A standard planar Kernel Density Estimation (KDE) aims to produce a smooth density surface of spatial point events over a 2-D geographic space. However the planar KDE may not be suited for characterizing certain point events, such as traffic accidents, which usually occur inside a 1-D linear space, the roadway network. This paper presents a novel network KDE approach to estimating the density of such spatial point events.One key feature of the new approach is that the network space is represented with basic linear units of equal network length, termed lixel (linear pixel), and related network topology. The use of lixel not only facilitates the systematic selection of a set of regularly spaced locations along a network for density estimation, but also makes the practical application of the network KDE feasible by significantly improving the computation efficiency. The approach is implemented in the ESRI ArcGIS environment and tested with the year 2005 traffic accident data and a road network in the Bowling Green, Kentucky area. The test results indicate that the new network KDE is more appropriate than standard planar KDE for density estimation of traffic accidents, since the latter covers space beyond the event context (network space) and is likely to overestimate the density values. The study also investigates the impacts on density calculation from two kernel functions, lixel lengths, and search bandwidths. It is found that the kernel function is least important in structuring the density pattern over network space, whereas the lixel length critically impacts the local variation details of the spatial density pattern. The search bandwidth imposes the highest influence by controlling the smoothness of the spatial pattern, showing local effects at a narrow bandwidth and revealing "hot spots" at larger or global scales with a wider bandwidth. More significantly, the idea of representing a linear network by a network system of equal-length lixels may potentially 3 lead the way to developing a suite of other network related spatial analysis and modeling methods.

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Given that many spatial interaction (SI) systems are often constituted in large databases with high thematic dimensionality, data complexity reduction tasks are essential. The opportunity exists for researchers to examine the formation of different types of SIs as well as their interdependencies by exploring the patterns embedded in the data. To circumvent the limitations of existing methods of flow data compression and visual exploration, we propose an integrated computational and visual approach, known as VISIDAMIN, for handling both SI data projection and SI data quantization at once. The computational method of self-organizing maps serves as the data mining engine in this process. Using a large domestic air travel dataset as a case study, we examine how the characteristics of the air transport system interact with the SI system to create relationships and structures within the US domestic airline market.

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