Fast Local Indicators of Spatial Association (LISA).

fastLISA

Fast, reproducible Local Indicators of Spatial Association (LISA) with arbitrary spatial weights.

fastLISA computes seven families of LISA statistics with a plain-C backend, optional OpenMP multi-threading, and a modern xoshiro256++ random number generator for permutation-based inference. It accepts anyspdeplistw spatial weights object — including custom and non-contiguity (e.g. distance-decay) weights — and returns compact, inspectable, spdep-compatible matrices.

Why fastLISA

The two established R tools force a trade-off:

• spdep accepts any listw and integrates with the R spatial ecosystem, but its conditional-permutation inference runs largely in R and is slow on large maps.
• rgeoda is fast, but builds its own weights internally — so custom weight values are ignored (it falls back to binary contiguity) — and returns objects that need package-specific accessors.

fastLISA closes the gap:

• Honours custom weight values. It uses the actual listw weights, so distance-decay and other non-binary schemes are respected (unlike rgeoda).
• Fast. At equal thread counts, the OpenMP-parallelised C kernels run about 2.5× faster than the compiled peer rgeoda, and roughly 8–10× faster than spdep, whose permutation loops run largely in R.
• Reproducible at any thread count. The permutation RNG is re-seeded per observation, so for a fixed iseed the pseudo-p-values are identical regardless of n.cores — a guarantee neither spdep nor rgeoda offers.
• Inspectable output. Results are plain matrices with spdep-style classes and cluster/quadrant attributes, not opaque pointers.

Statistics

Each returns the observed statistic, a permutation z-score, and a pseudo p-value (folded for Moran/G/G*, tail-adaptive for Geary), with optional permutation-moment columns. Cluster codes follow rgeoda conventions, including an Isolated category for observations with no neighbours.

Installation

Install the released version from CRAN:

install.packages("fastLISA")

Or the development version from source (requires a C99 compiler; OpenMP is used when available):

# install.packages("remotes")
remotes::install_github("lizhongc/fastLISA")

Or from a local clone:

R CMD INSTALL fastLISA

spdep is suggested for constructing listw weights and for the examples.

Quick start

library(spdep)
library(fastLISA)

nb <- cell2nb(7, 7)             # 49 cells on a 7 x 7 grid
lw <- nb2listw(nb, style = "W") # row-standardised weights
x  <- as.numeric(seq_len(49))   # a simple gradient

res <- local_moran(x, lw, nsim = 999L, iseed = 1L, n.cores = 1L)
head(res)

attr(res, "cluster")            # High-High / Low-Low / outliers / Isolated ...

Custom (e.g. distance-decay) weights are passed through unchanged:

coords  <- as.matrix(expand.grid(x = 1:7, y = 1:7))   # 49 grid points
dnb     <- dnearneigh(coords, 0, 2)                    # neighbours within distance 2
glist   <- lapply(nbdists(dnb, coords), function(d) exp(-d))  # distance decay
lw_exp  <- nb2listw(dnb, glist = glist, style = "B")
res_exp <- local_g(x, lw_exp, nsim = 999L, iseed = 1L)

All functions share the same interface: nsim permutations, an optional integer iseed for reproducibility, a significance cutoff p.value, n.cores (default 1L; raise it to use multiple OpenMP threads), and p.method to choose the pseudo-p-value rule — the standard "count" (default), or spdep's ties-averaged "rank", which differ only under exact ties.

Reproducibility

Because the RNG is re-seeded per observation rather than per thread, the same iseed yields bit-identical pseudo-p-values whether you run on 1 core or many:

a <- local_moran(x, lw, nsim = 999L, iseed = 42L, n.cores = 1L)
b <- local_moran(x, lw, nsim = 999L, iseed = 42L, n.cores = 8L)
identical(c(a), c(b))   # TRUE -- same statistics and pseudo-p-values

(c() strips attributes; the full objects differ only in the recorded call, which stores the n.cores value you passed.)

Documentation

See the package help (?local_moran, ?local_g, ?local_geary, ...) and the package vignette:

vignette("fastLISA")

References

• Anselin, L. (1995). Local Indicators of Spatial Association — LISA. Geographical Analysis 27(2), 93–115. https://doi.org/10.1111/j.1538-4632.1995.tb00338.x
• Getis, A. & Ord, J. K. (1992). The Analysis of Spatial Association by Use of Distance Statistics. Geographical Analysis 24(3), 189–206. https://doi.org/10.1111/j.1538-4632.1992.tb00261.x
• Anselin, L. (2019). A Local Indicator of Multivariate Spatial Association: Extending Geary's c. Geographical Analysis 51(2), 133–150. https://doi.org/10.1111/gean.12164

License

GPL-3.