Boundary Handling

Overview

Boundary policy comparison

Standard LOWESS neighbourhoods become asymmetric at the boundaries: fewer points exist on one side, pulling the local fit toward the data interior. The boundary_policy parameter controls how the data is padded to mitigate this effect.

Policy	Padding Strategy	Best For
`"extend"`	Repeat first / last value	Most datasets (default)
`"reflect"`	Mirror data at boundaries	Periodic or symmetric data
`"zero"`	Pad with zeros	Data known to approach zero
`"noboundary"`	No padding (Cleveland original)	Reference behaviour

Extend (Default)

Pads beyond both endpoints by replicating the first and last observed values. Prevents the fit from curling toward zero.

Use when: No strong prior on boundary behaviour; general-purpose smoothing.

library(rfastlowess)
set.seed(42)
x <- seq(0, 2 * pi, length.out = 100)
y <- sin(x) + rnorm(100, sd = 0.3)

model <- Lowess(boundary_policy = "extend")
result <- fit(model, x, y)
cat("First 6 smoothed values (extend policy):\n")
#> First 6 smoothed values (extend policy):
print(head(result$y))
#> [1] 0.5023423 0.5118995 0.5218795 0.5322473 0.5429093 0.5537345

Reflect

Mirrors data at both endpoints. Prevents inflection artifacts when the signal is periodic or symmetric.

Use when: Signal is periodic (e.g. time-of-day) or the boundary is a known symmetry point.

model <- Lowess(boundary_policy = "reflect")
result <- fit(model, x, y)
cat("First 6 smoothed values (reflect policy):\n")
#> First 6 smoothed values (reflect policy):
print(head(result$y))
#> [1] 0.6183818 0.6174389 0.6174211 0.6183044 0.6200242 0.6224897

Zero

Pads with zeros beyond the endpoints.

Use when: The signal is known to decay to zero at the boundaries (e.g. impulse responses, genomic signals at chromosome ends).

model <- Lowess(boundary_policy = "zero")
result <- fit(model, x, y)
cat("First 6 smoothed values (zero policy):\n")
#> First 6 smoothed values (zero policy):
print(head(result$y))
#> [1] 0.2889433 0.3090667 0.3296141 0.3505350 0.3717128 0.3929858

No Boundary Padding

Reproduces Cleveland’s original behaviour — no padding applied.

Use when: Comparing against reference implementations; the original Cleveland algorithm behaviour is required.

Note: Without padding, boundary fits can have higher variance and visible edge artefacts, particularly with small fraction values.

model <- Lowess(boundary_policy = "noboundary")
result <- fit(model, x, y)
cat("First 6 smoothed values (noboundary policy):\n")
#> First 6 smoothed values (noboundary policy):
print(head(result$y))
#> [1] 0.6766520 0.6769305 0.6769029 0.6765617 0.6759035 0.6749280

Comparing Policies

library(rfastlowess)
set.seed(42)
x <- seq(0, 2 * pi, length.out = 100)
y <- sin(x) + rnorm(100, sd = 0.3)

policies <- c("extend", "reflect", "zero", "noboundary")
colors   <- c("blue", "red", "green", "purple")

plot(x, y, pch = 16, col = "gray",
    main = "Boundary Policy Comparison")

for (i in seq_along(policies)) {
    model  <- Lowess(boundary_policy = policies[i])
    result <- fit(model, x, y)
    lines(result$x, result$y, col = colors[i], lwd = 2)
}

legend("topright", policies, col = colors, lwd = 2)

sessionInfo()
#> R version 4.6.1 (2026-06-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 26.04.1 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.32.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
#>  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
#>  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
#>  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
#>  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
#> 
#> time zone: Etc/UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
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#> other attached packages:
#> [1] rfastlowess_5.0.0 rmarkdown_2.32   
#> 
#> loaded via a namespace (and not attached):
#>  [1] digest_0.6.39    R6_2.6.1         fastmap_1.2.0    xfun_0.61       
#>  [5] maketools_1.3.2  cachem_1.1.0     knitr_1.52       htmltools_0.5.9 
#>  [9] buildtools_1.0.0 lifecycle_1.0.5  cli_3.6.6        sass_0.4.10     
#> [13] jquerylib_0.1.4  compiler_4.6.1   sys_3.4.3        tools_4.6.1     
#> [17] evaluate_1.0.5   bslib_0.12.0     yaml_2.3.12      otel_0.2.0      
#> [21] jsonlite_2.0.0   rlang_1.3.0