View source: R/calculate_features.R
calculate_features | R Documentation |
calculate_features
computes several features associated with a
categorical time series or between a categorical and a real-valued time series
calculate_features(series, n_series = NULL, lag = 1, type = NULL)
series |
An object of type |
n_series |
A real-valued time series. |
lag |
The considered lag (default is 1). |
type |
String indicating the feature one wishes to compute. |
Assume we have a CTS of length T
with range \mathcal{V}=\{1, 2, \ldots, r\}
,
\overline{X}_t=\{\overline{X}_1,\ldots, \overline{X}_T\}
, with \widehat{p}_i
being the natural estimate of the marginal probability of the i
th
category, and \widehat{p}_{ij}(l)
being the natural estimate of the joint probability
for categories i
and j
at lag l, i,j=1, \ldots, r
. Assume also that
we have a real-valued time series of length T
, \overline{Z}_t=\{\overline{Z}_1,\ldots, \overline{Z}_T\}
.
The function computes the following quantities depending on the argument
type
:
If type=gini_index
, the function computes the
estimated gini index, \widehat{g}=\frac{r}{r-1}(1-\sum_{i=1}^{r}\widehat{p}_i^2)
.
If type=entropy
, the function computes the
estimated entropy, \widehat{e}=\frac{-1}{\ln(r)}\sum_{i=1}^{r}\widehat{p}_i\ln \widehat{p}_i
.
If type=chebycheff_dispersion
, the function computes the
estimated chebycheff dispersion, \widehat{c}=\frac{r}{r-1}(1-\max_i\widehat{p}_i)
.
If type=gk_tau
, the function computes the
estimated Goodman and Kruskal's tau, \widehat{\tau}(l)=\frac{\sum_{i,j=1}^{r}\frac{\widehat{p}_{ij}(l)^2}{\widehat{p}_j}-\sum_{i=1}^r\widehat{p}_i^2}{1-\sum_{i=1}^r\widehat{p}_i^2}
.
If type=gk_lambda
, the function computes the
estimated Goodman and Kruskal's lambda, \widehat{\lambda}(l)=\frac{\sum_{j=1}^{r}\max_i\widehat{p}_{ij}(l)-\max_i\widehat{p}_i}{1-\max_i\widehat{p}_i}
.
If type=uncertainty_coefficient
, the function computes the
estimated uncertainty coefficient, \widehat{u}(l)=-\frac{\sum_{i, j=1}^{r}\widehat{p}_{ij}(l)\ln\big(\frac{\widehat{p}_{ij}(l)}{\widehat{p}_i\widehat{p}_j}\big)}{\sum_{i=1}^{r}\widehat{p}_i\ln \widehat{p}_i}
.
If type=pearson_measure
, the function computes the
estimated Pearson measure, \widehat{X}_T^2(l)=T\sum_{i,j=1}^{r}\frac{(\widehat{p}_{ij}(l)-\widehat{p}_i\widehat{p}_j)^2}{\widehat{p}_i\widehat{p}_j}
.
If type=phi2_measure
, the function computes the
estimated Phi2 measure, \widehat{\Phi}^2(l)=\frac{\widehat{X}_T^2(l)}{T}
.
If type=sakoda_measure
, the function computes the
estimated Sakoda measure, \widehat{p}^*(l)=\sqrt{\frac{r\widehat{\Phi}^2(l)}{(r-1)(1+\widehat{\Phi}^2(l))}}
.
If type=cramers_vi
, the function computes the
estimated Cramer's vi, \widehat{v}(l)=\sqrt{\frac{1}{r-1}\sum_{i,j=1}^r\frac{(\widehat{p}_{ij}(l)-\widehat{p}_i\widehat{p}_j)^2}{\widehat{p}_i\widehat{p}_j}}
.
If type=cohens_kappa
, the function computes the
estimated Cohen's kappa, \widehat{\kappa}(l)=\frac{\sum_{j=1}^{r}(\widehat{p}_{jj}(l)-\widehat{p}_j^2)}{1-\sum_{i=1}^r\widehat{p}_i^2}
.
If type=total_correlation
, the function computes the
the estimated sum \widehat{\Psi}(l)=\frac{1}{r^2}\sum_{i,j=1}^{r}\widehat{\psi}_{ij}(l)^2
,
where \widehat{\psi}_{ij}(l)
is the estimated correlation
\widehat{Corr}(Y_{t, i}, Y_{t-l, j})
, i,j=1,\ldots,r
, being \overline{\boldsymbol Y}_t=\{\overline{\boldsymbol Y}_1, \ldots, \overline{\boldsymbol Y}_T\}
,
with \overline{\boldsymbol Y}_k=(\overline{Y}_{k,1}, \ldots, \overline{Y}_{k,r})^\top
, the
binarized time series of \overline{X}_t
.
If type=spectral_envelope
, the function computes the
estimated spectral envelope.
If type=total_mixed_correlation_1
, the function computes the
estimated total mixed l-correlation given by
\widehat{\Psi}_1(l)=\frac{1}{r}\sum_{i=1}^{r}\widehat{\psi}_{i}(l)^2,
where
\widehat{\psi}_{i}(l)=\widehat{Corr}(Y_{t,i}, Z_{t-l})
, being \overline{\boldsymbol Y}_t=\{\overline{\boldsymbol Y}_1, \ldots, \overline{\boldsymbol Y}_T\}
,
with \overline{\boldsymbol Y}_k=(\overline{Y}_{k,1}, \ldots, \overline{Y}_{k,r})^\top
, the
binarized time series of \overline{X}_t
.
If type=total_mixed_correlation_2
, the function computes the
estimated total mixed q-correlation given by
\widehat{\Psi}_2(l)=\frac{1}{r}\sum_{i=1}^{r}\int_{0}^{1}\widehat{\psi}^\rho_{i}(l)^2d\rho,
where
\widehat{\psi}_{i}^\rho(l)=\widehat{Corr}\big(Y_{t,i}, I(Z_{t-l}\leq q_{Z_t}(\rho)) \big)
, being \overline{\boldsymbol Y}_t=\{\overline{\boldsymbol Y}_1, \ldots, \overline{\boldsymbol Y}_T\}
,
with \overline{\boldsymbol Y}_k=(\overline{Y}_{k,1}, \ldots, \overline{Y}_{k,r})^\top
, the
binarized time series of \overline{X}_t
, \rho \in (0, 1)
a probability
level, I(\cdot)
the indicator function and q_{Z_t}
the quantile
function of the corresponding real-valued process.
The corresponding feature.
Ángel López-Oriona, José A. Vilar
weiss2008measuringctsfeatures
sequence_1 <- GeneticSequences[which(GeneticSequences$Series==1),]
uc <- calculate_features(series = sequence_1, type = 'uncertainty_coefficient' )
# Computing the uncertainty coefficient
# for the first series in dataset GeneticSequences
se <- calculate_features(series = sequence_1, type = 'spectral_envelope' )
# Computing the spectral envelope
# for the first series in dataset GeneticSequences
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