SMap: Sequential locally weighted global linear map (S-map)

In rEDM: Empirical Dynamic Modeling ('EDM')

Sequential locally weighted global linear map (S-map)

Description

SMap performs time series forecasting based on localised (or global) nearest neighbor projection in the time series phase space as described in Sugihara 1994.

Usage

SMap(dataFrame = NULL, columns, target, lib, pred, E = NULL, Tp = 1, knn = 0,
     tau = -1, theta = 0, exclusionRadius = 0, embedded = FALSE,
     validLib = logical(0), noTime = FALSE, ignoreNan = TRUE,
     backend = "RANN", pathIn = "./", dataFile = "", pathOut = "./",
     predictFile = "", parameterList = FALSE, includeState = FALSE,
     verbose = FALSE, showPlot = FALSE)

Arguments

dataFrame	A data.frame of input data. The first column must be a time index or time values unless noTime = TRUE. The columns must be named.
columns	Column name(s) to build the embedding: character vector or space-separated string, or vector of column names used to create the library. If individual column names contain whitespace place names in a vector, or, append ',' to the name.
target	Target column name to predict.
lib	string or vector with start and stop indices of input data rows used to create the library from observations. Mulitple row index pairs can be specified with each pair defining the first and last rows of time series observation segments used to create the library.
pred	string with start and stop indices of input data rows used for predictions. A single contiguous range is supported.
E	Embedding dimension. Required (no default); must be a positive integer unless embedded = TRUE, in which case it is inferred as the number of columns.
Tp	Forecast interval (prediction horizon).
knn	Number of nearest neighbours. 0 selects the method default.
tau	Embedding delay (negative selects past lags).
theta	S-map localisation parameter (0 = global linear map).
exclusionRadius	Temporal (Theiler) exclusion radius around each prediction point. Excludes vectors from the search space of nearest neighbors if their relative time index is within exclusionRadius.
embedded	If TRUE, columns already form the embedding.
validLib	Logical vector marking admissible library rows (or length 0 for all).
noTime	If TRUE, synthesise a 1..N time index instead of using column 1.
ignoreNan	Remove rows with NaN in the embedding from the library and prediction sets.
pathIn	File path for input dataFile.
dataFile	Input dataFile, .csv format. The first column must be a time index or time values unless noTime is TRUE. The first row must be column names.
pathOut	Output file path for predictFile
predictFile	Output file name, .csv format.
backend	Nearest-neighbour backend: "RANN" (default) or "brute".
parameterList	Append named list of parameters/values to return.
includeState	If TRUE, also return an internal list of engine state: knn_neighbors, knn_distances, lib_i, pred_i, targetVec, embedding (1-based row indices; 0 = neighbour sentinel).
verbose	Emit diagnostic messages.
showPlot	If TRUE, draw a base-graphics plot of the result.

Details

If embedded is FALSE, the data column(s) are embedded to dimension E with time lag tau. This embedding forms an n-columns * E-dimensional phase space for the SMap projection. If embedded is TRUE, the data are assumed to contain an E-dimensional embedding with E equal to the number of columns. See the Note below for proper use of multivariate data (number of columns > 1).

If ignoreNan is TRUE, the library (lib) is internally redefined to exclude nan embedding vectors. If ignoreNan is FALSE no library adjustment is made. The (lib) can be explicitly specified to exclude nan library vectors.

Predictions are made using leave-one-out cross-validation, i.e. observation rows are excluded from the prediction regression.

In contrast to Simplex, SMap uses all available neighbors and weights them with an exponential decay in phase space distance with exponent theta. theta=0 uses all neighbors corresponding to a global autoregressive model. As theta increases, neighbors closer in vicinity to the observation are considered.

Value

A named list with three data.frames [[predictions, coefficients, singularValues]]. predictions has columns Observations, Predictions. The first column contains time or index values.

coefficients data.frame has time or index values in the first column. Columns 2 through E+2 (E+1 columns) are the SMap coefficients.

singularValues data.frame has time or index values in the first column. Columns 2 through E+2 (E+1 columns) are the SVD singularValues. The first value corresponds to the SVD bias (intercept) term.

If parameterList = TRUE a named list "parameters" is added.

If includeState = TRUE a named list "internal" is added.

Note

SMap should be called with columns explicitly corresponding to dimensions E. In the univariate case (number of columns = 1) with default embedded = FALSE, the time series will be time-delay embedded to dimension E, SMap coefficients correspond to each dimension.

If a multivariate data set is used (number of columns > 1) it must use embedded = TRUE with E equal to the number of columns. This prevents the function from internally time-delay embedding the multiple columns to dimension E. If the internal time-delay embedding is performed, then state-space columns will not correspond to the intended dimensions in the matrix inversion, coefficient assignment, and prediction. In the multivariate case, the user should first prepare the embedding (using Embed for time-delay embedding), then pass this embedding to SMap with appropriately specified columns, E, and embedded = TRUE.

References

Sugihara G. 1994. Nonlinear forecasting for the classification of natural time series. Philosophical Transactions: Physical Sciences and Engineering, 348 (1688):477-495.

rEDM documentation built on Aug. 30, 2026, 9:07 a.m.