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Adaptive Geometric Interval Classifier

Quantile, equal interval, and natural breaks methods are widely used data classification methods in geospatial analysis and cartography. However, when applied to data with skewed distributions, they can only reveal the variations of either high frequent values or extremes, which often leads to undesired and biased classification results. To handle this problem, Esri provided a compromise method, named geometric interval classification (GIC). Although GIC performs well for various classification tasks, its mathematics and solution process remain unclear. Moreover, GIC is theoretically only applicable to single-peak (single-modal), one-dimensional data. This paper first mathematically formulates GIC as a general optimization problem subject to equality constraint. We then further adapt such formulated GIC to handle multi-peak and multi-dimensional data. Both thematic data and remote sensing images are used in this study. The comparison with other classification methods demonstrates the advantage of GIC being able to highlight both middle and extreme values. As such, it can be regarded as a general data classification approach for thematic mapping and other geospatial applications.