Last updated: 2025-10-14
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Knit directory: CPLASS/
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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.
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 |
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 running CPLASS on a collection of paths, we introduced the
function CPLASS_paths.
Usage
CPLASS_paths(data, time_rate, PARALLEL = FALSE, lambda_r=1/30, iter_max = 5000, burn_in=500, s_cap=1, gamma=1.2, speed_pen=TRUE)
Arguments
| Argument | Description |
|---|---|
| data | A list of paths where for each path we can specify \(t,x,y\) |
| time_rate | Time step, e.g., 0.001, 0.01, 0.04, 0.05, 0.1, 1 |
| PARALLEL | If TRUE, running parallel computing; if
FALSE, running sequentially |
| 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 paths, in each path, there is a similar output with two
sublists segments_inferred and path_inferred
as described in the CPLASS function.