A method to improve Ripley's function to analyze spatial pattern by factor analysis

Abstract

The Ripley function is a spatial point pattern analysis method, which is used to characterize point processes at different distance scales. However, to use the spatial point pattern analysis in combination with other spatial pattern analysis methods, or to analyze the spatial pattern of a population and individuals, if the spatial pattern is affected by many influencing factors, the introduction of the dimension of scale in the subsequent analysis will lead to a large number of dimensions to be examined and lack of correlation, which makes the study impossible. Therefore, in this study, the Ripley's function was improved by reducing the dimensionality of the calculated results through factor analysis, so that the results obtained from Ripley's K function only show one spatial pattern, thus eliminating the influence of scale on the spatial pattern, and expressing the spatial pattern that best reflects the current population or individual. Four standard spatial point pattern datasets were used to verify the ability of factor analysis to respond to spatial patterns after dimensionality reduction for Ripley'K, Ripley'L, and Ripley'G. The results showed that for aggregated point patterns the accuracy of the calculated results after dimensionality reduction reached 100%, where For the random point pattern, the average accuracy is also above 95%, which indicates that the applicability of factor analysis dimensionality reduction to spatial pattern models is in the random point pattern and aggregation pattern. In terms of different scale point sets, it has good adaptability to all three scale point set sizes. In this way the application scenario of Ripley function will be more extensive.