardized variables. The spatial auto- and lag-regression coefficients are reduced to a series of statistic parameters and measurements, including conventional regressive coefficient, Pearson correlation coefficient, Moran's indexes, spatial cross-correlation coefficients, and the variance of prediction residuals. The formulae show determinate inherent relationships between spatial correlation coefficients and spatial regression coefficients. New finding is as below: the spatial autoregressive coefficient mainly depends on the Moran's index of the independent variable, while the spatial lag-regressive coefficient chiefly depends on the cross-correlation coefficient of independent variable and dependent variable. The observational data of an urban system in Beijing, Tianjin, and Hebei region of China were employed to verify the newly derived formulae, and the results are satisfying. The new formulae and their variates are helpful for understand spatial regression models from the perspective of spatial correlation and can be used to assist spatial regression modeling.

stat.ME↗