README.md

In acweisha/gFPCAClassif: Classification of Binary Functional Data

gFPCAClassif

The goal of gFPCAClassif is to model and train classifiers for binary-valued functional data. The package presents model-based classification methods for the binary-valued functional data. The package accounts for multiple different scenarios of the data. All of these models are built under the assumption that the binary data are binary-valued observations of smooth latent functions.

Installation

You can install the development version of gFPCAClassif like so: This package is currently available on GitHub at {https://github.com/acweisha/gFPCAClassif}

Example

This is a basic example which shows you how to solve a common problem:

To model the binary data, we fit the model without covariates, the number of eigenfunctions are determined by a PVE of 0.95,

gsFPCA.model = gsFPCA(X_dat_s = X_dat_train,
                Ys = acc_data_train$group, covariates = NA,
                pve = 0.95, Kb = 10, bs0="cr")

The smooth trajectories are estimated using the 10 cubic regression splines. The resulting object, , contains the estimated mean function, eigenfunctions, and the account’s corresponding principal component scores. The estimated principal components scores for each account can be easily viewed in the output by:

head(gsFPCA.model$scores_train)
#>             psi1        psi2        psi3
#> [1,]  0.46425138 -0.23886527 -0.12459635
#> [2,]  0.68930728 -0.12412110 -0.19138972
#> [3,] -0.57787830 -0.26004744  0.03867028
#> [4,]  0.73441177 -0.21517720 -0.16258036
#> [5,] -0.01012554 -0.06334019 -0.08914326
#> [6,]  0.34669469 -0.18249006  0.05152066

By providing the eigenfunctions and scores, researchers are able to interpret the values of the principal component scores and better understand the accounts’ posting patterns. The eigenfunctions are visualized by using the function:

matplot(gsFPCA.model$eigen_funcs, type="l", lwd = 2, 
        lty = 1, xlab = "Day", 
        main = "gsFPCA Eigenfunctions", xaxt="n")
axis(1, at = (0:13)*48+1, labels = 1:14)
legend("topright", 
       legend = 1:length(colnames(gsFPCA.model$scores_train)),
       col = 1:length(colnames(gsFPCA.model$scores_train)), 
       lty=1, lwd=2)

The eigenfunctions explain the variability in posting patterns. For example the first eigenfunction has a slight decline over the two weeks and is positive throughout the study duration. This eigenfunction indicates that the overall frequency of posts is a main source of variability among accounts’ posting patterns. The second eigenfunction addresses differences in the posting behavior between the first week versus the second week. Finally, the third eigenfunction addresses differences of the posting habits during the middle of the study from the posting habits at the beginning and end of the study.

To predict the groups of new individuals we use the function and input the trained with the posting data from the new accounts,

gsFPCA.results = gsFPCA_predict(gsFPCA.model,
                        X_dat_s_new = X_dat_test)

The function predicts the groups of new accounts based on their binary functional data. Comparing the results to true values show us that the accurately discriminate 88% of the users.

 table(gsFPCA.results, acc_data_test$group)
#>               
#> gsFPCA.results  1  2
#>              1 45  6
#>              2  5 44

The previous analysis trained and tested the classifier using only the binary-valued functional data. We can include the number of followers for each account as an additional covariate in the nonparametric Bayes classifier. The updated model was fitted considering the number of followers and binary functional data is fit and evaluated by:

gsFPCA.model.ff = gsFPCA(X_dat_s = X_dat_train,
                      Ys = acc_data_train$group, 
                      covariates = cbind.data.frame(followers =
                      acc_data_train$followers_count),
                      pve = 0.95, Kb = 10, bs0="cr")
gsFPCA.results = gsFPCA_predict(gsFPCA.model.ff,
                      X_dat_s_new =  X_dat_test,
                      covariates_new=cbind.data.frame(followers=
                      acc_data_test$followers_count))
table(gsFPCA.results, acc_data_test$group)
#>               
#> gsFPCA.results  1  2
#>              1 46 18
#>              2  4 32

Adding the number of followers for each account actually decreased the performance of the classifier as the updated classifier accurately labeled 82% of the new accounts. Similar results are observed when including the number of friends into the models.

As explained in Section , Both the and the models are implemented using the function. To apply the multi-level structure to the social media data, the provided binary data need to be restructured. In the previous approach, the binary data for an account was treated as a single series of observations from the two week interval. In the multi-level approach, the data consists multiple series per individual. In the social media application we consider each day is a separate series. Due to the nature of the social media data, there are days, when the account does not post at any point during day. Because there can be inactive days the is more appropriate to model the data.

Recall, the binary data are formatted based on 30 minute intervals therefore there are 48 observations per day, m = 48. Therefore to format the binary-valued matrix as described in Section , we need to have each row correspond to a given individual on a given day. The formatted binary data of the training and testing set accounts for the multi-level models are provided in the and matrices. The formatted data is used to fit the by:

gmfpca.cur = gMFPCA(X_dat = X_dat_m_train,
                    Ys = acc_data_train$group, J = 14, N=400, 
                    covariates = NA, gAR = T, q = 3, pve1 = 0.95,
                    pve2 = 0.75,  approximation = "linear")

Based on the data, the probability of an account posting within the 30 minutes interval is large enough such that the linear approximation method is recommended. If this probability is small and posts are rare, then the exponential approximation is more appropriate. The trained model contains the mean function, both sets of eigenfunctions, scores, and the trained models for each group. The individual level eigenfunctions (Figure ) can be displayed using the following code. The individual level eigenfunctions explain how the posting patterns within a day differs among accounts.

matplot(gmfpca.cur$eigen_funcs1, type="l", lwd = 3, lty = 1,
        xlab = "Time", main = "gsFPCA Eigenfunctions", xaxt="n")
axis(1, at = (0:4)*12, labels = c("12am", "6am", "12pm",
        "6pm", "12am"))
legend("bottomright", 
        legend=c(1:length(gmfpca.cur$eigen_vals1)),
        col=1:length(gmfpca.cur$eigen_vals1), lty=1, lwd=2)

Because there are two groups in the provided data, there are two fitted models in the object, one model for each group. The lag in the both of these models is to be q = 3. The fitted model for the genuine accounts can be retrieved and viewed by

 gmfpca.cur$gar_models_ls[[2]]
#> $model
#> 
#> Call:  bayesglm(formula = formula.cur, family = binomial, data = data.s.cur2, 
#>     prior.df = Inf, scaled = FALSE)
#> 
#> Coefficients:
#> (Intercept)           S1           S2           S3  
#>     -0.9244       2.8785       2.2737       0.4148  
#> 
#> Degrees of Freedom: 2199 Total (i.e. Null);  2196 Residual
#> Null Deviance:       367.5 
#> Residual Deviance: 279.2     AIC: 287.2
#> 
#> $initial_probs
#> [1] 0.005415162 0.001805054 0.001353791 0.010379061 0.002707581 0.009927798
#> [7] 0.012184116 0.956227437
#> 
#> $initial_combos
#>      Var1 Var2 Var3
#> [1,]    0    0    0
#> [2,]    1    0    0
#> [3,]    0    1    0
#> [4,]    1    1    0
#> [5,]    0    0    1
#> [6,]    1    0    1
#> [7,]    0    1    1
#> [8,]    1    1    1

The model consists of two components: the autoregressive model estimates and the initial probabilities. The initial probabilities are the probabilities which define the estimated probability mass function for the possible combinations of the first q initial states. From the fitted it is clear that the automated account’s active state is highly affected by the active status of the previous two days.

The function is used to predict the groups given the binary-valued functional data for new accounts.

gmFPCA.results = gmFPCA_predict(gmfpca.cur, 
                                X_dat_m_new = X_dat_m_test)

table(gmFPCA.results, acc_data_test$group)
#>               
#> gmFPCA.results  1  2
#>              1 50  1
#>              2  0 49

The trained classifier is able to accurately discriminate 99% of the accounts in the testing set. This accuracy is larger than the gsFPCA approach, suggesting that group differences occur in the within day posting patterns.

acweisha/gFPCAClassif documentation built on Dec. 18, 2021, 10:23 p.m.