Predict Signature and Pattern Vectors

Uses neural network outputs to predict the state signatures and patterns in a complex system. Adjusts for sparsity using zero tolerance.

Usage

predictionY(E, projNNy, zeroTolerance = (E + 1)/2)

Arguments

E

Integer, the embedding dimension of the system, indicating the length of the signature vector minus one.

projNNy

A list containing two elements: Signatures, a matrix where each column represents a component in the signature vector across different observations, and Weights, a numeric vector representing the weights associated with each observation.

zeroTolerance

A numeric value used to determine the sparsity threshold in the signature matrix. Default is set to (E+1)/2.

Value

A dataframe with two columns: predictedSignatureY which contains the predicted signature vector, and predictedPatternY which contains the corresponding pattern vector.

Details

Predict the signatures and patterns for a complex system

This function predicts the signature and pattern vectors for a given state based on projections and weights derived from neural network outputs within a complex system. The predictions adjust according to a specified zero tolerance level to manage sparsity.

Examples

set.seed(123)
E <- 3
tau <- 1
Mx <- matrix(rnorm(300), nrow = 100)
My <- matrix(rnorm(300), nrow = 100)
Dx <- distanceMatrix(Mx, "minkowski")
Dy <- distanceMatrix(My, "minkowski")
SMx <- signatureSpace(Mx, E)
SMy <- signatureSpace(My, E)
PSMx <- patternSpace(SMx, E)
PSMy <- patternSpace(SMy, E)
CCSPAN <- (E - 1) * tau
NNSPAN <- E + 1
i <- 15
h <- 2
NNx <- pastNNsInfo(CCSPAN, NNSPAN, Mx, Dx, SMx, PSMx, i, h)
timesX <- NNx$times
projNNy <- projectedNNsInfo(My, Dy, SMy, PSMy, timesX, i, h)
predicted <- predictionY(E, projNNy)
print(predicted)
#>   predictedSignatureY predictedPatternY
#> 1          -0.6503927                78
#> 2           0.4162032                78