## 1 Introduction  
Since 2010, the multistage hydraulic fracturing for horizontal wells has been established as a method for producing shale gas and tight oil, especially in North America. As of 2018, shale gas accounted for over 50% of total natural gas production in the US (Figure 1) [1]. Future production profiles and estimated ultimate recovery (EUR) of shale gas wells are obtained by such methods as reservoir simulation [2], hydraulic fracturing modeling, rate transient analysis (RTA), and decline curve analysis (DCA). However, the reservoir simulation implies high uncertainty in representing flow behavior due to reservoir properties, complexity of reservoir, absorption or desorption flow, and variation of fracture permeability [3; 4; 5; 6; 7]. It is a time-consuming and a challenge task. In case of RTA, data of flow pressure and reservoir property over time are necessary, and the end of transient linear flow can be accurately predicted only by deriving the stimulated reservoir volume (SRV) through microseismic (MS) analysis. In this way, the estimated ultimate recovery (EUR) can be calculated [8]. However, property data are difficult to acquires, and the MS analysis implies uncertainty, which are the disadvantages of RTA. For this reason, many studies have actively attempted to apply a DCA in order to predict the productivity of a shale reservoirs. The DCA method proposed by [PERSON] [9] has been widely applied to traditional oil and gas reservoirs. This method assumes the pseudo steady state flow. However, shale gas has low permeability and is produced in hydraulic fractured horizontal wells, which delays the entry into the boundary dominated flow (BDF) regime. Accordingly, it is not possible to forecast a production profile by using initial production data. Some studies proposed new decline curve analysis methods considering production profiles of shale and tight reservoirs (super-hyperbolic decline method; superbolic, power law exponential decline method; PLE, modified-stretched exponential decline; YM-SEPD, Duong method, logistic growth model; LGM) [10; 11; 12; 13; 14]. However, these DCA methods tend to over and underestimate production rates due to the difference among various flow characteristics like reservoir property, hydraulic fracturing design, and natural fracture network. To overcome the above weakness, a study [15] was also conducted to propose a cumulative production incline rate index that selects an appropriate DCA methods. However, the DCA methods requires at least one year of production data. Shale reservoirs have a reported economic recovery of three years and require a model that can know the productivity of the wells to be developed before drilling or early stage of production. To overcome the limitations of simulation and DCA methods, machine learning techniques were studied and applied by many researchers for predicting productivity in shale and tight reservoirs. [PERSON] [16] quantitatively assessed the impact of shale gas development by conducting pattern recognition analysis and analyzing the correlation between productivity and other factors like rock mechanical property, hydraulic fracturing and well completion data, and reservoir property. [PERSON] et al. [17] predicted the cumulative production rate of the Wolfcamp reservoir in USA by using various supervised learning techniques, such as regression analysis, support vector machine (SVM), and gradient boosting machine (GBM). In addition, the classification and regression tree (CART) using regression analysis was performed to identify the importance of input data and select useful input data for productivity. This attempt aimed to improve the prediction performance of a model. Clustering analysis is one of unsupervised learning techniques. This technique measures the similarity of datasets and classifies target groups in order to identify similarity of objects belonging to the same group and difference among groups.