clockSim (version 0.1.1)

compute_rmse: Trajectory similarity: Root Mean Squared Error RMSE

Description

RMSE is used to characterize how absolute values of two trajectory \(\vec{X}(t), \vec{Y}(t)\) agree with each other. There are normalized and default versions:

Usage

compute_rmse(res_mat1, res_mat2, normalize = "none")

Value

RMSE of the two trajectory, vector with length = number of input states.

Arguments

res_mat1

Trajectory matrix 1, first column must be time while others are states.

res_mat2

Trajectory matrix 2, first column must be time while others are states.

normalize

Normalization method, one of "none", "range", "sd".

Details

Default (value scales with variable \(i\)):

\(\mbox{RMSE}_i=\sqrt{\frac{\Sigma(X_i(t^j)-Y_i(t^j))^2}{N}}\)

Normalized (value normalized by range for each variable \(i\)):

\(\mbox{NRMSE}_i=\frac{\mbox{RMSE}}{\mbox{spread}}\) (spread is customizable)

For normalization, spread is always computed ONLY from res_mat1. res_mat2 is normalized using spread computed from mat1 to still retain the property that RMSE allows comparing absolute values of two trajectories.

In this case, normalization is used to prevent numerically large states from dominating RMSE results, giving a more thorough comparison of trajectories.

Examples

# Perfect agreement (zero error)
mat1 <- cbind(time = 1:3, state1 = c(1, 2, 3), state2 = c(4, 5, 6))
mat2 <- mat1
compute_rmse(mat1, mat2)

# Simple error case
#   state1 = sqrt(mean(c(0,0,0.5)^2)) = 0.29
#   state2 = sqrt(mean(c(0,0.2,0)^2)) = 0.12
mat3 <- cbind(time = 1:3, state1 = c(1, 2, 3.5), state2 = c(4, 5.2, 6))
compute_rmse(mat1, mat3)

# Normalized example (NRMSE = RMSE / spread)
#   state1 = state2 = 1/20 = 0.05
mat4 <- cbind(time = 1:3, state1 = c(10, 20, 30), state2 = c(40, 50, 60))
mat5 <- cbind(time = 1:3, state1 = c(11, 21, 31), state2 = c(41, 51, 61))
compute_rmse(mat4, mat5, "range")  # c(1/20, 1/20) = c(0.05, 0.05)