
Research Article


The RFMbased Institutional Customers Clustering: Case Study of a Digital
Content Provider 

Spring C. Hsu



ABSTRACT

The RFM (recency, frequency and monetary) model has been widely applied for personal customers’ analysis, but limited for the institutional customers. Therefore, the study takes a digital content provider with institutional customers of a variety of Small and Medium Enterprises (SMEs) in Taipei city for RFM clustering and deploys an innovative method combining RFM model and fuzzy cmeans (FCM) for analysis. Clustering results suggest that September and October are the two busiest months of transactions for major customers. Moreover, major customers have twice of transactions and total transaction amount of 6,462 USD; i.e., an average transaction amount of 3,231 USD. Consequently, for a digital content provider, the enough staff and equipment preparations must ready before September and October to make sure a high quality service for major customers. The average transaction amount implies that the approximate cost of 3,250 USD is the upper bound of willing to pay for many SMEs. Therefore, to deliver the customized service packages with the charges close to 3,250 USD are the first priority of services development for a digital content provider.





Received: November 01, 2011;
Accepted: March 28, 2012;
Published: June 04, 2012


INTRODUCTION
As the business environment changes from the productoriented to the customeroriented
to understand the customer behavior is thus becoming more important. The RFM
model has been widely applied in many practical areas and showed the ability
to profile the customer behaviors (Bhensdadia and Kosta,
2011; Bizhani and Tarokh, 2011; Blattberg
et al., 2008; Buttle, 2009; Kohavi
and Parekh, 2004; Sekhavat et al., 2010).
The RFM method is the popular method used in market segmentation that shows
profitable groups of customers. Companies easily find valuable customer behaviors
and then develop effectively corresponding marketing strategies by adopting
the RFM model.
Literature characterized the general RFM definitions as follows (Hughes,
1994; Stone, 1995; Wei et al.,
2010). R is the time of last transaction during an analyzing period and
the latest transactions account for the bigger R values. F is the frequency
of transactions during an analyzing period and the higher the frequency is,
the bigger F will. M is the total amount of spent money during an analyzing
period and the much the monetary is, the bigger M will. Chao
et al. (2008) indicated that the F and M values are more important
for profiling customers. Moreover, Eq. 1 defines the RFM Score,
where α, β and γ denote the weights of R, F and M, respectively.
For these weights, Hughes (1994) simply regarded the RFM
Score with equal weights, but Stone (1995) regarded that
the weights are not equal according to different industries:
Some of the variant studies relevant to the RFM model accompanied with neural
network methods. However, because of the caseadapted assumptions, these studies
showed their limit for general applications (Geyik, 2007;
Lee and Hong, 2008). Liu and Shih
(2005) tried to rate Customer Lifetime Value (CLV) by the RFM model. Their
study clustered customers according to their lifetime value expressed with weighted
RFM. However, Li et al. (2006) developed a timely
RFM (TRFM) model that conducts the relationship of product properties and purchase
periodicity. However, their model is also limited to specific caseadapted assumptions.
Moreover, the clustering methods play important roles to carry out the RFM
model. Except for the conventional hierarchical method, the widely applied clustering
methods are the kmeans and fuzzy cmeans (FCM) (Aggelis
and Christodoulakis, 2005; Alvarez et al., 2007;
Cheng and Chen, 2009; Hamzehei
et al., 2011; Hsieh, 2004; Hu
and Jing, 2008; Kenesei et al., 2006; Wu
et al., 2005; Wu et al., 2009; Zhang
et al., 2011). Panda and Patra (2008) indicated
that the fuzzy cmeans is especially a good choice for circular and spherical
clusters. Moreover, Mingoti and Lima (2006) made a comparison
for some nonhierarchical and hierarchical clustering algorithms including selforganization
map (SOM) neural networks and fuzzy cmeans methods. Their results showed that
fuzzy cmeans had good performance in all cases being stable even in existing
of outliers and overlapping and SOM neural network did not do well in almost
all cases being influenced by variable and cluster numbers. Similar to Mingoti
and Lima’s study, Velmurugan and Santhanam (2010,
2011) also got the conclusions for effectiveness of
conducting fuzzy cmeans in practical cases. Finally, whatever clustering methods
to use, Bose and Chen (2010) indicated that it is important
to use multiple techniques for a better clustering.
From the discussions above, it is found that the fuzzy cmeans has good performance of clustering. Therefore, this study deployed the fuzzy cmeans method for analysis. MATERIALS AND METHOD Clustering in brief: The purpose of cluster analysis is to find characteristics that are similar in some data and these data agree these characteristics are divided into several clusters. Therefore, the characteristics in the same cluster are highly homogeneous. General cluster methods are based on the distance as the basis of classification. Data points with high relative distance are regarded more similar and then classified into the same group. Cluster analysis is not a statistical inference technique, but a method to quantify the structural characteristics of a set of data points. Therefore, the clustering does not need any assumptions and generally important concerns of normality and linearity have little influence on the cluster analysis.
The hierarchical and partitioned methods are two major categories in cluster
analysis. The partitioned method is to break up the original clusters and reform
new clusters in various stages of clustering. The kmeans method is the
commonly used partitioned clustering method (Ali et
al., 2009; AlBashish et al., 2011;
Muda et al., 2011). The goal of kmeans
method is to search the least squared summation of distances for all input data
and their corresponding cluster centers. Moreover, to get an initial cluster
number for kmeans, the twostage hybrid method is widely used. The first
stage applies the hierarchical clustering, mountain clustering, or subtractive
clustering to suggest the proper cluster number and then the second stage to
deploy the kmeans partitioned classification.
FUZZY CLUSTERING
Initializing number of clusters: After the kmeans method, a
fuzzy based kmeans method is proposed as fuzzy cmeans method (Alamelumangai
and Devishree, 2012; Bezdek, 1981; Dunn,
1973, 1974; Dechang and Xiaolin,
2008; Song et al., 2011; WeiYi
et al., 2011). Fuzzy cmeans is a method of clustering that allows
an observation to belong with two or more clusters. This method is often used
in pattern recognition. Similar to kmeans method, a prior confirmation
of cluster number is needed to process the fuzzy cmeans method. However, not
as the kmeans method, the membership of input data points is not clearly
belonged to specific clusters in fuzzy cmeans method. This study initializes
the cluster number via subtractive clustering before conducting fuzzy cmeans
method. Because subtractive clustering is a fast, onepass algorithm for estimating
the cluster number in a set of data (AbuGhoush et al.,
2010; Chiu, 1996); and the cluster numbers obtained
from the subtractive clustering are usually used to initialize other fuzzy clustering
or forecasting methods (Castellanos and James, 2009;
Singh and Nagraja, 2011). Moreover, since the subtractive
clustering is a commonly used method, this study makes the subtractive clustering
directly via the GUI (Graphical User Interface) of mathematical software MATLAB
7.4.
Fuzzy cmeans algorithms: Equation 2 represents the
objective function J of fuzzy cmeans method, where n is the size of data points,
k is the cluster number, x_{j} is jth input vector, c_{i} is
ith cluster center and u_{ij} is point j’s membership of cluster
i. In addition, m is fuzziness exponent and usually equal to two (Abraham
et al., 2006; Miyamoto et al., 2008):
It is based on minimization of the objective function to do the fuzzy cmeans
method. Moreover, the procedure of fuzzy cmeans algorithm is specified as follows
(Celikyilmaz and Turksen, 2009; Mirkin,
2011; Pedrycz, 2007):
• 
Calculate the cluster centers by Eq. 4: 
• 
Calculate the objective function with Eq. 2.
This objective function varies from process to process of clustering. The
iteration is stopped when goal ε is achieved; otherwise, go
to procedure (4) 
• 
Update membership function as Eq. 5 to cluster
data under the constraint of Eq. 3. x_{j}c_{i}
stands for distance from point j to current cluster center i. x_{j}c_{s}
stands for distance from point j to other cluster centers s. After updating
the membership function, go back to procedure (2): 
Moreover, this study make the fuzzy cmeans clustering via the program code developed by this study and run it in the mathematical software MATLAB 7.4.
THE CASE STUDY
The casecompany, DIGITO Technology Co. Ltd., is a digital content provider in Taipei city. With experienced marketing integrators and ecommerce technicians, the company provides application software and a variety of integrated services of internet digital content for many SMEs and some large enterprises. Aim to offer customers a onestop total solution for digital content, major service patterns of the casecompany are listed in Table 1. Customers of the casecompany come from a variety of industries, such as entertainment, media, food, furniture and beverages. As the result of complexity of customer composition, finding the core and clear behaviors of customers is thus an important issue to give more suitable services to customers. Therefore, according to the complex operation conditions of the casecompany, the fuzzy clustering method is deployed to analyze the customer behaviors of the casecompany.
Preprocessing of data: The analyzed raw data concern the time during
January 1, 2008 and March 31, 2011, with the total of 273 data points of customers.
Table 1: 
Service patterns of DIGITO technology 

Source: Website of DIGITO Technology, 2011 
Table 2: 
Fragments of RFM values 

Table 3: 
Suggested cluster numbers by subtractive clustering 

For the preprocessing of the data, the RFM variables are first redefined or
calculated as follows.
R is the last transaction date of customers. Since the R value contributes to the RFM scoring determination, a numeric value is necessary. Therefore, R is redefined as the sequential number after the first date of concerned analysis time 2008/1/1 to 2011/3/31. For example, a customer that has conducted last transaction on 2008/1/1 is characterized by R = 1 and the other customer that has conducted last transaction on 2009/1/31 is characterized by R = 366+31 = 397. F is the count of transactions the customer conducted within the analysis period. M is the total amount of transaction the customer made within the analysis period. Moreover, RFM Score is summation of R, F and M values. Fragmented samples of the preprocessed R, F and M values are listed in Table 2. Customers clustering: The two stages clustering process with subtractive clustering and fuzzy cmeans are deployed to learn the cluster numbers and then to carry out the clustering. The subtractive clustering function of mathematical software MATLAB 7.4 is used learning the proper cluster numbers. In the subtractive clustering, the influence range is set as 0.5, squash is set as 1.25 and accept and reject ratios are 0.5 and 0.15, respectively. Moreover, to make sure all the important variables or variable sets are not ignored; two phases of subtractive clustering are made, shows as Table 3.

Fig. 1: 
Scatter plot of original RFM data 
In phaseI, individual RFM variables and simple RFM score with equal weights are considered.
The variable R is subtracted into three clusters and the others are subtracted
into a cluster. The clustering results of phaseI infers that variable R plays
an important role in the case. Accordingly, a new weighted RFM score with weights
of α = 3/(3+1+1) = 3/3, β = 1/(3+1+1) = 1/5, γ = 1/(3+1+1) =
1/5 is deployed in phaseII clustering. Meanwhile, to make sure that the inherent
different scales of variables R, F and M do not interfere with calculation of
RFM scores, a normalized RFM score is also developed in this study. To calculate
this normalized RFM score, variables R, F and M are first normalized by Eq.
(6), where x_{j}^{’} denotes rescaled/normalized values
of data point x_{j}. Furthermore, a RFM score with normalized data points
and different weights is also proposed as “weighted normalized RFM score.”
Finally, the clustering with R, F and M three variables together is also made
in phaseII. It is concluded from Table 3 that accounts for
the variables R, F and M together makes a subtractive clustering suggestion
with three clusters. Therefore, it is confirmed that this is the key result
that deserved an indepth analysis:
Consequently, the three variables R, F and M are selected together to make
clusters and the scatter plot of original data are shown as Fig.
1.
Table 4: 
Fragments of fuzzy membership values 

To do the fuzzy clustering, this study writes the fuzzy cmeans clustering
program codes that executed under the mathematical software MATLAB 7.4. In the
fuzzy cmeans clustering, exponent for the partition matrix m is set as 2 and
least amount of improvement is set as 1e5. The fuzzy cmeans program then runs
98 iterations and converges with the objective function value of 2.88x10^{14},
Fig. 2. Meanwhile, Table 4 shows fragment
of memberships of fuzzy partitioning and the fuzzy clustering results are shown
in Table 5. The visualized clustering results are shown in
Fig. 3.
However, it is easily to spot an apparent outlier point on the right back corner in Fig. 3. With the corresponding R, F and M values of this outlier point, it is found in the original data set as customer number No. 228 (with the values of R = 1095, F = 22 and M = 31,147,000, respectively). Therefore, it is necessary to remove the outlier from original data set and executes the fuzzy clustering process with the trimmed data set. With the trimmed data set, the program then runs 78 iterations and converges with the objective function value of 1.09x10^{14} (Fig. 4).

Fig. 2: 
Iterations of objective function for original data 

Fig. 3: 
Clustering and centering plot of original RFM data 
Table 5: 
Clustering outcomes with original RFM data 

Note: percentages stand for the data points partitioned to
clusters 
Comparing Fig. 2 with 4, removing the outlier
data point facilitates efficiency of the convergence process. Finally, the fuzzy
clustering results with trimmed data set are shown in Table 6.
The visualized clustering results with trimmed data set are shown in Fig.
5.

Fig. 4: 
Iterations of objective function for trimmed data 

Fig. 5: 
Clustering and centering plot of trimmed RFM data 
Table 6: 
Clustering outcomes with trimmed RFM data 

Note: percentages stand for the data points partitioned to
clusters 
It is now concluded that for the casecompany data, the clustering with three variables R, F and M is appropriately portioned into three clusters. Where cluster C_{1} approximately accounts for 90% of all data (approximate R = 613 = 2009/9/4, F = 2, M = 190,114; i.e., M/F = 95,057), cluster C_{2} approximately accounts for 7% of all data (approximate R = 694 = 2009/10/24, F = 8, M = 4,149,380; i.e., M/F = 518,673) and cluster C_{3} approximately accounts for simply 3% of all data (approximate R = 863 = 2010/5/12, F = 12, M = 12,258,541; i.e., M/F = 1,021,545). In brief, the cluster C_{1} represents the “major customers” for the casecompany. It has the average transactions of two times and average transaction amount of 95 thousand NTD (i.e., 3,231 USD; exchange rate NTD/USD=29.418, March 31, 2011, Central Bank of Taiwan). Moreover, the frequencies show that September and October are the two busiest transaction months of major customers. The cluster C_{2} represents the “firstminor customers” for the casecompany. It has the average transactions of eight times and average transaction amount of 519 thousand NTD (i.e., 17,631 USD). Moreover, the cluster C_{3} represents the “secondminor customers” for the casecompany. It has the average transactions of 12 times and average transaction amount of an million NTD (i.e., 34,725 USD). Observe that, the major customers (i.e., C_{1}) account for 90% of all customers, but making lower contributions to revenues for the casecompany. Comparatively, the minor customers (i.e., C_{2} and C_{3}) account for 10% of all customers, but making higher contributions to revenues for the casecompany. Finally, remind that since the casecompanyserves many SMEs and few large enterprise customers, the major customers of clustering results consist of SMEs and the minor consist of large enterprises. The results suggest that if the casecompany wants to keep or even increase market shares, it should focus on the SMEs, otherwise, if the casecompany wants to increase revenues, the large enterprises should be targeted. CONCLUSIONS The behaviors of institutional customers are not commonly mentioned in literature. This study analyzes the casecompany that mainly provides digital content services to institutional customers. Meanwhile, this study deployed an innovative method combining RFM model and FCM clustering for analyzing the casecompany. The analyzed period ranges from January 1, 2008 through March 31, 2011, with originally 273 raw customer data and finally to analyze 272 data after trimming an outlier point. This study deployed the two stages clustering process with subtractive clustering and fuzzy cmeans to learn the cluster numbers and then to carry out the clustering via variables of RFM model. This study applied the creative way to decide the weights of RFM scores via importance ranking of R, F and M subtractive clustering outcomes. Without any assumptions or constraints, the clustering approach of this study effectively and easily makes simultaneously clustering on R, F and M variables.
Three customer categories named “major customers,” “firstminor
customers,” and “secondminor customers” are clustered in this
study. The major customers account for 90% of all customers, but making lower
contributions to revenues for the casecompany. Comparatively, the minor customers
account for 10% of all customers, but making higher contributions to revenues
for the casecompany. The major customers of clustering results consist of SMEs
and the minor consist of large enterprises. The results suggest that if the
casecompany wants to keep or even increase market shares, it should focus on
the SMEs; otherwise, if the casecompany wants to increase revenues, it should
target the large enterprises.
Suppose that the major customers are critical to the casecompany, it is found that September and October are the two busiest transaction months of major customers. Moreover, the major customers in the casecompany have the approximate average transaction amount of 3,231 USD. This study concluded that for a digital content provider, the enough staff and equipment preparations must ready before September and October these two busy months to make sure the high quality service for major customers. Finally, since the average transaction amount is below 3,250 USD, it infers that the cost of 3,250 USD is the upper bound of willing to pay for many SMEs. Therefore, to deliver the customized service packages with the charges close to 3,250 USD are the first priority of services development.

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