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CPLASS functions

For a single path

Description

This function runs the Continuous Piecewise Linear Approximation with Stochastic Search (CPLASS) algorithm on a 2D data in the form of \((x_i,y_i)_{i=1}^n\) observed at time \((t_i)_{i=1}^n\) believed to follow a continuous piecewise linear regression model (Gaussian noise). It is used for detecting changes in velocity problem. CPLASS returns the time changes, the estimated parameters.

Usage

 CPLASS(t,x, y,time_rate, lambda_r=1/30, iter_max = 5000, burn_in=500, s_cap=1, gamma=1.2, speed_pen=TRUE)

Arguments

Argument	Description
x	A vector containing the data sequence (Cargo locations in x-axis)
y	A vector containing the data sequence (Cargo locations in y-axis)
t	A vector containing time
time_rate	Time step, e.g., 0.001, 0.01, 0.04, 0.05, 0.1, 1
lambda_r	the rate used in the proposal of a new vector of changepoints
iter_max	The maximum number of iterations for running Metropolis-Hastings searching algorithm
burn_in	The number of burn-in steps in MH search algorithm
s_cap	The threshold for the output speed. If the inferred speed exceed `s_cap` and the `speed_pen` is activated, then the extra speed penalty will be introduced
gamma	The power in the strengthened Schwarz Information Criterion (sSIC)
speed_pen	If `TRUE`, adding the speed penalty to the penalty function; if `FALSE`, we only use the linear penalty term sSIC

Output

A list of segment_inferred and path_inferred will be returned after running the algorithm.

The segment_inferred is a tibble containing 8 columns

Columns	Description
cp_times	The inferred change times
durations	The inferred segment durations
states	A binary vector labeling the state of the associated segments, `0` for stationary, `1` for motile. The labels are created using the cut-off method with a threshold of 100nm/s
speeds	The inferred segment speeeds
vx	The inferred velocity with respect to x-axis
vy	The inferred velocity with respect to y-axis

The path_inferred is a tibble containing 6 columns

Columns	Description
t	The input time
j	The label of time points corresponding to the labels of segments after using the cut-off method
x	The observed data with respect to x-axis
y	The observed data with respect to y-axis
a	The inferred piecewise linear lines (anchor locations w.r.t x-axis)
b	The inferred piecewise linear lines (anchor locations w.r.t y-axis)

For a collection of paths

For running CPLASS on a collection of paths, we introduced the function CPLASS_paths.