Related papers: A comparison between two OLS-based approaches to e…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…
The spatial pattern of urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper…
Ordinary least squares (OLS) linear regression is one of the most basic statistical techniques for data analysis. In the main stream literature and the statistical education, the study of linear regression is typically restricted to the…
Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article…
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…
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
In this paper we propose a multivariate ordinal regression model which allows the joint modeling of three-dimensional panel data containing both repeated and multiple measurements for a collection of subjects. This is achieved by a…
We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild…
In statistics, series of ordinary least squares problems (OLS) are used to study the linear correlation among sets of variables of interest; in many studies, the number of such variables is at least in the millions, and the corresponding…
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…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric…
The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at…
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between…
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a measure of scale dependence, which indicates the scale-free distribution of urban…
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…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
In this letter, we consider the problem of field estimation using binary measurements. Previous work has formulated the problem as a parameter estimation problem, with the parameter estimation carried out in an online manner using…
This article deals with asimple issue: if we have grouped data with a binary dependent variable and want to include fixed effects (group specific intercepts) in the specification, is Ordinary Least Squares (OLS) in any way superior to a…