A Statistical Toolbox For Mining And Modeling Spatial Data

Most data mining projects in spatial economics start with an evaluation of a set of attribute variables on a sample of spatial entities, looking for the existence and strength of spatial autocorrelation, based on the Moran’s and the Geary’s coefficients, the adequacy of which is rarely challenged, despite the fact that when reporting on their properties, many users seem likely to make mistakes and to foster confusion. My paper begins by a critical appraisal of the classical definition and rational of these indices. I argue that while intuitively founded, they are plagued by an inconsistency in their conception. Then, I propose a principled small change leading to corrected spatial autocorrelation coefficients, which strongly simplifies their relationship, and opens the way to an augmented toolbox of statistical methods of dimension reduction and data visualization, also useful for modeling purposes. A second section presents a formal framework, adapted from recent work in statistical learning, which gives theoretical support to our definition of corrected spatial autocorrelation coefficients. More specifically, the multivariate data mining methods presented here, are easily implementable on the existing (free) software, yield methods useful to exploit the proposed corrections in spatial data analysis practice, and, from a mathematical point of view, whose asymptotic behavior, already studied in a series of papers by Belkin & Niyogi, suggests that they own qualities of robustness and a limited sensitivity to the Modifiable Areal Unit Problem (MAUP), valuable in exploratory spatial data analysis

Improving the Multi-Dimensional Comparison of Simulation Results: A Spatial Visualization Approach

Results from simulation experiments are important in applied spatial econometrics to, for instance, assess the performance of spatial estimators and tests for finite samples. However, the traditional tabular and graphi- cal formats for displaying simulation results in the literature have several disadvantages. These include loss of results, lack of intuitive synthesis, and difficulty in comparing results across multiple dimensions. We pro- pose to address these challenges through a spatial visualization approach. This approach visualizes model precision and bias as well as the size and power of tests in map format. The advantage of this spatial approach is that these maps can display all results succinctly, enable an intuitive interpretation, and compare results efficiently across multiple dimensions of a simulation experiment. Due to the respective strengths of tables, graphs and maps, we propose this spatial approach as a supplement to traditional tabular and graphical display formats. To allow readers to generate maps such as the ones presented in this article, a package (written in Python) has been made available by the authors as free/libre software. The package includes an example as well as a short tutorial for researchers without programming experience and can be downloaded at: https://github.com/darribas/simVizMap.

From SpaceStat to CyberGIS: Twenty Years of Spatial Data Analysis Software

This essay assesses the evolution of the way in which spatial data analytical methods have been incorporated into software tools over the past two decades. It is part retrospective and prospective, going beyond a historical review to outline some ideas about important factors that drove the software development, such as methodological advances, the open source movement and the advent of the internet and cyberinfrastructure. The review highlights activities carried out by the author and his collaborators and uses SpaceStat, GeoDa, PySAL and recent spatial analytical web services developed at the ASU GeoDa Center as illustrative examples. It outlines a vision for a spatial econometrics workbench as an example of the incorporation of spatial analytical functionality in a cyberGIS.

Focus Is All You Need: Loss Functions For Event-based Vision

Event cameras are novel vision sensors that output pixel-level brightness changes ("events") instead of traditional video frames. These asynchronous sensors offer several advantages over traditional cameras, such as, high temporal resolution, very high dynamic range, and no motion blur. To unlock the potential of such sensors, motion compensation methods have been recently proposed. We present a collection and taxonomy of twenty two objective functions to analyze event alignment in motion compensation approaches (Fig. 1). We call them Focus Loss Functions since they have strong connections with functions used in traditional shape-from-focus applications. The proposed loss functions allow bringing mature computer vision tools to the realm of event cameras. We compare the accuracy and runtime performance of all loss functions on a publicly available dataset, and conclude that the variance, the gradient and the Laplacian magnitudes are among the best loss functions. The applicability of the loss functions is shown on multiple tasks: rotational motion, depth and optical flow estimation. The proposed focus loss functions allow to unlock the outstanding properties of event cameras.Comment: 29 pages, 19 figures, 4 table

Providing scientific visualisation for spatial data analysis: criteria and an assessment of SAGE

A consistent theme in recent work on developing exploratory spatial data analysis (ESDA) has been the importance attached to visualization techniques, particularly following the pioneering development of packages such as REGARD by Haslett et al (1990). The focus on visual techniques is often justified in two ways: (a) the power of modern graphical interfaces means that graphics is no longer a way of simply presenting results in the form of maps or graphs, but a tool for the extraction of information from data; (b)graphical, exploratory methods are felt to be more intuitive for non-specialists to use than methods of numerical spatial statistics enabling wider participation in the process of getting data insights. Despite the importance attached to visualisation techniques, very little work has been done to assess the effectiveness of techniques, either in the wider scientific visualisation community, or among those working with spatial data. This paper will describe a theoretical framework for developing visualisation tools for ESDA that incorporates a data model of what the analyst is looking for based on the concepts of "rough" and "smooth" elements of a data set and a theoretical scheme for assessing visual tools. The paper will include examples of appropriate tools and a commentary on the effectiveness of some existing packages

The Spatial Autocorrelation Analysis For Transport Accessibility In Selected Regions Of The European Union

The main purpose of this article is to assess and analyze the occurrence of spatial autocorrelation in connection with the transport accessibility (measured by density of a motorway network). The general hypothesis is: between European regions, there is a positive spatial autocorrelation in connection with the problems of transport accessibility. Research subjects are selected European regions at NUTS level 2. To evaluate the occurrence of spatial autocorrelation the classic Moran I statistic has been used

A multi-angle plane wave imaging approach for high frequency 2D flow visualization in small animals: simulation study in the murine arterial system

To preclinically investigate the role of hemodynamics in atherogenesis, mouse models are particularly useful due to the rapid disease development. As such, murine blood flow visualization has become an important tool, with current US systems equipped with traditional 1D flow imaging techniques, lacking spatial and/or temporal resolution to accurately resolve in-vivo flow fields. Hence, we investigated multi-angle plane wave imaging for ultrafast, 2D vector flow visualization and compared this approach with conventional pulsed Doppler in the setting of a mouse aorta with abdominal aortic aneurysm. For this purpose, we used a multiphysics model which allowed direct comparison of synthetic US images with the true flow field behind the image. In case of the abdominal aorta, we showed the mean flow estimation improved 9 % when using 2D vector Doppler compared to conventional Doppler, but still underestimated the true flow because the full spatial velocity distribution remained unknown. We also evaluated a more challenging measurement location, the mesenteric artery (aortic side branch), often assessed in a short-axis view close to the origin of the branch to avoid the smaller dimensions downstream. Even so, complex out-ofplane flow dynamics hampered a reliable flow assessment for both techniques. Hence, both cases illustrated the need for 3D vascular imaging, allowing acquisition of the full 3D spatial velocity profile