Optimum profit-driven churn decision making: innovative artificial neural networks in telecom industry

Abstract

Knowledge-based churn prediction and decision making is invaluable for telecom companies due to highly competitive markets. The comprehensiveness and action ability of a data-driven churn prediction system depend on the effective extraction of hidden patterns from the data. Generally, data analytics is employed to extrapolate the extracted patterns from the training dataset to the test set. In this study, one more step is taken; the improved prediction performance is attained by capturing the individuality of each customer while discovering the hidden pattern from the train set and then applying all the knowledge to the test set. The proposed churn prediction system is developed using artificial neural networks that take advantage of both self-organizing and error-driven learning approaches (ChP-SOEDNN). We are introducing a new dimension to the study of churn prediction in telecom industry: a systematic and profit-driven churn decision-making framework. The comparison of the ChP-SOEDNN with other techniques shows its superiority regarding both accuracy and misclassification cost. Misclassification cost is a realistic criterion this article introduces to measure the success of a method in finding the best set of decisions that leads to the minimum possible loss of profit. Moreover, ChP-SOEDNN shows capability in devising a cost-efficient retention strategy for each cluster of customers, in addition to strength in dealing with the typical issue of imbalanced class distribution that is common in churn prediction problems.

Appendices

Appendix 1

Accepting the predicted membership of test set based on the SOM that is trained using train set and validation set as the test set membership is an important assumption. Therefore, it has been tested by comparing the similarity between the membership of test set cases when SOM learns with all customers in the dataset and when SOM learns only using train and validation sets.

In the literature, there are measures for comparing the similarities of two sets of clusterings. Clustering, unlike classification, does not have the luxury of class labels and this fact creates challenges to compare and evaluate the performance of different methods. There are two proposed approaches for comparing two sets of clusters (C and C′) on the same set of data points: counting pairs and set matching [41]. We only introduce two common measures to compare clusters through counting pairs. When comparing C and C′, each pair of data points falls under one of four cases based on their memberships in C and C′. These four cases are denoted by $\bullet \bullet$, $\circ \circ$, $\bullet \circ$, $\circ \bullet$. Here, two filled circles denote that both of the data points are in the same cluster under both C and C′, and two hollow circles signify that under neither C nor C′ is the pair in the same class. These two cases capture the similarities between C and C′. On the other hand, one filled circle and one hollow circle show that the pair has been the member of the same cluster under only one of C and C′, but not the other. Equation 10 and Eq. 11 represent, respectively, Fowlkes and Mallows and Rand’s measures. In these formulas N$\bullet \bullet$, N$\circ \circ$, n, k, k′, nk, and nk′, respectively, stand for the number of pairs that fall under the same cluster under both C and C′, the number of pairs that are not the members of the same cluster under neither C nor C′, the number of data points, the number of clusters under C, the number of clusters under C′, the number of data points which are members of cluster k in C, and the number of data points which are member of cluster k′ under C′

$$F\left( {C,C^{\prime } } \right) = \sqrt {\frac{{N_{ \bullet \bullet } }}{{\mathop \sum \nolimits_{k} n_{k} \left( {n_{k} - 1} \right)/2}} \times \frac{{N_{ \bullet \bullet } }}{{\mathop \sum \nolimits_{{k^{\prime }}} n_{{k^{\prime } }} \left( {n_{{k^{\prime } }} - 1} \right)/2}}}$$

(10)

$$R\left( {C,C^{{^{\prime } }} } \right) = \frac{{N_{ \bullet \bullet } + N_{ \circ \circ } }}{{n\left( {n - 1} \right)/2}}.$$

(11)

Although these measures are capable of comparing two different SOM outputs [27], there is another dimension in the output of SOM more than clustering that these measures do not capture. In a normal clustering, there is not a defined relationship between two clusters; however, if each neuron in SOM is assumed to be a cluster, each cluster has neighboring clusters. In fact, this is the reason why in Step-6 of the SOED procedure (Algorithm 1) XY coordinates are assigned to the members of each cluster. Measures introduced in Eqs. 10 and 11 cannot capture this added dimension. The base of both of these equations is how similar the clustering technique has segmented all pairs of data points into different clusters. The proposed comparison measure, expressly designed for SOM outputs with the same topologies, captures the same similarity while including the neighboring dimension. In Eq. 12, n, α, Loc_C(i), dist(P1, P2) are, respectively, the number of data points, a constant parameters which falls between zero and the maximum distant possible between any two clusters in the SOM output, the location of the cluster which has data point i as a member, and the distant between P1 and P2. Preliminary experiments determine α, so SOMC returns 0 for the input of two random clusterings. Here, α may differ based on the different topology of SOM outputs. α is set to be 1.97 in the case of 7 × 7 SOM output

$${\text{SOMC}}\left( {O,O^{{^{{\prime }} }} } \right) = \frac{{\mathop \sum \nolimits_{i = j}^{n} \mathop \sum \nolimits_{j = 1}^{n} \left( {\alpha - {\text{dist}}\left( {{\text{Loc}}\_C\left( i \right),{\text{Loc}}\_C\left( j \right)} \right)} \right)}}{{\alpha \times n \times \left( {n - 1} \right)/2}}.$$

(12)

The comparisons between different SOM made by Keramati and Jafari-Marandi [27] revealed that Rand’s measures (Eq. 11) could not be as distinguishing as Fowlkes and Mallows (Eq. 10). Table 4 presents the Fowlkes and Mallows (FM—Eq. 10) and the proposed measure in Eq. 12 (SOMC) for the output of different SOM settings: Complete Data (CD), Train Data (TD), 10% TD, Benchmark 1 (B1), Benchmark 2 (B2). Complete Data and Train Data stand for the experiments that are the main point of comparison in Table 5. Complete Data (CD) is the SOM setting that uses the complete data (train set, validation set, and test set) to drive the membership vector of the test set. Train Data (TD) only uses the train set and the validation set for the same output. Also, 10% TD only uses 10% of the train set for the same output. Moreover, Benchmark 1 (B1) is a simulation procedure of SOM output which creates a random membership vector of the test set, whereas Benchmark 2 (B2) is an intentional membership vector of the test set in which all the cases are the member of cluster 1. B1 and B2 serve as points of reference for the understanding of the range of the applied measures. FM ranges between 0 and 1: zero being no similarity and one perfect matching. SOMC ranges between − 1 and 1: negative one being negative matching, zero random matching, and one complete matching. Every cell in Table 4 is the average of ten experiments to control for the random nature of SOM. On the other hand, every cell in Table 5 is the value of the SOMC or FM for the presented example.

Table 5 SOMC, and Fowlkes and Mallows (FM) measures for different SOM outputs

The comparison between the membership of test set records based on the CD and TD cases shows there is a meaningful similarity. Based on this similarity, we assume the validity of the predicted membership of test set based on the SOM that is trained using train set and validation set. Misclassification cost of the members of the test set is calculated based on the customer revenue calculated for each cluster in MOD.

Appendix 2

Profiling of clusters of customers is valuable because it creates insights on the kind of customers that are in the dividing part of SEOD map. Figure 5a shows these regions within the employed SOED map. N1 to N7 are the clusters residing non-churn cases, and C1 to C5 are the clusters of churn cases whose profiling are worthwhile for SOED’s procedure. It is helpful to look at the average value of each attribute with the help of a color-coded map based on all the clusters’ scaled average. Figure 15 presents these for all the attributes in the dataset.

Fig. 15

SOED colored map for all the dataset attributes

Appendix 3

See Tables 6, 7, 8, 9, 10, and 11, respectively, representing the 20 validation runs for CS MLP 1–4, CS DT, and CS AdaBoost (Table 12).

Table 6 SOM hit rate examples for Table 4 experiments

Table 7 CS MLP 1: 20 validation runs

Table 8 CS MLP 2: 20 validation runs

Table 9 CS MLP 3: 20 validation runs

Table 10 CS MLP 4: 20 validation runs

Table 11 CS DT: 20 validation runs

Table 12 CS AdaBoost: 20 validation runs