| Title: | Time Series Representations |
|---|---|
| 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. |
| Authors: | Peter Laurinec [aut, cre] |
| Maintainer: | Peter Laurinec <[email protected]> |
| License: | GPL-3 | file LICENSE |
| Version: | 1.1.0 |
| Built: | 2025-02-04 04:10:17 UTC |
| Source: | https://github.com/petolau/tsrepr |
The clipping computes bit-level (clipped representation) from a vector.
clipping(x)clipping(x)
x |
the numeric vector (time series) |
Clipping transforms time series to bit-level representation.
It is defined as follows:
where is a value of a time series
and is average of a time series.
the integer vector of zeros and ones
Peter Laurinec, <[email protected]>
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
clipping(rnorm(50))clipping(rnorm(50))
The functions computes regression coefficients from a linear model.
lmCoef(X, Y) rlmCoef(X, Y) l1Coef(X, Y)lmCoef(X, Y) rlmCoef(X, Y) l1Coef(X, Y)
X |
the model (design) matrix of independent variables |
Y |
the vector of dependent variable (time series) |
The numeric vector of regression coefficients
Peter Laurinec, <[email protected]>
design_matrix <- matrix(rnorm(10), ncol = 2) lmCoef(design_matrix, rnorm(5)) rlmCoef(design_matrix, rnorm(5)) l1Coef(design_matrix, rnorm(5))design_matrix <- matrix(rnorm(10), ncol = 2) lmCoef(design_matrix, rnorm(5)) rlmCoef(design_matrix, rnorm(5)) l1Coef(design_matrix, rnorm(5))
The denorm_atan denormalises time series from Arctangent function.
denorm_atan(x)denorm_atan(x)
x |
the numeric vector (time series) |
the numeric vector of denormalised values
Peter Laurinec, <[email protected]>
denorm_atan(runif(50))denorm_atan(runif(50))
The denorm_boxcox denormalises time series by two-parameter Box-Cox method.
denorm_boxcox(x, lambda = 0.1, gamma = 0)denorm_boxcox(x, lambda = 0.1, gamma = 0)
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) |
the numeric vector of denormalised values
Peter Laurinec, <[email protected]>
denorm_z, denorm_min_max, denorm_atan
denorm_boxcox(runif(50))denorm_boxcox(runif(50))
The denorm_min_max denormalises time series by min-max method.
denorm_min_max(x, min, max)denorm_min_max(x, min, max)
x |
the numeric vector (time series) |
min |
the minimum value |
max |
the maximal value |
the numeric vector of denormalised values
Peter Laurinec, <[email protected]>
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
norm_min_max, norm_min_max_list
# 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)# 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)
The denorm_yj denormalises time series by Yeo-Johnson method
denorm_yj(x, lambda = 0.1)denorm_yj(x, lambda = 0.1)
x |
the numeric vector (time series) to be denormalised |
lambda |
the numeric value - power transformation parameter (default is 0.1) |
the numeric vector of denormalised values
Peter Laurinec, <[email protected]>
denorm_z, denorm_min_max, denorm_boxcox
denorm_yj(runif(50))denorm_yj(runif(50))
The denorm_z denormalises time series by z-score method.
denorm_z(x, mean, sd)denorm_z(x, mean, sd)
x |
the numeric vector (time series) |
mean |
the mean value |
sd |
the standard deviation value |
the numeric vector of denormalised values
Peter Laurinec, <[email protected]>
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
# 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)# 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)
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.
elec_loadelec_load
A data frame with 50 rows and 672 variables.
Anonymized.
Fast statistic functions (helpers) for representations computation.
maxC(x) minC(x) meanC(x) sumC(x) medianC(x)maxC(x) minC(x) meanC(x) sumC(x) medianC(x)
x |
the numeric vector |
the numeric value
Peter Laurinec, <[email protected]>
maxC(rnorm(50)) minC(rnorm(50)) meanC(rnorm(50)) sumC(rnorm(50)) medianC(rnorm(50))maxC(rnorm(50)) minC(rnorm(50)) meanC(rnorm(50)) sumC(rnorm(50)) medianC(rnorm(50))
the maape computes MAAPE (Mean Arctangent Absolute Percentage Error) of a forecast.
maape(x, y)maape(x, y)
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
the numeric value in %
Peter Laurinec, <[email protected]>
Sungil Kim, Heeyoung Kim (2016) A new metric of absolute percentage error for intermittent demand forecasts, International Journal of Forecasting 32(3):669-679
maape(runif(50), runif(50))maape(runif(50), runif(50))
The mae computes MAE (Mean Absolute Error) of a forecast.
mae(x, y)mae(x, y)
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
the numeric value
Peter Laurinec, <[email protected]>
mae(runif(50), runif(50))mae(runif(50), runif(50))
the mape computes MAPE (Mean Absolute Percentage Error) of a forecast.
mape(x, y)mape(x, y)
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
the numeric value in %
Peter Laurinec, <[email protected]>
mape(runif(50), runif(50))mape(runif(50), runif(50))
The mase computes MASE (Mean Absolute Scaled Error) of a forecast.
mase(real, forecast, naive)mase(real, forecast, naive)
real |
the numeric vector of real values |
forecast |
the numeric vector of forecasted values |
naive |
the numeric vector of naive forecast |
the numeric value
Peter Laurinec, <[email protected]>
mase(rnorm(50), rnorm(50), rnorm(50))mase(rnorm(50), rnorm(50), rnorm(50))
The mdae computes MdAE (Median Absolute Error) of a forecast.
mdae(x, y)mdae(x, y)
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
the numeric value
Peter Laurinec, <[email protected]>
mdae(runif(50), runif(50))mdae(runif(50), runif(50))
The mse computes MSE (Mean Squared Error) of a forecast.
mse(x, y)mse(x, y)
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
the numeric value
Peter Laurinec, <[email protected]>
mse(runif(50), runif(50))mse(runif(50), runif(50))
The norm_atan normalises time series by Arctangent to max (-1,1) range.
norm_atan(x)norm_atan(x)
x |
the numeric vector (time series) |
the numeric vector of normalised values
Peter Laurinec, <[email protected]>
norm_atan(rnorm(50))norm_atan(rnorm(50))
The norm_boxcox normalises time series by two-parameter Box-Cox normalisation.
norm_boxcox(x, lambda = 0.1, gamma = 0)norm_boxcox(x, lambda = 0.1, gamma = 0)
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) |
the numeric vector of normalised values
Peter Laurinec, <[email protected]>
norm_z, norm_min_max, norm_atan
norm_boxcox(runif(50))norm_boxcox(runif(50))
The norm_min_max normalises time series by min-max method.
norm_min_max(x)norm_min_max(x)
x |
the numeric vector (time series) |
the numeric vector of normalised values
Peter Laurinec, <[email protected]>
norm_min_max(rnorm(50))norm_min_max(rnorm(50))
The norm_min_max_list normalises time series by min-max method and returns normalization parameters (min and max).
norm_min_max_list(x)norm_min_max_list(x)
x |
the numeric vector (time series) |
the list composed of:
the numeric vector of normalised values of time series
the min value
the max value
Peter Laurinec, <[email protected]>
norm_min_max_list(rnorm(50))norm_min_max_list(rnorm(50))
The norm_min_max_params normalises time series by min-max method with defined parameters.
norm_min_max_params(x, min, max)norm_min_max_params(x, min, max)
x |
the numeric vector (time series) |
min |
the numeric value |
max |
the numeric value |
the numeric vector of normalised values
Peter Laurinec, <[email protected]>
norm_min_max_params(rnorm(50), 0, 1)norm_min_max_params(rnorm(50), 0, 1)
The norm_yj normalises time series by Yeo-Johnson normalisation.
norm_yj(x, lambda = 0.1)norm_yj(x, lambda = 0.1)
x |
the numeric vector (time series) |
lambda |
the numeric value - power transformation parameter (default is 0.1) |
the numeric vector of normalised values
Peter Laurinec, <[email protected]>
norm_z, norm_min_max, norm_boxcox
norm_yj(runif(50))norm_yj(runif(50))
The norm_z normalises time series by z-score.
norm_z(x)norm_z(x)
x |
the numeric vector (time series) |
the numeric vector of normalised values
Peter Laurinec, <[email protected]>
norm_z(runif(50))norm_z(runif(50))
The norm_z_list normalizes time series by z-score and returns normalization parameters (mean and standard deviation).
norm_z_list(x)norm_z_list(x)
x |
the numeric vector (time series) |
the list composed of:
the numeric vector of normalised values of time series
the mean value
the standard deviation
Peter Laurinec, <[email protected]>
norm_z_list(runif(50))norm_z_list(runif(50))
The norm_z_params normalises time series by z-score with defined mean and standard deviation.
norm_z_params(x, mean, sd)norm_z_params(x, mean, sd)
x |
the numeric vector (time series) |
mean |
the numeric value |
sd |
the numeric value - standard deviation |
the numeric vector of normalised values
Peter Laurinec, <[email protected]>
norm_z_params(runif(50), 0.5, 1)norm_z_params(runif(50), 0.5, 1)
The repr_dct computes DCT (Discrete Cosine Transform) representation from a time series.
repr_dct(x, coef = 10)repr_dct(x, coef = 10)
x |
the numeric vector (time series) |
coef |
the number of coefficients to extract from DCT |
The length of the final time series representation is equal to set coef parameter.
the numeric vector of DCT coefficients
Peter Laurinec, <[email protected]>
repr_dct(rnorm(50), coef = 4)repr_dct(rnorm(50), coef = 4)
The repr_dft computes DFT (Discrete Fourier Transform) representation from a time series by FFT (Fast Fourier Transform).
repr_dft(x, coef = 10)repr_dft(x, coef = 10)
x |
the numeric vector (time series) |
coef |
the number of coefficients to extract from FFT |
The length of the final time series representation is equal to set coef parameter.
the numeric vector of DFT coefficients
Peter Laurinec, <[email protected]>
repr_dft(rnorm(50), coef = 4)repr_dft(rnorm(50), coef = 4)
The repr_dwt computes DWT (Discrete Wavelet Transform) representation (coefficients) from a time series.
repr_dwt(x, level = 4, filter = "d4")repr_dwt(x, level = 4, filter = "d4")
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 |
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.
the numeric vector of DWT coefficients
Peter Laurinec, <[email protected]>
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
# Interpretation: DWT with Daubechies filter of length 4 and # 3rd level of DWT coefficients extracted. repr_dwt(rnorm(50), filter = "d4", level = 3)# Interpretation: DWT with Daubechies filter of length 4 and # 3rd level of DWT coefficients extracted. repr_dwt(rnorm(50), filter = "d4", level = 3)
The repr_exp computes exponential smoothing seasonal coefficients.
repr_exp(x, freq, alpha = TRUE, gamma = TRUE)repr_exp(x, freq, alpha = TRUE, gamma = TRUE)
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 |
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.
the numeric vector of seasonal coefficients
Peter Laurinec, <[email protected]>
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
repr_lm, repr_gam, repr_seas_profile,
HoltWinters
repr_exp(rnorm(96), freq = 24)repr_exp(rnorm(96), freq = 24)
The repr_feaclip computes representation of time series based on feature extraction from bit-level (clipped) representation.
repr_feaclip(x)repr_feaclip(x)
x |
the numeric vector (time series) |
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:
the numeric vector of length 8
Peter Laurinec, <[email protected]>
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
repr_featrend, repr_feacliptrend
repr_feaclip(rnorm(50))repr_feaclip(rnorm(50))
The repr_feacliptrend computes representation of time series
based on feature extraction from bit-level representations (clipping and trending).
repr_feacliptrend(x, func, pieces = 2L, order = 4L)repr_feacliptrend(x, func, pieces = 2L, order = 4L)
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 |
FeaClipTrend combines FeaClip and FeaTrend representation methods. See documentation of these two methods (check See Also section).
the numeric vector of frequencies of features
Peter Laurinec, <[email protected]>
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
repr_feacliptrend(rnorm(50), maxC, 2, 4)repr_feacliptrend(rnorm(50), maxC, 2, 4)
The repr_featrend computes representation of time series based on feature extraction from bit-level (trending) representation.
repr_featrend(x, func, pieces = 2L, order = 4L)repr_featrend(x, func, pieces = 2L, order = 4L)
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) |
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.
the numeric vector of the length pieces
Peter Laurinec, <[email protected]>
repr_feaclip, repr_feacliptrend
# 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)# 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)
The repr_gam computes seasonal GAM regression coefficients. Additional exogenous variables can be also added.
repr_gam(x, freq = NULL, xreg = NULL)repr_gam(x, freq = NULL, xreg = NULL)
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 |
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).
the numeric vector of GAM regression coefficients
Peter Laurinec, <[email protected]>
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
repr_gam(rnorm(96), freq = 24)repr_gam(rnorm(96), freq = 24)
The repr_list computes list of representations from list of time series
repr_list( x, func = NULL, args = NULL, normalise = FALSE, func_norm = norm_z, windowing = FALSE, win_size = NULL )repr_list( x, func = NULL, args = NULL, normalise = FALSE, func_norm = norm_z, windowing = FALSE, win_size = NULL )
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 |
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.
the numeric list of representations of time series
Peter Laurinec, <[email protected]>
# 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)# 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)
The repr_lm computes seasonal regression coefficients from a linear model.
Additional exogenous variables can be also added.
repr_lm(x, freq = NULL, method = "lm", xreg = NULL)repr_lm(x, freq = NULL, method = "lm", xreg = NULL)
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 |
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.
the numeric vector of regression coefficients
Peter Laurinec, <[email protected]>
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
# 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")# 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")
The repr_matrix computes matrix of representations from matrix of time series
repr_matrix( x, func = NULL, args = NULL, normalise = FALSE, func_norm = norm_z, windowing = FALSE, win_size = NULL )repr_matrix( x, func = NULL, args = NULL, normalise = FALSE, func_norm = norm_z, windowing = FALSE, win_size = NULL )
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 |
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.
the numeric matrix of representations of time series
Peter Laurinec, <[email protected]>
# 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)# 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)
The repr_paa computes PAA representation from a vector.
repr_paa(x, q, func)repr_paa(x, q, func)
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 |
PAA with possibility to use arbitrary aggregation function. The original method uses average as aggregation function.
the numeric vector
Peter Laurinec, <[email protected]>
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
repr_dwt, repr_dft, repr_dct, repr_sma
repr_paa(rnorm(11), 2, meanC)repr_paa(rnorm(11), 2, meanC)
The repr_pip computes PIP (Perceptually Important Points) representation from a time series.
repr_pip(x, times = 10, return = "points")repr_pip(x, times = 10, return = "points")
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). |
the values based on the argument return (see above)
Peter Laurinec, <[email protected]>
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
repr_pip(rnorm(100), times = 12, return = "both")repr_pip(rnorm(100), times = 12, return = "both")
The repr_pla computes PLA (Piecewise Linear Approximation) representation from a time series.
repr_pla(x, times = 10, return = "points")repr_pla(x, times = 10, return = "points")
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). |
the values based on the argument return (see above)
Peter Laurinec, <[email protected]>
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
repr_pla(rnorm(100), times = 12, return = "both")repr_pla(rnorm(100), times = 12, return = "both")
The repr_sax creates SAX symbols for a univariate time series.
repr_sax(x, q = 2, a = 6, eps = 0.01)repr_sax(x, q = 2, a = 6, eps = 0.01)
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. |
the character vector of SAX representation
Peter Laurinec, <[email protected]>
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
x <- rnorm(48) repr_sax(x, q = 4, a = 5)x <- rnorm(48) repr_sax(x, q = 4, a = 5)
The repr_seas_profile computes mean seasonal profile representation from a time series.
repr_seas_profile(x, freq, func)repr_seas_profile(x, freq, func)
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. |
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).
the numeric vector
Peter Laurinec, <[email protected]>
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
repr_seas_profile(rnorm(48*10), 48, meanC)repr_seas_profile(rnorm(48*10), 48, meanC)
The repr_sma computes Simple Moving Average (SMA) from a time series.
repr_sma(x, order)repr_sma(x, order)
x |
the numeric vector (time series) |
order |
the order of simple moving average |
the numeric vector of smoothed values of the length = length(x) - order + 1
Peter Laurinec, <[email protected]>
repr_sma(rnorm(50), 4)repr_sma(rnorm(50), 4)
The repr_windowing computes representations from windows of a vector.
repr_windowing(x, win_size, func = NULL, args = NULL)repr_windowing(x, win_size, func = NULL, args = NULL)
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. |
This function applies specified representation method (function) to every non-overlapping window (subsequence, piece) of a time series.
the numeric vector
Peter Laurinec, <[email protected]>
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
# 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))# 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))
The rleC computes RLE from bit-level (clipping or trending representation) vector.
rleC(x)rleC(x)
x |
the integer vector (from |
the list of values and counts of zeros and ones
# clipping clipped <- clipping(rnorm(50)) rleC(clipped) # trending trended <- trending(rnorm(50)) rleC(trended)# clipping clipped <- clipping(rnorm(50)) rleC(clipped) # trending trended <- trending(rnorm(50)) rleC(trended)
The rmse computes RMSE (Root Mean Squared Error) of a forecast.
rmse(x, y)rmse(x, y)
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
the numeric value
Peter Laurinec, <[email protected]>
rmse(runif(50), runif(50))rmse(runif(50), runif(50))
The smape computes sMAPE (Symmetric Mean Absolute Percentage Error) of a forecast.
smape(x, y)smape(x, y)
x |
the numeric vector of real values |
y |
the numeric vector of forecasted values |
the numeric value in %
Peter Laurinec, <[email protected]>
smape(runif(50), runif(50))smape(runif(50), runif(50))
The trending Computes bit-level (trending) representation from a vector.
trending(x)trending(x)
x |
the numeric vector (time series) |
Trending transforms time series to bit-level representation.
It is defined as follows:
where is a value of a time series.
the integer vector of zeros and ones
Peter Laurinec, <[email protected]>
trending(rnorm(50))trending(rnorm(50))
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.
| 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
Peter Laurinec
Maintainer: Peter Laurinec <[email protected]>