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Lee’s L (Lee 2001) was developed from relating Moran’s I to Pearson correlation, and is defined as

\[ L_{X,Y} = \frac{n}{\sum_{i=1}^n \sum_{j=1}^n w_{ij}} \frac{\sum_{i=1}^n \left[ \sum_{j=1}^n w_{ij} (x_j - \bar{x}) \right] \left[ \sum_{j=1}^n w_{ij} (y_j - \bar{y}) \right]}{\sqrt{\sum_{i=1}^n (x_i - \bar{x})^2}\sqrt{\sum_{i=1}^n (y_i - \bar{y})^2} }, \]

where \(n\) is the number of spots or locations, \(i\) and \(j\) are different locations, or spots in the Visium context, \(x\) and \(y\) are variables with values at each location, and \(w_{ij}\) is a spatial weight, which can be inversely proportional to distance between spots or an indicator of whether two spots are neighbors, subject to various definitions of neighborhood.

Below is a list of vignettes that use Lee’s L. The links point to the sections that use Lee’s L. The corresponding Google Colab notebooks are also linked to. The list is sorted by technology.

Vignette Colab Notebook Description
Bivariate spatial statistics Colab Notebook Perform global and local Lee’s L and bivariate local Moran’s I on mouse skeletal muscle Visiumd dataset


Lee, Sang-Il. 2001. “Developing a Bivariate Spatial Association Measure: An Integration of Pearson’s r and Moran’s I.” J. Geogr. Syst. 3 (4): 369–85.