calculate_subfeatures function

Computes several subfeatures associated with a categorical time series

calculate_features computes several subfeatures associated with a categorical time series or between a categorical and a real-valued time series UTF-8

calculate_subfeatures(series, n_series, lag = 1, type = NULL)

Arguments

• series: An object of type tsibble (see R package tsibble), whose column named Value contains the values of the corresponding CTS. This column must be of class factor and its levels must be determined by the range of the CTS.
• n_series: A real-valued time series.
• lag: The considered lag (default is 1).
• type: String indicating the subfeature one wishes to compute.

Returns

The corresponding subfeature

Details

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 subfeatures depending on the argument type:

• If type=entropy, the function computes the subfeatures associated with the estimated entropy, $\widehat{p}_i\ln(\widehat{p}_i)$, $i=1,2, \ldots,r$.
• If type=gk_tau, the function computes the subfeatures associated with the estimated Goodman and Kruskal's tau, $\frac{\widehat{p}_{ij}(l)^2}{\widehat{p}_j}$, $i,j=1,2, \ldots,r$.
• If type=gk_lambda, the function computes the subfeatures associated with the estimated Goodman and Kruskal's lambda, $\max_i\widehat{p}_{ij}(l)$, $i=1,2, \ldots,r$.
• If type=uncertainty_coefficient, the function computes the subfeatures associated with the estimated uncertainty coefficient, $\widehat{p}_{ij}(l)\ln\Big(\frac{\widehat{p}_{ij}(l)}{\widehat{p}_i\widehat{p}_j}\Big)$, $i,j=1,2, \ldots,r$.
• If type=pearson_measure, the function computes the subfeatures associated with the estimated Pearson measure, $\frac{(\widehat{p}_{ij}(l)-\widehat{p}_i\widehat{p}_j)^2}{\widehat{p}_i\widehat{p}_j}$, $i,j=1,2, \ldots,r$.
• If type=phi2_measure, the function computes the subfeatures associated with the estimated Phi2 measure, $\frac{(\widehat{p}_{ij}(l)-\widehat{p}_i\widehat{p}_j)^2}{\widehat{p}_i\widehat{p}_j}$, $i,j=1,2, \ldots,r$.
• If type=sakoda_measure, the function computes the subfeatures associated with the estimated Sakoda measure, $\frac{(\widehat{p}_{ij}(l)-\widehat{p}_i\widehat{p}_j)^2}{\widehat{p}_i\widehat{p}_j}$, $i,j=1,2, \ldots,r$.
• If type=cramers_vi, the function computes the subfeatures associated with the estimated Cramer's vi, $\frac{(\widehat{p}_{ij}(l)-\widehat{p}_i\widehat{p}_j)^2}{\widehat{p}_i\widehat{p}_j}$, $i,j=1,2, \ldots,r$.
• If type=cohens_kappa, the function computes the subfeatures associated with the estimated Cohen's kappa, $\widehat{p}_{ii}(l)-\widehat{p}_i^2$, $i=1,2, \ldots,r$.
• If type=total_correlation, the function computes the subfeatures associated with the total correlation, $\widehat{\psi}_{ij}(l)$, $i,j=1,2, \ldots,r$ (see type='total_mixed_cor' in the function calculate_features).
• If type=total_mixed_correlation_1, the function computes the subfeatures associated with the total mixed l-correlation, $\widehat{\psi}_{i}(l)$, $i=1,2, \ldots,r$ (see type='total_mixed_correlation_1' in the function calculate_features).
• If type=total_mixed_correlation_2, the function computes the subfeatures associated with the total mixed q-correlation, $\int_{0}^{1}\widehat{\psi}^\rho_{i}(l)^2d\rho$, $i=1,2, \ldots,r$ (see type='total_mixed_correlation_2' in the function calculate_features).

Examples

sequence_1 <- GeneticSequences[which(GeneticSequences$Series==1),]
suc <- calculate_subfeatures(series = sequence_1, type = 'uncertainty_coefficient')
# Computing the subfeatures associated with the uncertainty coefficient
# for the first series in dataset GeneticSequences
scv <- calculate_subfeatures(series = sequence_1, type = 'cramers_vi' )
# Computing the subfeatures associated with the cramers vi
# for the first series in dataset GeneticSequences

References

Rdpack::insert_ref(key="weiss2008measuring",package="ctsfeatures")

Author(s)

Ángel López-Oriona, José A. Vilar