non-Euclidean Distance Research Articles

A Geographically Temporal Weighted Regression Approach with Travel Distance for House Price Estimation

Previous studies have demonstrated that non-Euclidean distance metrics can improve model fit in the geographically weighted regression (GWR) model. However, the GWR model often considers spatial nonstationarity and does not address variations in local temporal issues. Therefore, this paper explores a geographically temporal weighted regression (GTWR) approach that accounts for both spatial and temporal nonstationarity simultaneously to estimate house prices based on travel time distance metrics. Using house price data collected between 1980 and 2016, the house price response and explanatory variables are then modeled using both the GWR and the GTWR approaches. Comparing the GWR model with Euclidean and travel distance metrics, the GTWR model with travel distance obtains the highest value for the coefficient of determination ( R 2 ) and the lowest values for the Akaike information criterion (AIC). The results show that the GTWR model provides a relatively high goodness of fit and sufficient space-time explanatory power with non-Euclidean distance metrics. The results of this study can be used to formulate more effective policies for real estate management.

A Spatial Fuzzy Clustering Algorithm With Kernel Metric Based on Immune Clone for SAR Image Segmentation

The fuzzy c-means (FCM) clustering algorithm has been widely used in image segmentation. However, FCM exhibits poor robustness to noise, often leading to unsatisfactory segmentations on noisy images. Additionally, the FCM algorithm is sensitive to the choice of initial cluster centers. In order to solve these problems, this paper proposes clone kernel spatial FCM (CKS_FCM), which improves segmentation performance in several ways. First, in CKS_FCM, an immune clone algorithm is used to generate the initial cluster centers, which helps prevent the algorithm from converging on local optima. Second, CKS_FCM improves the robustness to noise by incorporating spatial information into the objective function of FCM. Third, CKS_FCM uses a non-Euclidean distance based on a kernels metric, instead of the Euclidean distance conventionally used in FCM, to enhance the segmentation accuracy (SA). We present experimental results on both real and synthetic SAR images, which suggest that the proposed method can generate higher accuracy, and obtain more robustness to noise, as compared against six state-of-the-art methods from the literatures.

Probabilistic Graphical Modeling Method for Inferring Hydraulic Conductivity Maps from Hydraulic Head Maps

AbstractThe ability to design and employ groundwater distribution models plays an important role in the development and application of regional water management policies and resource exploration. This paper presents a probabilistic reasoning approach for estimating groundwater levels over a geological map based on a limited number of available observations of hydraulic head and conductivity levels. The approach adapts, expands, and combines non-Euclidean distance kriging, probabilistic graphical modeling, and expectation maximization to provide a viable alternative to the currently existing, simulation-based methods of spatial interpolation. Upon outlining a conceptual framework for the proposed approach, this paper investigates the feasibility of using its key component, the Markov random field, with a flexible (learned) structure that recovers hydraulic conductivity maps from the knowledge of hydraulic head on those maps. The model is trained on a medium-sized data set of simulated hydraulic maps, and r...

EXTRAGALACTIC SYNCHROTRON TRANSIENTS IN THE ERA OF WIDE-FIELD RADIO SURVEYS. I. DETECTION RATES AND LIGHT CURVE CHARACTERISTICS

The impending era of wide-field radio surveys has the potential to revolutionize our understanding of astrophysical transients. Here we evaluate the prospects of a wide range of planned and hypothetical radio surveys using the properties and volumetric rates of known and hypothetical classes of extragalactic synchrotron radio transients (e.g., on-axis and off-axis gamma-ray bursts (GRBs), supernovae, tidal disruption events, compact object mergers). Utilizing these sources and physically motivated considerations we assess the allowed phase space of radio luminosity and peak timescale for extragalactic transients. We also include for the first time effects such as redshift evolution of the rates, K-corrections, and non-Euclidean luminosity distance, which affect the detection rates of the most sensitive surveys. The number of detected events is calculated by means of a Monte Carlo method, using the various survey properties (depth, cadence, area) and realistic detection criteria that include a cut on the minimum variability of the transients during the survey and an assessment of host galaxy contamination. We find that near-term GHz frequency surveys (ASKAP/VAST, Very Large Array Sky Survey) will detect few events: on- and off-axis long GRBs (LGRBs) and off-axis tidal disruption events, and neutron star binary mergers if of the mergers result in a stable millisecond magnetar. Low-frequency surveys (e.g., LOFAR) are unlikely to detect any transients, while a hypothetical large-scale mm survey may detect ?40 on-axis LGRBs. On the other hand, we find that SKA1 surveys at GHz have the potential to uncover thousands of transients, mainly on-axis and off-axis LGRBs, on-axis short GRBs, off-axis TDEs, and neutron star binary mergers with magnetar remnants.

A space-time model for carbapenemase-producing Klebsiella pneumoniae (KPC) cluster quantification in a high-complexity hospital.

A retrospective space-time permutation model with non-Euclidean distance criteria was applied within a high-complexity hospital setting to quantitatively explore cluster patterns of 273 patients infected with or colonized by carbapenemase-producing Klebsiella pneumoniae during 4 years. Results were compared to standard nosocomial active-surveillance methods. Two clusters were identified in the period, suggesting that space-time strategies for cluster quantification within confined environments may be useful.

A Fuzzy Neural Network Based on Non-Euclidean Distance Clustering for Quality Index Model in Slashing Process

The quality index model in slashing process is difficult to build by reason of the outliers and noise data from original data. To the above problem, a fuzzy neural network based on non-Euclidean distance clustering is proposed in which the input space is partitioned into many local regions by the fuzzy clustering based on non-Euclidean distance so that the computation complexity is decreased, and fuzzy rule number is determined by validity function based on both the separation and the compactness among clusterings. Then, the premise parameters and consequent parameters are trained by hybrid learning algorithm. The parameters identification is realized; meanwhile the convergence condition of consequent parameters is obtained by Lyapunov function. Finally, the proposed method is applied to build the quality index model in slashing process in which the experimental data come from the actual slashing process. The experiment results show that the proposed fuzzy neural network for quality index model has lower computation complexity and faster convergence time, comparing with GP-FNN, BPNN, and RBFNN.

Calibrating a Geographically Weighted Regression Model with Parameter-specific Distance Metrics

Geographically Weighted Regression (GWR) is a local technique that models spatially varying relationships, where Euclidean distance is traditionally used as default in its calibration. However, empirical work has shown that the use of non-Euclidean distance metrics in GWR can improve model performance, at least in terms of predictive fit. Furthermore, the relationships between the dependent and each independent variable may have their own distinctive response to the weighting computation, which is reflected by the choice of distance metric. Thus, we propose a back-fitting approach to calibrate a GWR model with parameter-specific distance metrics. To objectively evaluate this new approach, a simple simulation experiment is carried out that not only enables an assessment of prediction accuracy, but also parameter accuracy. The results show that the approach can provide both more accurate predictions and parameter estimates, than that found with standard GWR. Accurate localised parameter estimation is crucial to GWR's main use as a method to detect and assess relationship non-stationarity.

The Research of Algorithm of Optimum Route Calculation in Express Traffic System Based on Time Measure

The express traffic system could divide into highway traffic system and ordinary road traffic system, which have different linkage attributes and traffic attributes for segments and nodes. The time consumption space of traveling in the system is a non-Euclidean distance space. From the traffic condition of the express traffic system, the foundation data, principles and methods of NEDS algorithm are introduced. The steps and methods of optimum route planning in the express traffic system are deeply discussed. At the end, an example of optimum route planning in Henan express traffic system is given.

Techniques for Understanding User Usage Behavior on the Internet

Techniques for Understanding User Usage Behavior on the Internet

Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data

Geographically weighted regression (GWR) is an important local technique for exploring spatial heterogeneity in data relationships. In fitting with Tobler’s first law of geography, each local regression of GWR is estimated with data whose influence decays with distance, distances that are commonly defined as straight line or Euclidean. However, the complexity of our real world ensures that the scope of possible distance metrics is far larger than the traditional Euclidean choice. Thus in this article, the GWR model is investigated by applying it with alternative, non-Euclidean distance (non-ED) metrics. Here we use as a case study, a London house price data set coupled with hedonic independent variables, where GWR models are calibrated with Euclidean distance (ED), road network distance and travel time metrics. The results indicate that GWR calibrated with a non-Euclidean metric can not only improve model fit, but also provide additional and useful insights into the nature of varying relationships within the house price data set.

Approximations by LR-type fuzzy numbers

Recently, many scholars investigated interval, triangular, and trapezoidal approximations of fuzzy numbers. These publications can be grouped into two classes: Euclidean distance class and non-Euclidean distance class. Most approximations in Euclidean distance class can be calculated by formulas, but calculating approximations in the other class is more complicated. Furthermore, approximations in Euclidean distance class can be divided into two subclasses. One is to study approximations of fuzzy numbers without constraints, the other one is to study approximations preserving some attributes. In this paper, we use LR-type fuzzy numbers to approximate fuzzy numbers. The proposed approximations will generalize all recent approximations without constraints in Euclidean class. Also, an efficient formula is provided.

Relativistic differential-difference momentum operators and noncommutative differential calculus

The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.

Effective FCM noise clustering algorithms in medical images

The main motivation of this paper is to introduce a class of robust non-Euclidean distance measures for the original data space to derive new objective function and thus clustering the non-Euclidean structures in data to enhance the robustness of the original clustering algorithms to reduce noise and outliers. The new objective functions of proposed algorithms are realized by incorporating the noise clustering concept into the entropy based fuzzy C-means algorithm with suitable noise distance which is employed to take the information about noisy data in the clustering process. This paper presents initial cluster prototypes using prototype initialization method, so that this work tries to obtain the final result with less number of iterations. To evaluate the performance of the proposed methods in reducing the noise level, experimental work has been carried out with a synthetic image which is corrupted by Gaussian noise. The superiority of the proposed methods has been examined through the experimental study on medical images. The experimental results show that the proposed algorithms perform significantly better than the standard existing algorithms. The accurate classification percentage of the proposed fuzzy C-means segmentation method is obtained using silhouette validity index.

Relativistic kinetic momentum operators, half-rapidities and noncommutative differential calculus

It is shown that the generating function for the matrix elements of irreps of Lorentz group is the common eigenfunction of the interior derivatives of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions in the Relativistic Configuration Space (RCS). These derivatives commute and can be interpreted as the quantum mechanical operators of the relativistic momentum corresponding to the half of the non-Euclidean distance in the Lobachevsky momentum space (the mass shell).

An improved distance metric for the interpolation of link-based traffic data using kriging: a case study of a large-scale urban road network

The interpolation of link-based traffic data is an important topic for transportation researchers and engineers. In recent years the kriging method has been used in traffic data interpolation from the viewpoint of spatial analysis. This method has shown promising results, especially for a large-scale road network. However, existing studies using the Euclidean distance metric, which is widely used in traditional kriging, fail to accurately describe the spatial distance in a road network. In this article we introduce road network distance to describe spatial distance between road links, and we propose an improved distance metric called approximate road network distance (ARND), based on the isometric embedding theory, for solving the problem of the invalid spatial covariance function in kriging caused by the non-Euclidean distance metric. An improved Isomap algorithm is also proposed for obtaining the ARND metric. This study is tested on a large-scale urban road network with sparse road-link travel speeds derived from approximately 1200 ‘floating cars’ (GPS-enabled taxis). Comparison was conducted on both the Euclidean distance metric and the ARND metric. The validation results show that the use of the ARND metric can obtain better interpolation accuracy in different time periods and urban regions with different road network structures. Therefore, we conclude that the improved distance metric has the ability for improving kriging interpolation accuracy for link-based traffic data within real situations, providing more reliable basic traffic data for various traffic applications.

Iterative three-dimensional rigid object pose estimation with contour correspondence

Pose estimation of a three-dimensional (3D) rigid object based on monocular vision is a fundamental problem in computer vision. Existing methods usually presume that there is a certain feature projection correspondence available a priori between the input image and object's 3D model, which substantially reduces the mathematical complexity of the problem. However, in actual applications this presumption rarely holds. How to estimate the pose of a general 3D object with no feature projection correspondence available a priori is still not well resolved. In this study, the authors propose a new 3D rigid object pose estimation method based on object's contour and non-Euclidean multi-feature distance map, which solves both the pose estimation problem and the feature projection correspondence problem simultaneously and iteratively. Experiment results show that our method also has good performance in convergence speed, convergence radius and noise robustness.

Power series and analyticity over the quaternions

We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a quaternionic power series centered at 0 in its domain of convergence (which is a ball B(0,R) centered at 0). At each point p of this ball, f admits expansions in terms of appropriately defined 'regular power series centered at p'. The expansion holds in a ball Sigma(p, R-|p|), defined with respect to a (non-Euclidean) distance sigma. We thus say that f is 'sigma-analytic' in B(0,R). Furthermore, we remark that Sigma(p, R-|p|) is not always an Euclidean neighborhood of p; when it is, we say that f is 'quaternionic analytic' at p. It turns out that f is quaternionic analytic only near the real axis. We then relate these notions of anayticity to the class of regular quaternionic functions introduced in Adv. Math. 216 (2007), 279-301, and recently extended. Indeed, sigma-analyticity proves equivalent to regularity, in the same way as complex analyticity is equivalent to holomorphy. Hence the theory of regular quaternionic functions, which is quickly developing, reveals a new feature that reminds the nice properties of holomorphic complex functions.

Geographically Weighted Regression Using a Non-Euclidean Distance Metric with a Study on London House Price Data

Geographically Weighted Regression (GWR) is a local modelling technique to estimate regression models with spatially varying relationships. Generally, the Euclidean distance is the default metric for calibrating a GWR model in previous research and applications; however, it may not always be the most reasonable choice due to a partition by some natural or man-made features. Thus, we attempt to use a non-Euclidean distance metric in GWR. In this study, a GWR model is established to explore spatially varying relationships between house price and floor area with sampled house prices in London. To calibrate this GWR model, network distance is adopted. Compared with the other results from calibrations with Euclidean distance or adaptive kernels, the output using network distance with a fixed kernel makes a significant improvement, and the river Thames has a clear cut-off effect on the parameter estimations.

Weighted semi-trapezoidal approximations of fuzzy numbers

Recently, many scholars investigated interval, triangular, and trapezoidal approximations of fuzzy numbers. These publications can be grouped into two classes: Euclidean distance class and non-Euclidean distance class. Most approximations in Euclidean distance class can be calculated by formulas, but calculating approximations in the other class is more complicated. In the present paper, we study a special class of non-linear approximations with respect to a weighted Euclidean distance. We call it “weighted semi-trapezoidal approximations”. The proposed approximations generalize all recent approximations in Euclidean distance class. First, we embed fuzzy numbers into a Hilbert space. Then compute weighted semi-trapezoidal approximations by means of best approximations in a closed convex subset of the Hilbert space. Finally, we propose formulas of matrix type, which is more clear than the previous contributions.

Generating function for extended Jacobi polynomials, noncommutative differential calculus and the relativistic energy and momentum operators

It is shown that the generating function for the matrix elements of irreps of Lorentz group is the common eigenfunction of the interior derivatives of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions. These derivatives commute and can be interpreted as the quantum mechanical operators of the relativistic momentum corresponding to the half of the non-Euclidean distance from the origin in the Lobachevsky momentum space.