Sales forecasting is one of the most important issues in managing information technology (IT) chain store sales since an IT chain store has many branches. Integrating feature extraction method and prediction tool, such as support vector regression (SVR), is a useful method for constructing an effective sales forecasting scheme. Independent component analysis (ICA) is a novel feature extraction technique and has been widely applied to deal with various forecasting problems. But, up to now, only the basic ICA method (i.e., temporal ICA model) was applied to sale forecasting problem. In this paper, we utilize three different ICA methods including spatial ICA (sICA), temporal ICA (tICA), and spatiotemporal ICA (stICA) to extract features from the sales data and compare their performance in sales forecasting of IT chain store. Experimental results from a real sales data show that the sales forecasting scheme by integrating stICA and SVR outperforms the comparison models in terms of forecasting error. The stICA is a promising tool for extracting effective features from branch sales data and the extracted features can improve the prediction performance of SVR for sales forecasting.
Independent component analysis (ICA) is one of the most widely applied blind source separation (BSS) techniques for separating the source from the received signals without any prior knowledge of the source signal [
Lu et al. [
For time series forecasting problems, the first important step is usually to use feature extraction to reveal the underlying/interesting information that cannot be found directly from the observed data. The performance of predictors can be improved by using the features as inputs [
The basic ICA was originally developed to deal with the problems similar to the “cocktail party” problem in which many people are speaking at once. It assumed that the extracted ICs are independent in time (independence of the voices) [
Many studies have been reported on using sICA and/or stICA algorithms to extract the distinguishability information from time series data. Calhoun et al. [
Sales forecasting is one of the most important issues for information technology (IT) companies [
The sales of a branch of an IT chain store may be affected by other neighboring branches of the same IT chain store. Therefore, to forecast sales of a branch, the historical sales data of this branch and its neighboring branches will be good predictor variables. The historical sales data of the branches of an IT chain store are highly correlated in space or time or both. Thus, three different ICA algorithms are used in this study to extract features from the branch sales data of an IT chain store. The feature extraction performance of the three different ICA algorithms is compared by using the two-stage forecasting scheme.
In this study, we propose a sales forecasting model for the branches of an IT chain store by integrating ICA algorithms and SVR. SVR based on statistical learning theory is an effective neural network algorithm and has been receiving increasing attention for solving nonlinear regression estimation problems. The SVR is derived from the structural risk minimization principle to estimate a function by minimizing an upper bound of the generalization error [
In the proposed sales forecasting scheme, we first use three different ICA algorithms (i.e., tICA, sICA, and stICA) on the predictor variables to estimate ICs. The ICs can be used to represent underlying/hidden information of the predictor variables. The ICs are then used as the input variables of the SVR for building the prediction model. In order to evaluate the performance of the three different ICA algorithms, a real branch sales data of an IT chain store is used as the illustrative example.
The rest of this paper is organized as follows. Section
In general, stICA finds a linear decomposition, by maximizing the degree of independence over space as well as over time, without necessarily producing independence in either space or time. It permits a tradeoff between the independence of arrays and the independence of time courses. Different from stICA, tICA enforces independence constraints over time, to seek a set of independent time courses. While, sICA compels independence constraints over space, to find a set of independent arrays [
Let
For temporal ICA (tICA), it embodies the assumption that
For spatial ICA (sICA), it is assumed that
In spatiotemporal ICA (stICA), it is trying to find the decomposition
Support vector regression (SVR) is an artificial intelligent forecasting tool based on statistical learning theory and structural risk minimization principle [
Traditional regression gets the coefficients through minimizing the square error which can be considered as empirical risk based on loss function. Vapnik [
After selecting proper modifying coefficient
This study uses a two-stage sales forecasting scheme. In this scheme, we use different ICA algorithms as feature extraction method and utilize support vector regression as prediction tool. The schematic representation of the proposed sales forecasting scheme is illustrated in Figure
The proposed sales forecasting scheme.
As shown in Figure
Then, the three different ICA algorithms including tICA, sICA, and stICA are used in the scaled data to estimate ICs. In the third step, the ICs contained hidden information of the prediction variables are used as input variables to construct SVR sales forecasting model. Since this study uses three ICA algorithms to extract features, based on the two-stage scheme, four sales forecasting methods including tICA-SVR, sICA-SVR, t-stICA-SVR, and s-stICA-SVR are presented in this study. For the tICA-SVR, the tICA algorithm is used to generate temporal ICs (called t_ICs). The sICA algorithm is utilized to estimate spatial ICs (called s_ICs) for sICA-SVR method. As stICA algorithm generates two different sets of ICs which are used to represent the temporal ICs (called t-st_ICs) and spatial ICs (called s-st_ICs), respectively; the t-stICA-SVR forecasting model using t-st_ICs as inputs and s-stICA-SVR prediction scheme applying s-st_ICs as prediction variables are developed.
For evaluating the performance of the three different ICA algorithms for sales forecasting for IT chain store, a real weekly branch sales dataset of an IT chain store is used in this study. This data contains 10 neighboring branches. There are totally 96 data points in each branch. The first 70 data points (72.9% of the total sample points) are used as the training sample and the remaining 26 data points (27.1% of the total sample points) are used as testing sample. Figures
(a)–(j) The sales data of the 10 branches.
The prediction results of the four two-stage sales forecasting schemes including tICA-SVR, sICA-SVR, t-stICA-SVR, and s-stICA-SVR methods are compared to the SVR model without using ICA for feature extraction (called the single SVR model). All of the five forecasting schemes are used for one-step ahead forecasting of monthly sales data (i.e., one-month ahead forecasting). In building the SVR forecasting model, the LIBSVM package proposed by Chang and Lin [
The prediction performance is evaluated using the following statistical metrics, namely, the root mean square error (RMSE), mean absolute difference (MAD), and mean absolute percentage error (MAPE). RMSE, MAD, and MAPE are measures of the deviation between actual and predicted values. The smaller the values of RMSE, MAD, and MAPE, the closer are the predicted time series values to that of the actual value. The definitions of these criteria are as below:
In this study, 10 branches’ sales data are used to assess the performance of the five forecasting methods. In this section, first, we use the sales data of Branch 1 as evaluation sample. That is, Branch 1 is the first target branch.
In the modeling of single SVR model for Branch 1, the scaled values of the 10 predictor variables are directly used as inputs. In selecting the parameters for modeling SVR, the parameter set (
Model selection results of the single SVR model.
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Training MSE | Testing MSE |
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29 | 2−5 | 0.0521 | 0.0688 |
2−7 | 0.0537 | 0.0678 | |
2−9 | 0.0552 | 0.0667 | |
2−11 | 0.0547 | 0.0664 | |
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211 | 2−5 | 0.0712 | 0.0582 |
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2−9 | 0.0407 | 0.0523 | |
2−11 | 0.0407 | 0.0567 | |
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213 | 2−5 | 0.0539 | 0.0673 |
2−7 | 0.0555 | 0.0655 | |
2−9 | 0.0561 | 0.0676 | |
2−11 | 0.0572 | 0.0672 |
For the tICA-SVR model, first, the original predictor variables are scaled and then passed to tICA algorithm to estimate ICs, that is, features. The ICs are then used for building SVR forecasting model. Ten ICs are estimated by the tICA algorithm since 10 predictors are used. As the same process with above single SVR, the parameter set (
Model selection results of the tICA-SVR model.
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Training MSE | Testing MSE |
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27 | 2−3 | 0.0401 | 0.0541 |
2−5 | 0.0391 | 0.0523 | |
2−7 | 0.0380 | 0.0515 | |
2−9 | 0.0377 | 0.0495 | |
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29 | 2−3 | 0.0396 | 0.0537 |
2−5 | 0.0388 | 0.0529 | |
2−7 | 0.0379 | 0.0541 | |
2−9 | 0.0379 | 0.0592 | |
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211 | 2−3 | 0.0390 | 0.0609 |
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2−7 | 0.0376 | 0.0753 | |
2−9 | 0.0395 | 0.0508 |
Using the similar process, the sICA-SVR model uses sICA algorithm to generate spatial ICs (i.e., s_ICs); the t-stICA-SVR model and s-stICA-SVR model utilize stICA algorithm to respectively estimate temporal ICs (i.e., t-st_ICs) and spatial ICs (i.e., s-st_ICs). Tables
Model selection results of the sICA-SVR model.
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Training MSE | Testing MSE |
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29 | 2−7 | 0.0410 | 0.0639 |
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2−11 | 0.0395 | 0.0791 | |
2−13 | 0.0415 | 0.0533 | |
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211 | 2−7 | 0.0416 | 0.0564 |
2−9 | 0.0407 | 0.0555 | |
2−11 | 0.0398 | 0.0568 | |
2−13 | 0.0398 | 0.0622 | |
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213 | 2−7 | 0.0421 | 0.0568 |
2−9 | 0.0411 | 0.0549 | |
2−11 | 0.0399 | 0.0541 | |
2−13 | 0.0396 | 0.0520 |
Model selection results of the t-stICA-SVR model.
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Training MSE | Testing MSE |
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27 | 2−3 | 0.0324 | 0.0438 |
2−5 | 0.0316 | 0.0423 | |
2−7 | 0.0307 | 0.0417 | |
2−9 | 0.0305 | 0.0401 | |
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29 | 2−3 | 0.0320 | 0.0434 |
2−5 | 0.0314 | 0.0428 | |
2−7 | 0.0306 | 0.0438 | |
2−9 | 0.0306 | 0.0479 | |
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211 | 2−3 | 0.0304 | 0.0610 |
2−5 | 0.0315 | 0.0493 | |
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2−9 | 0.0320 | 0.0411 |
Model selection results of the s-stICA-SVR model.
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Training MSE | Testing MSE |
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29 | 2−7 | 0.0343 | 0.0459 |
2−9 | 0.0334 | 0.0453 | |
2−11 | 0.0325 | 0.0463 | |
2−13 | 0.0322 | 0.0506 | |
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211 | 2−7 | 0.0320 | 0.0463 |
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2−11 | 0.0326 | 0.0440 | |
2−13 | 0.0324 | 0.0423 | |
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213 | 2−7 | 0.0334 | 0.0521 |
2−9 | 0.0320 | 0.0389 | |
2−11 | 0.0321 | 0.0644 | |
2−13 | 0.0338 | 0.0435 |
The forecasting results of Branch 1 using the tICA-SVR, sICA-SVR, t-stICA-SVR, s-stICA-SVR, and single SVR models are computed and listed in Table
Forecasting results of Branch 1 using the five forecasting models.
Models | RMSE | MAD | MAPE |
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tICA-SVR | 70.596 | 17.551 | 13.97% |
sICA-SVR | 104.946 | 50.635 | 21.32% |
t-stICA-SVR |
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s-stICA-SVR | 33.757 | 10.922 | 13.11% |
Single SVR | 115.529 | 55.741 | 24.84% |
Using a similar modeling process as abovementioned, the five forecasting models are conducted for forecasting sales of Branch 2 to Branch 10. Table
Sales forecasting results of Branch 2 to Branch 10.
Models | Branches | ||||||||
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B2 | B3 | B4 | B5 | B6 | B7 | B8 | B9 | B10 | |
tICA-SVR | 16.45% | 13.92% | 15.61% | 17.75% | 15.39% | 17.49% | 12.33% | 12.40% | 14.20% |
sICA-SVR | 17.37% | 22.12% | 17.44% | 17.95% | 16.88% | 17.71% | 21.26% | 16.36% | 24.92% |
t-stICA-SVR |
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s-stICA-SVR | 12.26% | 13.86% | 15.11% | 16.07% | 9.34% | 15.04% | 9.60% | 10.75% | 13.50% |
Single SVR | 26.93% | 25.87% | 21.58% | 25.04% | 21.76% | 22.33% | 28.75% | 21.90% | 30.36% |
Moreover, it also can be seen from the Tables
In order to further evaluate and compare the performance of the five forecasting schemes (i.e., tICA-SVR, sICA-SVR, t-stICA-SVR, s-stICA-SVR, and single SVR models), 3-month ahead and 6-month ahead forecasts are also considered in this study. The forecasting errors of the five abovementioned forecasting schemes under three different forecast horizons are computed and listed in Table
Forecasting accuracy comparison of the five forecasting schemes under three different forecast horizons.
Models | Branches | |||||||||
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B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 | B9 | B10 | |
1-month ahead forecast | ||||||||||
tICA-SVR | 13.97% | 16.45% | 13.92% | 15.61% | 17.75% | 15.39% | 17.49% | 12.33% | 12.40% | 14.20% |
sICA-SVR | 21.32% | 17.37% | 22.12% | 17.44% | 17.95% | 16.88% | 17.71% | 21.26% | 16.36% | 24.92% |
t-stICA-SVR |
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s-stICA-SVR | 13.11% | 12.26% | 13.86% | 15.11% | 16.07% | 9.34% | 15.04% | 9.60% | 10.75% | 13.50% |
Single SVR | 24.84% | 26.93% | 25.87% | 21.58% | 25.04% | 21.76% | 22.33% | 28.75% | 21.90% | 30.36% |
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3-month ahead forecast | ||||||||||
tICA-SVR | 18.41% | 18.36% | 20.29% | 24.70% | 26.71% | 25.02% | 18.62% | 17.00% | 21.17% | 16.45% |
sICA-SVR | 28.90% | 18.96% | 30.12% | 25.61% | 26.78% | 26.56% | 19.88% | 27.76% | 24.20% | 30.01% |
t-stICA-SVR |
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s-stICA-SVR | 19.16% | 19.98% | 17.63% | 18.08% | 20.45% | 16.61% | 20.17% | 12.54% | 17.77% | 15.13% |
Single SVR | 33.68% | 35.13% | 29.02% | 27.51% | 29.06% | 27.69% | 28.05% | 31.84% | 25.16% | 32.32% |
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6-month ahead forecast | ||||||||||
tICA-SVR | 33.08% | 29.36% | 33.71% | 35.05% | 35.45% | 29.95% | 31.24% | 25.77% | 31.94% | 31.48% |
sICA-SVR | 36.88% | 30.30% | 35.54% | 32.14% | 29.39% | 32.35% | 36.88% | 35.80% | 30.20% | 38.63% |
t-stICA-SVR |
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s-stICA-SVR | 26.84% | 27.31% | 26.19% | 27.46% | 34.52% | 23.28% | 34.83% | 28.13% | 26.93% | 30.45% |
Single SVR | 37.10% | 40.48% | 44.76% | 36.82% | 42.79% | 38.80% | 35.86% | 47.77% | 38.06% | 50.27% |
Forecasting sales of branches is a crucial aspect of the marketing and inventory management in IT chain store. In this paper, we used three different ICA algorithms including tICA, sICA, and stICA for sales forecasting and compared the feature extraction performance of the three different ICA algorithms. Four sales forecasting methods including tICA-SVR, sICA-SVR, t-stICA-SVR, and s-stICA-SVR were presented in this study. In the proposed sales forecasting methods, we first used three different ICA algorithms (i.e., tICA, sICA, and stICA) on the predictor variables to estimate ICs. The ICs can be used to represent underlying/hidden information of the predictor variables. The ICs are then used as the input variables of the SVR for building the prediction model. A real weekly sales data including 10 branches of an IT chain store was used for evaluating the performance of the sales forecasting methods. Experimental results showed that the t-stICA-SVR and s-stICA-SVR models can produce the lowest prediction error in forecasting sales of the 10 branches. They outperformed the comparison methods used in this study. Thus, compared to tICA and sICA algorithms, stICA algorithm can estimate more effective ICs and improve sales forecasting performance for IT chain store. Moreover, we also found that, compared to spatial ICs, the temporal ICs are more suitable features for forecasting branch sales.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is partially supported by the National Science Council of the Republic of China, Grant no. NSC 102-2221-E-231-012- and Ming De young scholars program, Grant no. 14XNJ001.