| Type: | Package |
| Title: | Quantum Walk-Based Data Analysis and Prediction |
| Version: | 1.1.20 |
| Date: | 2024-10-11 |
| Author: | Binghuang Pan [aut, cre], Zhaoyuan Yu [aut], Xu Hu [ctb], Yuhao Teng [ctb] |
| Maintainer: | Binghuang Pan <bright1up@163.com> |
| Description: | The modeling and prediction of graph-associated time series(GATS) based on continuous time quantum walk. This software is mainly used for feature extraction, modeling, prediction and result evaluation of GATS, including continuous time quantum walk simulation, feature selection, regression analysis, time series prediction, and series fit calculation. A paper is attached to the package for reference. |
| Imports: | pls, CORElearn, Rcpp, methods |
| LinkingTo: | Rcpp,RcppEigen |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| LazyData: | true |
| LazyDataCompression: | xz |
| RoxygenNote: | 7.1.2 |
| Depends: | R (≥ 3.5.0) |
| NeedsCompilation: | yes |
| Packaged: | 2024-10-10 16:12:04 UTC; rstudio |
| Repository: | CRAN |
| Date/Publication: | 2024-10-10 16:30:08 UTC |
Evaluation
Description
calculate the Coefficient of Determination, Root Mean Squared Error and the Mean Absolute Error between two series.
Usage
qwdap.eval(series1, series2)
Arguments
series1 |
The series1. |
series2 |
The series2. |
Value
Three indicators, the Coefficient of Determination, Root Mean Squared Error and Mean Absolute Error.
Examples
set.seed(1)
res.eval <- qwdap.eval(rnorm(100,0,2),rnorm(100,0,1))
Principle Component Regression
Description
Principle component regression. This is a linear regression method used to establish the linear relationship between the original time series and the modes generated by quantum walks.
Usage
qwdap.pcr(in_data, data_range, plotting)
Arguments
in_data |
a 'QWMS' object, which includes the target series and the selected modes which can be obtained from modes selection. |
data_range |
the range of the train samples. |
plotting |
whether to plot. |
Value
a 'QWMODEL' object which includes the information of regression analysis.
Examples
data("traffic.n1")
res.pcr <- qwdap.pcr(traffic.n1,c(1,500), FALSE)
Partial Least Squares Regression
Description
Partial least squares regression. This is a linear regression method used to establish the linear relationship between the original time series and the modes generated by quantum walks.
Usage
qwdap.plsr(in_data, data_range, plotting)
Arguments
in_data |
a 'QWMS' object, which includes the target series and the selected modes which can be obtained from modes selection. |
data_range |
the range of the train samples. |
plotting |
whether to plot. |
Value
a 'QWMODEL' object which includes the information of regression analysis.
Examples
data("traffic.n1")
res.plsr <- qwdap.plsr(traffic.n1,c(1,500),FALSE)
Projection Pursuit Regression
Description
Projection pursuit regression. This is a nonlinear regression method used to establish the nonlinear relationship between the original time series and the modes generated by quantum walks.
Usage
qwdap.ppr(in_data, data_range, plotting)
Arguments
in_data |
a 'QWMS' object, which includes the target series and the selected modes which can be obtained from modes selection. |
data_range |
the range of the train samples. |
plotting |
whether to plot. |
Value
a 'QWMODEL' object which includes the information of regression analysis.
Examples
data("traffic.n1")
res.ppr <- qwdap.ppr(traffic.n1,c(1,500))
Prediction
Description
Based on the established model, make predict. The core algorithm of VAR prediction comes from MTS(ver. 1.1.1).
Usage
qwdap.predict(in_model, data_range)
Arguments
in_model |
a 'QWMODEL' object, which is the model built by Stepwise Regression, PCR, PLSR, PPR, VAR in this package. |
data_range |
indicate the index range of the part data generated by quantum walks for predict. |
Value
the predict data.
Examples
data(traffic.model.n1)
res.predict <- qwdap.predict(traffic.model.n1,c(501,720))
Quantum Walk
Description
Generate the modes, the probabilities that the walker being found at vertices. An adjacency matrix is need for the process.
Usage
qwdap.qwalk(edges, startindex, lens, scals, getfloat)
Arguments
edges |
your N*N adjacency matrix saved as list. |
startindex |
the initial position of the quantum walker. |
lens |
the number of records required in a round of sampling by a scaling factor. Set the length of the series according to requirements. |
scals |
the scaling factors used. |
getfloat |
Whether to return floating point data. |
Details
'qwdap.qwalk()' is used to generated modes for time series analysis, the result is a object of class 'CTQW', the modes are saved in the object as a 3-dim array, and the parameters are also store in the object. The continuous time quantum walk is a continuous process, the modes are generated with a series of times, the parameter 'scals' can be understood as the tolerance of the arithmetic time series. Multiply tolerances can be passed in to obtain modes on different time scales through parameter 'scals'. The probability of the series with the probabilities that the walker being found at the vertices, and the length depends on parameter 'lens'. The data generated by this function is not recorded from the initial state. The shortest distance between all vertices and the initial position of the quantum walker is obtained by the Dijkstra algorithm.The probabilities corresponding to each vertex are recorded starting from the vertex furthest in the shortest distance is not 0. The function is single thread.
Value
a object of class 'CTQW', the quantum walk results and some parameters.
Author(s)
Pan Binghuang
Examples
edges <- matrix(c(0,1,0,0,0,0,0,
1,0,1,0,0,0,0,
0,1,0,1,0,0,0,
0,0,1,0,1,0,0,
0,0,0,1,0,1,0,
0,0,0,0,1,0,1,
0,0,0,0,0,1,0),
nrow = 7)
res.qwalk <- qwdap.qwalk(edges,1,100,scals=seq(from=0.01, by=0.01, length.out=5))
RReliefF
Description
Mode selection by RReliefF. The purpose of this function is to select the part modes with similar characteristics to the observed time series from the modes generated by the quantum walk. And it is based on the data model.
Usage
qwdap.rrelieff(real, ctqw, index, num, plotting)
Arguments
real |
the real series observed. |
ctqw |
the 'CTQW' object. |
index |
the index of the data for mode selection. |
num |
the number of series required. |
plotting |
whether to plot. |
Details
The 'QWMS' object include the original time series and the modes generated by quantum walks.
Value
a 'QWMS' object.
Examples
data("traffic.qw")
data("trafficflow")
res.rrelieff <- qwdap.rrelieff(trafficflow,traffic.qw,1,30,TRUE)
Model by Stepwise Regression
Description
Stepwise regression. This is a linear regression method used to establish the linear relationship between the original time series and the modes generated by quantum walks.
Usage
qwdap.swr(in_data, data_range, plotting)
Arguments
in_data |
a 'QWMS' object, which includes the target series and the selected modes which can be obtained from modes selection. |
data_range |
the range of the train samples. |
plotting |
whether to plot. |
Value
a 'QWMODEL' object which includes the information of regression analysis.
Examples
data("traffic.n1")
res.swr <- qwdap.swr(traffic.n1,c(1,500))
Mode Selection by Stepwise Regression
Description
Mode selection by Stepwise Regression. The purpose of this function is to select the part modes with similar characteristics to the observed time series from the modes generated by the quantum walk. And it is based on the linear model. The core algorithm comes from StepReg(ver. 1.4.2).
Usage
qwdap.sws(real, ctqw, index, select_method, plotting)
Arguments
real |
the real series observed. |
ctqw |
the 'CTQW' object. |
index |
the index of the data for mode selection. |
select_method |
choose a stepwise method. |
plotting |
whether to plot. |
Details
The 'QWMS' object include the original time series and the modes generated by quantum walks.
Value
a 'QWMS' object.
Examples
data("traffic.qw")
data("trafficflow")
res.sws <- qwdap.sws(trafficflow,traffic.qw,1,"bidirection",TRUE)
Vector Autoregressive Model
Description
Vector autoregressive model. This is a regression method used to establish the temporal relationship between the original time series and the modes generated by quantum walks. The core algorithm comes from MTS(ver. 1.1.1).
Usage
qwdap.var(in_data, data_range, plotting)
Arguments
in_data |
a 'QWMS' object, which includes the target series and the selected modes which can be obtained from modes selection. |
data_range |
the range of the train samples. |
plotting |
whether to plot. |
Value
a 'QWMODEL' object which includes the information of regression analysis.
Examples
data("traffic.n1")
res.var <- qwdap.var(traffic.n1,c(1,500))
The estabulished model by Stepwise Regression of the 'N1' station
Description
This data is the linear model built by Stepwise Regression of the highway traffic flow data of the 'N1' stations, and includes the observed data and the modes generated by quantum walk.
Usage
data(traffic.model.n1)Format
A 'QWMODEL' object.
Source
Pan BH(2021).
Data of the 'N1' station
Description
This data is the highway traffic flow data and the modes generated by quantum walk of the 'N1' stations.
Usage
data(traffic.n1)Format
A 'QWMS' object.
Source
Pan BH(2021).
A set of modes generated by quantum walk
Description
This data is generated by function 'qwdap.qwalk()' with 100 scaling factors form 0.01 to 1 and the parameter 'edges' is the adjancy matrix of 7 vertices connected end to end.
Usage
data(traffic.qw)Format
A 'CTQW' object.
Source
Pan BH(2021).
Highway traffic flow data
Description
This data set has a total of 720 records of 7 research stations, namely Tangshan (N1), Jurong (N2), Heyang (N3), Danyang (N4), Luoshuyan (N5), Xuejia (N6) and ChangzhouBei (N7).
Usage
data(trafficflow)Format
A dataframe with 720 observations on the 7 stations.
Source
Yu ZY, Hu X(2020).