| Type: | Package |
| Title: | Time Series Representations |
| Version: | 1.1.0 |
| Date: | 2020-07-12 |
| Description: | Methods for representations (i.e. dimensionality reduction, preprocessing, feature extraction) of time series to help more accurate and effective time series data mining. Non-data adaptive, data adaptive, model-based and data dictated (clipped) representation methods are implemented. Also various normalisation methods (min-max, z-score, Box-Cox, Yeo-Johnson), and forecasting accuracy measures are implemented. |
| License: | GPL-3 | file LICENSE |
| Encoding: | UTF-8 |
| LazyData: | true |
| Depends: | R (≥ 2.10) |
| Imports: | Rcpp (≥ 0.12.12), MASS, quantreg, wavelets, mgcv, dtt |
| LinkingTo: | Rcpp |
| RoxygenNote: | 7.1.0 |
| URL: | https://petolau.github.io/package/, https://github.com/PetoLau/TSrepr/ |
| BugReports: | https://github.com/PetoLau/TSrepr/issues |
| Suggests: | knitr, rmarkdown, ggplot2, data.table, moments, testthat |
| VignetteBuilder: | knitr |
| NeedsCompilation: | yes |
| Packaged: | 2020-07-12 21:59:54 UTC; PeterLaurinec |
| Author: | Peter Laurinec 
[aut, cre] |
| Maintainer: | Peter Laurinec <tsreprpackage@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2020-07-13 06:50:15 UTC |
TSrepr package
Description
Package contains methods for time series representations computation. Representation methods of time series are for dimensionality and noise reduction, emphasizing of main characteristics of time series data and speed up of consequent usage of machine learning methods.
Details
| Package: | TSrepr |
| Type: | Package |
| Date: | 2018-01-26 - Inf |
| License: | GPL-3 |
The following functions for time series representations are included in the package:
-
repr_paa - Piecewise Aggregate Approximation (PAA)
-
repr_dwt - Discrete Wavelet Transform (DWT)
-
repr_dft - Discrete Fourier Transform (DFT)
-
repr_dct - Discrete Cosine Transform (DCT)
-
repr_sma - Simple Moving Average (SMA)
-
repr_pip - Perceptually Important Points (PIP)
-
repr_sax - Symbolic Aggregate Approximation (SAX)
-
repr_pla - Piecewise Linear Approximation (PLA)
-
repr_seas_profile - Mean seasonal profile
-
repr_lm - Model-based seasonal representations based on linear model (lm, rlm, l1)
-
repr_gam - Model-based seasonal representations based on generalized additive model (GAM)
-
repr_exp - Exponential smoothing seasonal coefficients
-
repr_feaclip - Feature extraction from clipping representation (FeaClip)
-
repr_featrend - Feature extraction from trending representation (FeaTrend)
-
repr_feacliptrend - Feature extraction from clipping and trending representation (FeaClipTrend)
There are also implemented additional useful functions as:
-
repr_windowing - applies above mentioned representations to every window of a time series
-
repr_matrix - applies above mentioned representations to every row of a matrix of time series
-
repr_list - applies above mentioned representations to every member of a list of time series
-
norm_z, norm_min_max, norm_boxcox, norm_yj, norm_atan - normalisation functions
-
norm_z_params, norm_min_max_params - normalisation functions with defined parameters
-
norm_z_list, norm_min_max_list - normalisation functions with output also of scaling parameters
-
denorm_z, denorm_min_max, denorm_boxcox, denorm_yj, denorm_atan - denormalisation functions
Author(s)
Peter Laurinec
Maintainer: Peter Laurinec <tsreprpackage@gmail.com>
Creates bit-level (clipped representation) from a vector
Description
The clipping computes bit-level (clipped representation) from a vector.
Usage
clipping(x)
Arguments
x |
the numeric vector (time series) |
Details
Clipping transforms time series to bit-level representation.
It is defined as follows:
repr_t = {1 if x_t > \mu , 0 otherwise,}
where x_t is a value of a time series
and \mu is average of a time series.
Value
the integer vector of zeros and ones
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Bagnall A, Ratanamahatana C, Keogh E, Lonardi S, Janacek G (2006) A bit level representation for time series data mining with shape based similarity. Data Mining and Knowledge Discovery 13(1):11-40
Laurinec P, and Lucka M (2018) Interpretable multiple data streams clustering with clipped streams representation for the improvement of electricity consumption forecasting. Data Mining and Knowledge Discovery. Springer. DOI: 10.1007/s10618-018-0598-2
See Also
Examples
clipping(rnorm(50))
Functions for linear regression model coefficients extraction
Description
The functions computes regression coefficients from a linear model.
Usage
lmCoef(X, Y)
rlmCoef(X, Y)
l1Coef(X, Y)
Arguments
X |
the model (design) matrix of independent variables |
Y |
the vector of dependent variable (time series) |
Value
The numeric vector of regression coefficients
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
design_matrix <- matrix(rnorm(10), ncol = 2)
lmCoef(design_matrix, rnorm(5))
rlmCoef(design_matrix, rnorm(5))
l1Coef(design_matrix, rnorm(5))
Arctangent denormalisation
Description
The denorm_atan denormalises time series from Arctangent function.
Usage
denorm_atan(x)
Arguments
x |
the numeric vector (time series) |
Value
the numeric vector of denormalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
denorm_atan(runif(50))
Two-parameter Box-Cox denormalisation
Description
The denorm_boxcox denormalises time series by two-parameter Box-Cox method.
Usage
denorm_boxcox(x, lambda = 0.1, gamma = 0)
Arguments
x |
the numeric vector (time series) to be denormalised |
lambda |
the numeric value - power transformation parameter (default is 0.1) |
gamma |
the non-negative numeric value - parameter for holding the time series positive (offset) (default is 0) |
Value
the numeric vector of denormalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
denorm_z, denorm_min_max, denorm_atan
Examples
denorm_boxcox(runif(50))
Min-Max denormalisation
Description
The denorm_min_max denormalises time series by min-max method.
Usage
denorm_min_max(x, min, max)
Arguments
x |
the numeric vector (time series) |
min |
the minimum value |
max |
the maximal value |
Value
the numeric vector of denormalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Laurinec P, Lucká M (2018) Clustering-based forecasting method for individual consumers electricity load using time series representations. Open Comput Sci, 8(1):38–50, DOI: 10.1515/comp-2018-0006
See Also
norm_min_max, norm_min_max_list
Examples
# Normalise values and save normalisation parameters:
norm_res <- norm_min_max_list(rnorm(50, 5, 2))
# Denormalise new data with previous computed parameters:
denorm_min_max(rnorm(50, 4, 2), min = norm_res$min, max = norm_res$max)
Yeo-Johnson denormalisation
Description
The denorm_yj denormalises time series by Yeo-Johnson method
Usage
denorm_yj(x, lambda = 0.1)
Arguments
x |
the numeric vector (time series) to be denormalised |
lambda |
the numeric value - power transformation parameter (default is 0.1) |
Value
the numeric vector of denormalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
denorm_z, denorm_min_max, denorm_boxcox
Examples
denorm_yj(runif(50))
Z-score denormalisation
Description
The denorm_z denormalises time series by z-score method.
Usage
denorm_z(x, mean, sd)
Arguments
x |
the numeric vector (time series) |
mean |
the mean value |
sd |
the standard deviation value |
Value
the numeric vector of denormalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Laurinec P, Lucká M (2018) Clustering-based forecasting method for individual consumers electricity load using time series representations. Open Comput Sci, 8(1):38–50, DOI: 10.1515/comp-2018-0006
See Also
Examples
# Normalise values and save normalisation parameters:
norm_res <- norm_z_list(rnorm(50, 5, 2))
# Denormalise new data with previous computed parameters:
denorm_z(rnorm(50, 4, 2), mean = norm_res$mean, sd = norm_res$sd)
2 weeks of electricity load data from 50 consumers.
Description
A dataset containing the electricity consumption time series from 50 consumers of the length of 2 weeks. Every day is 48 measurements (half-hourly data). Each row represents one consumers time series.
Usage
elec_load
Format
A data frame with 50 rows and 672 variables.
Source
Anonymized.
Fast statistic functions (helpers)
Description
Fast statistic functions (helpers) for representations computation.
Usage
maxC(x)
minC(x)
meanC(x)
sumC(x)
medianC(x)
Arguments
x |
the numeric vector |
Value
the numeric value
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
Examples
maxC(rnorm(50))
minC(rnorm(50))
meanC(rnorm(50))
sumC(rnorm(50))
medianC(rnorm(50))
MAAPE
Description
the maape computes MAAPE (Mean Arctangent Absolute Percentage Error) of a forecast.
Usage
maape(x, y)
Arguments
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
Value
the numeric value in %
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Sungil Kim, Heeyoung Kim (2016) A new metric of absolute percentage error for intermittent demand forecasts, International Journal of Forecasting 32(3):669-679
Examples
maape(runif(50), runif(50))
MAE
Description
The mae computes MAE (Mean Absolute Error) of a forecast.
Usage
mae(x, y)
Arguments
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
Value
the numeric value
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
Examples
mae(runif(50), runif(50))
MAPE
Description
the mape computes MAPE (Mean Absolute Percentage Error) of a forecast.
Usage
mape(x, y)
Arguments
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
Value
the numeric value in %
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
Examples
mape(runif(50), runif(50))
MASE
Description
The mase computes MASE (Mean Absolute Scaled Error) of a forecast.
Usage
mase(real, forecast, naive)
Arguments
real |
the numeric vector of real values |
forecast |
the numeric vector of forecasted values |
naive |
the numeric vector of naive forecast |
Value
the numeric value
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
Examples
mase(rnorm(50), rnorm(50), rnorm(50))
MdAE
Description
The mdae computes MdAE (Median Absolute Error) of a forecast.
Usage
mdae(x, y)
Arguments
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
Value
the numeric value
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
Examples
mdae(runif(50), runif(50))
MSE
Description
The mse computes MSE (Mean Squared Error) of a forecast.
Usage
mse(x, y)
Arguments
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
Value
the numeric value
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
Examples
mse(runif(50), runif(50))
Arctangent normalisation
Description
The norm_atan normalises time series by Arctangent to max (-1,1) range.
Usage
norm_atan(x)
Arguments
x |
the numeric vector (time series) |
Value
the numeric vector of normalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
norm_atan(rnorm(50))
Two-parameter Box-Cox normalisation
Description
The norm_boxcox normalises time series by two-parameter Box-Cox normalisation.
Usage
norm_boxcox(x, lambda = 0.1, gamma = 0)
Arguments
x |
the numeric vector (time series) |
lambda |
the numeric value - power transformation parameter (default is 0.1) |
gamma |
the non-negative numeric value - parameter for holding the time series positive (offset) (default is 0) |
Value
the numeric vector of normalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
norm_z, norm_min_max, norm_atan
Examples
norm_boxcox(runif(50))
Min-Max normalisation
Description
The norm_min_max normalises time series by min-max method.
Usage
norm_min_max(x)
Arguments
x |
the numeric vector (time series) |
Value
the numeric vector of normalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
norm_min_max(rnorm(50))
Min-Max normalization list
Description
The norm_min_max_list normalises time series by min-max method and returns normalization parameters (min and max).
Usage
norm_min_max_list(x)
Arguments
x |
the numeric vector (time series) |
Value
the list composed of:
- norm_values
the numeric vector of normalised values of time series
- min
the min value
- max
the max value
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
norm_min_max_list(rnorm(50))
Min-Max normalisation with parameters
Description
The norm_min_max_params normalises time series by min-max method with defined parameters.
Usage
norm_min_max_params(x, min, max)
Arguments
x |
the numeric vector (time series) |
min |
the numeric value |
max |
the numeric value |
Value
the numeric vector of normalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
norm_min_max_params(rnorm(50), 0, 1)
Yeo-Johnson normalisation
Description
The norm_yj normalises time series by Yeo-Johnson normalisation.
Usage
norm_yj(x, lambda = 0.1)
Arguments
x |
the numeric vector (time series) |
lambda |
the numeric value - power transformation parameter (default is 0.1) |
Value
the numeric vector of normalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
norm_z, norm_min_max, norm_boxcox
Examples
norm_yj(runif(50))
Z-score normalisation
Description
The norm_z normalises time series by z-score.
Usage
norm_z(x)
Arguments
x |
the numeric vector (time series) |
Value
the numeric vector of normalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
norm_z(runif(50))
Z-score normalization list
Description
The norm_z_list normalizes time series by z-score and returns normalization parameters (mean and standard deviation).
Usage
norm_z_list(x)
Arguments
x |
the numeric vector (time series) |
Value
the list composed of:
- norm_values
the numeric vector of normalised values of time series
- mean
the mean value
- sd
the standard deviation
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
norm_z_list(runif(50))
Z-score normalisation with parameters
Description
The norm_z_params normalises time series by z-score with defined mean and standard deviation.
Usage
norm_z_params(x, mean, sd)
Arguments
x |
the numeric vector (time series) |
mean |
the numeric value |
sd |
the numeric value - standard deviation |
Value
the numeric vector of normalised values
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
norm_z_params(runif(50), 0.5, 1)
DCT representation
Description
The repr_dct computes DCT (Discrete Cosine Transform) representation from a time series.
Usage
repr_dct(x, coef = 10)
Arguments
x |
the numeric vector (time series) |
coef |
the number of coefficients to extract from DCT |
Details
The length of the final time series representation is equal to set coef parameter.
Value
the numeric vector of DCT coefficients
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
repr_dct(rnorm(50), coef = 4)
DFT representation by FFT
Description
The repr_dft computes DFT (Discrete Fourier Transform) representation from a time series by FFT (Fast Fourier Transform).
Usage
repr_dft(x, coef = 10)
Arguments
x |
the numeric vector (time series) |
coef |
the number of coefficients to extract from FFT |
Details
The length of the final time series representation is equal to set coef parameter.
Value
the numeric vector of DFT coefficients
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
repr_dft(rnorm(50), coef = 4)
DWT representation
Description
The repr_dwt computes DWT (Discrete Wavelet Transform) representation (coefficients) from a time series.
Usage
repr_dwt(x, level = 4, filter = "d4")
Arguments
x |
the numeric vector (time series) |
level |
the level of DWT transformation (default is 4) |
filter |
the filter name (default is "d6").
Can be: "haar", "d4", "d6", ..., "d20", "la8", "la10", ..., "la20", "bl14", "bl18", "bl20",
"c6", "c12", ..., "c30". See more info at |
Details
This function extracts DWT coefficients.
You can use various wavelet filters, see all of them here wt.filter.
The number of extracted coefficients depends on the level selected.
The final representation has length equal to floor(n / 2^level), where n is a length of original time series.
Value
the numeric vector of DWT coefficients
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Laurinec P, Lucka M (2016) Comparison of representations of time series for clustering smart meter data. In: Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering and Computer Science 2016, pp 458-463
See Also
Examples
# Interpretation: DWT with Daubechies filter of length 4 and
# 3rd level of DWT coefficients extracted.
repr_dwt(rnorm(50), filter = "d4", level = 3)
Exponential smoothing seasonal coefficients as representation
Description
The repr_exp computes exponential smoothing seasonal coefficients.
Usage
repr_exp(x, freq, alpha = TRUE, gamma = TRUE)
Arguments
x |
the numeric vector (time series) |
freq |
the frequency of the time series |
alpha |
the smoothing factor (default is TRUE - automatic determination of smoothing factor), or number between 0 to 1 |
gamma |
the seasonal smoothing factor (default is TRUE - automatic determination of seasonal smoothing factor), or number between 0 to 1 |
Details
This function extracts exponential smoothing seasonal coefficients and uses them as time series representation.
You can set smoothing factors (alpha, gamma) manually, but recommended is automatic method (set to TRUE).
The trend component is not included in computations.
Value
the numeric vector of seasonal coefficients
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Laurinec P, Lucka M (2016) Comparison of representations of time series for clustering smart meter data. In: Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering and Computer Science 2016, pp 458-463
Laurinec P, Loderer M, Vrablecova P, Lucka M, Rozinajova V, Ezzeddine AB (2016) Adaptive time series forecasting of energy consumption using optimized cluster analysis. In: Data Mining Workshops (ICDMW), 2016 IEEE 16th International Conference on, IEEE, pp 398-405
See Also
repr_lm, repr_gam, repr_seas_profile,
HoltWinters
Examples
repr_exp(rnorm(96), freq = 24)
FeaClip representation of time series
Description
The repr_feaclip computes representation of time series based on feature extraction from bit-level (clipped) representation.
Usage
repr_feaclip(x)
Arguments
x |
the numeric vector (time series) |
Details
FeaClip is method of time series representation based on feature extraction from run lengths (RLE) of bit-level (clipped) representation. It extracts 8 key features from clipped representation.
There are as follows:
repr = \{ max_1 - max. from run lengths of ones,
sum_1 - sum of run lengths of ones,
max_0 - max. from run lengths of zeros,
crossings - length of RLE encoding - 1,
f_0 - number of first zeros,
l_0 - number of last zeros,
f_1 - number of first ones,
l_1 - number of last ones \} .
Value
the numeric vector of length 8
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Laurinec P, and Lucka M (2018) Interpretable multiple data streams clustering with clipped streams representation for the improvement of electricity consumption forecasting. Data Mining and Knowledge Discovery. Springer. DOI: 10.1007/s10618-018-0598-2
See Also
repr_featrend, repr_feacliptrend
Examples
repr_feaclip(rnorm(50))
FeaClipTrend representation of time series
Description
The repr_feacliptrend computes representation of time series
based on feature extraction from bit-level representations (clipping and trending).
Usage
repr_feacliptrend(x, func, pieces = 2L, order = 4L)
Arguments
x |
the numeric vector (time series) |
func |
the aggregation function for FeaTrend procedure (sumC or maxC) |
pieces |
the number of parts of time series to split |
order |
the order of simple moving average |
Details
FeaClipTrend combines FeaClip and FeaTrend representation methods. See documentation of these two methods (check See Also section).
Value
the numeric vector of frequencies of features
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Laurinec P, and Lucka M (2018) Interpretable multiple data streams clustering with clipped streams representation for the improvement of electricity consumption forecasting. Data Mining and Knowledge Discovery. Springer. DOI: 10.1007/s10618-018-0598-2
See Also
Examples
repr_feacliptrend(rnorm(50), maxC, 2, 4)
FeaTrend representation of time series
Description
The repr_featrend computes representation of time series based on feature extraction from bit-level (trending) representation.
Usage
repr_featrend(x, func, pieces = 2L, order = 4L)
Arguments
x |
the numeric vector (time series) |
func |
the function of aggregation, can be sumC or maxC or similar aggregation function |
pieces |
the number of parts of time series to split (default to 2) |
order |
the order of simple moving average (default to 4) |
Details
FeaTrend is method of time series representation based on feature extraction from run lengths (RLE) of bit-level (trending) representation. It extracts number of features from trending representation based on number of pieces defined. From every piece, 2 features are extracted. You can define what feature will be extracted, recommended functions are max and sum. For example if max is selected, then maximum value of run lengths of ones and zeros are extracted.
Value
the numeric vector of the length pieces
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
repr_feaclip, repr_feacliptrend
Examples
# default settings
repr_featrend(rnorm(50), maxC)
# compute FeaTrend for 4 pieces and make more smoothed ts by order = 8
repr_featrend(rnorm(50), sumC, 4, 8)
GAM regression coefficients as representation
Description
The repr_gam computes seasonal GAM regression coefficients. Additional exogenous variables can be also added.
Usage
repr_gam(x, freq = NULL, xreg = NULL)
Arguments
x |
the numeric vector (time series) |
freq |
the frequency of the time series. Can be vector of two frequencies (seasonalities) or just an integer of one frequency. |
xreg |
the numeric vector or the data.frame with additional exogenous regressors |
Details
This model-based representation method extracts regression coefficients from a GAM (Generalized Additive Model).
The extraction of seasonal regression coefficients is automatic.
The maximum number of seasonalities is 2 so it is possible to compute representation for double-seasonal time series.
The first set seasonality (frequency) is main, so for example if we have hourly time series (freq = c(24, 24*7)),
the number of extracted daily seasonal coefficients is 24 and the number of
weekly seasonal coefficients is 7, because the length of second seasonality representation is always freq_1 / freq_2.
The smooth function for seasonal variables is set to cubic regression spline.
There is also possibility to add another independent variables (xreg).
Value
the numeric vector of GAM regression coefficients
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Laurinec P, Lucka M (2016) Comparison of representations of time series for clustering smart meter data. In: Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering and Computer Science 2016, pp 458-463
Laurinec P, Loderer M, Vrablecova P, Lucka M, Rozinajova V, Ezzeddine AB (2016) Adaptive time series forecasting of energy consumption using optimized cluster analysis. In: Data Mining Workshops (ICDMW), 2016 IEEE 16th International Conference on, IEEE, pp 398-405
Laurinec P, Lucká M (2018) Clustering-based forecasting method for individual consumers electricity load using time series representations. Open Comput Sci, 8(1):38–50, DOI: 10.1515/comp-2018-0006
See Also
Examples
repr_gam(rnorm(96), freq = 24)
Computation of list of representations list of time series with different lengths
Description
The repr_list computes list of representations from list of time series
Usage
repr_list(
x,
func = NULL,
args = NULL,
normalise = FALSE,
func_norm = norm_z,
windowing = FALSE,
win_size = NULL
)
Arguments
x |
the list of time series, where time series can have different lengths |
func |
the function that computes representation |
args |
the list of additional (or required) parameters of func (function that computes representation) |
normalise |
normalise (scale) time series before representations computation? (default is FALSE) |
func_norm |
the normalisation function (default is |
windowing |
perform windowing? (default is FALSE) |
win_size |
the size of the window |
Details
This function computes representation to an every member of a list of time series (that can have different lengths) and returns list of time series representations.
It can be combined with windowing (see repr_windowing) and normalisation of time series.
Value
the numeric list of representations of time series
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
# Create random list of time series with different lengths
list_ts <- list(rnorm(sample(8:12, 1)), rnorm(sample(8:12, 1)), rnorm(sample(8:12, 1)))
repr_list(list_ts, func = repr_sma,
args = list(order = 3))
# return normalised representations, and normalise time series by min-max normalisation
repr_list(list_ts, func = repr_sma,
args = list(order = 3), normalise = TRUE, func_norm = norm_min_max)
Regression coefficients from linear model as representation
Description
The repr_lm computes seasonal regression coefficients from a linear model.
Additional exogenous variables can be also added.
Usage
repr_lm(x, freq = NULL, method = "lm", xreg = NULL)
Arguments
x |
the numeric vector (time series) |
freq |
the frequency of the time series. Can be vector of two frequencies (seasonalities) or just an integer of one frequency. |
method |
the linear regression method to use. It can be "lm", "rlm" or "l1". |
xreg |
the data.frame with additional exogenous regressors or the single numeric vector |
Details
This model-based representation method extracts regression coefficients from a linear model.
The extraction of seasonal regression coefficients is automatic.
The maximum number of seasonalities is 2 so it is possible to compute representation for double-seasonal time series.
The first set seasonality (frequency) is main, so for example if we have hourly time series (freq = c(24, 24*7)),
the number of extracted daily seasonal coefficients is 24 and the number of
weekly seasonal coefficients is 7, because the length of second seasonality representation is always freq_1 / freq_2.
There is also possibility to add another independent variables (xreg).
You have three possibilities for selection of a linear model method.
"lm" is classical OLS regression.
"rlm" is robust linear model using psi huber function and is implemented in MASS package.
"l1" is L1 quantile regression model (also robust linear regression method) implemented in package quantreg.
Value
the numeric vector of regression coefficients
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Laurinec P, Lucka M (2016) Comparison of representations of time series for clustering smart meter data. In: Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering and Computer Science 2016, pp 458-463
Laurinec P, Loderer M, Vrablecova P, Lucka M, Rozinajova V, Ezzeddine AB (2016) Adaptive time series forecasting of energy consumption using optimized cluster analysis. In: Data Mining Workshops (ICDMW), 2016 IEEE 16th International Conference on, IEEE, pp 398-405
Laurinec P, Lucká M (2018) Clustering-based forecasting method for individual consumers electricity load using time series representations. Open Comput Sci, 8(1):38–50, DOI: 10.1515/comp-2018-0006
See Also
Examples
# Extracts 24 seasonal regression coefficients from the time series by linear model
repr_lm(rnorm(96), freq = 24, method = "lm")
# Try also robust linear models ("rlm" and "l1")
repr_lm(rnorm(96), freq = 24, method = "rlm")
repr_lm(rnorm(96), freq = 24, method = "l1")
Computation of matrix of representations from matrix of time series
Description
The repr_matrix computes matrix of representations from matrix of time series
Usage
repr_matrix(
x,
func = NULL,
args = NULL,
normalise = FALSE,
func_norm = norm_z,
windowing = FALSE,
win_size = NULL
)
Arguments
x |
the matrix, data.frame or data.table of time series, where time series are in rows of the table |
func |
the function that computes representation |
args |
the list of additional (or required) parameters of func (function that computes representation) |
normalise |
normalise (scale) time series before representations computation? (default is FALSE) |
func_norm |
the normalisation function (default is |
windowing |
perform windowing? (default is FALSE) |
win_size |
the size of the window |
Details
This function computes representation to an every row of a matrix of time series and returns matrix of time series representations.
It can be combined with windowing (see repr_windowing) and normalisation of time series.
Value
the numeric matrix of representations of time series
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
# Create random matrix of time series
mat_ts <- matrix(rnorm(100), ncol = 10)
repr_matrix(mat_ts, func = repr_paa,
args = list(q = 5, func = meanC))
# return normalised representations, and normalise time series by min-max normalisation
repr_matrix(mat_ts, func = repr_paa,
args = list(q = 2, func = meanC), normalise = TRUE, func_norm = norm_min_max)
# with windowing
repr_matrix(mat_ts, func = repr_feaclip, windowing = TRUE, win_size = 5)
PAA - Piecewise Aggregate Approximation
Description
The repr_paa computes PAA representation from a vector.
Usage
repr_paa(x, q, func)
Arguments
x |
the numeric vector (time series) |
q |
the integer of the length of the "piece" |
func |
the aggregation function. Can be meanC, medianC, sumC, minC or maxC or similar aggregation function |
Details
PAA with possibility to use arbitrary aggregation function. The original method uses average as aggregation function.
Value
the numeric vector
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Keogh E, Chakrabarti K, Pazzani M, Mehrotra Sh (2001) Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases. Knowledge and Information Systems 3(3):263-286
See Also
repr_dwt, repr_dft, repr_dct, repr_sma
Examples
repr_paa(rnorm(11), 2, meanC)
PIP representation
Description
The repr_pip computes PIP (Perceptually Important Points) representation from a time series.
Usage
repr_pip(x, times = 10, return = "points")
Arguments
x |
the numeric vector (time series) |
times |
the number of important points to extract (default 10) |
return |
what to return? Can be important points ("points"), places of important points in a vector ("places") or "both" (data.frame). |
Value
the values based on the argument return (see above)
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Fu TC, Chung FL, Luk R, and Ng CM (2008) Representing financial time series based on data point importance. Engineering Applications of Artificial Intelligence, 21(2):277-300
Examples
repr_pip(rnorm(100), times = 12, return = "both")
PLA representation
Description
The repr_pla computes PLA (Piecewise Linear Approximation) representation from a time series.
Usage
repr_pla(x, times = 10, return = "points")
Arguments
x |
the numeric vector (time series) |
times |
the number of important points to extract (default 10) |
return |
what to return? Can be "points" (segments), places of points (segments) in a vector ("places") or "both" (data.frame). |
Value
the values based on the argument return (see above)
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Zhu Y, Wu D, Li Sh (2007) A Piecewise Linear Representation Method of Time Series Based on Feature Points. Knowledge-Based Intelligent Information and Engineering Systems 4693:1066-1072
Examples
repr_pla(rnorm(100), times = 12, return = "both")
SAX - Symbolic Aggregate Approximation
Description
The repr_sax creates SAX symbols for a univariate time series.
Usage
repr_sax(x, q = 2, a = 6, eps = 0.01)
Arguments
x |
the numeric vector (time series) |
q |
the integer of the length of the "piece" in PAA |
a |
the integer of the alphabet size |
eps |
is the minimum threshold for variance in x and should be a numeric value. If x has a smaller variance than eps, it will represented as a word using the middle alphabet. |
Value
the character vector of SAX representation
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Lin J, Keogh E, Lonardi S, Chiu B (2003) A symbolic representation of time series, with implications for streaming algorithms. Proceedings of the 8th ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery - DMKD'03
See Also
Examples
x <- rnorm(48)
repr_sax(x, q = 4, a = 5)
Mean seasonal profile of time series
Description
The repr_seas_profile computes mean seasonal profile representation from a time series.
Usage
repr_seas_profile(x, freq, func)
Arguments
x |
the numeric vector (time series) |
freq |
the integer of the length of the season |
func |
the aggregation function. Can be meanC or medianC or similar aggregation function. |
Details
This function computes mean seasonal profile representation for a seasonal time series. The length of representation is length of set seasonality (frequency) of a time series. Aggregation function is arbitrary (best choice is for you maybe mean or median).
Value
the numeric vector
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Laurinec P, Lucka M (2016) Comparison of representations of time series for clustering smart meter data. In: Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering and Computer Science 2016, pp 458-463
Laurinec P, Loderer M, Vrablecova P, Lucka M, Rozinajova V, Ezzeddine AB (2016) Adaptive time series forecasting of energy consumption using optimized cluster analysis. In: Data Mining Workshops (ICDMW), 2016 IEEE 16th International Conference on, IEEE, pp 398-405
Laurinec P, Lucká M (2018) Clustering-based forecasting method for individual consumers electricity load using time series representations. Open Comput Sci, 8(1):38–50, DOI: 10.1515/comp-2018-0006
See Also
Examples
repr_seas_profile(rnorm(48*10), 48, meanC)
Simple Moving Average representation
Description
The repr_sma computes Simple Moving Average (SMA) from a time series.
Usage
repr_sma(x, order)
Arguments
x |
the numeric vector (time series) |
order |
the order of simple moving average |
Value
the numeric vector of smoothed values of the length = length(x) - order + 1
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
Examples
repr_sma(rnorm(50), 4)
Windowing of time series
Description
The repr_windowing computes representations from windows of a vector.
Usage
repr_windowing(x, win_size, func = NULL, args = NULL)
Arguments
x |
the numeric vector (time series) |
win_size |
the length of the window |
func |
the function for representation computation. For example |
args |
the list of additional arguments to the func (representation computation function). The args list must be named. |
Details
This function applies specified representation method (function) to every non-overlapping window (subsequence, piece) of a time series.
Value
the numeric vector
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
References
Laurinec P, and Lucka M (2018) Interpretable multiple data streams clustering with clipped streams representation for the improvement of electricity consumption forecasting. Data Mining and Knowledge Discovery. Springer. DOI: 10.1007/s10618-018-0598-2
See Also
Examples
# func without arguments
repr_windowing(rnorm(48), win_size = 24, func = repr_feaclip)
# func with arguments
repr_windowing(rnorm(48), win_size = 24, func = repr_featrend,
args = list(func = maxC, order = 2, pieces = 2))
RLE (Run Length Encoding) written in C++
Description
The rleC computes RLE from bit-level (clipping or trending representation) vector.
Usage
rleC(x)
Arguments
x |
the integer vector (from |
Value
the list of values and counts of zeros and ones
Examples
# clipping
clipped <- clipping(rnorm(50))
rleC(clipped)
# trending
trended <- trending(rnorm(50))
rleC(trended)
RMSE
Description
The rmse computes RMSE (Root Mean Squared Error) of a forecast.
Usage
rmse(x, y)
Arguments
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
Value
the numeric value
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
Examples
rmse(runif(50), runif(50))
sMAPE
Description
The smape computes sMAPE (Symmetric Mean Absolute Percentage Error) of a forecast.
Usage
smape(x, y)
Arguments
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
Value
the numeric value in %
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
Examples
smape(runif(50), runif(50))
Creates bit-level (trending) representation from a vector
Description
The trending Computes bit-level (trending) representation from a vector.
Usage
trending(x)
Arguments
x |
the numeric vector (time series) |
Details
Trending transforms time series to bit-level representation.
It is defined as follows:
repr_t = {1 if x_t - x_{t+1} < 0 , 0 otherwise,}
where x_t is a value of a time series.
Value
the integer vector of zeros and ones
Author(s)
Peter Laurinec, <tsreprpackage@gmail.com>
See Also
Examples
trending(rnorm(50))