## 1 Introduction  
Surface roughness is becoming a significant index to evaluate the quality of products; for example, it is used as an indicator in an in-line monitoring system in the milling process [1]. Surface roughness can also be an indicator to directly monitor the mechanical characteristics of the workpiece, such as fatigue, surface friction, and fracture resistance [2]. The machining parameters affecting the surface roughness are grouped into six major categories: tool properties, work piece properties, machine tool properties, dynamic properties, thermal properties, and cutting properties [3]. Hence, monitoring and predicting the surface roughness in end-milling operations are complex and difficult tasks. Most research studies utilize various intelligent recognition models combined with the inputs of controllable machining parameters, such as feed rate, depth of cut, and spindle speed, to produce a predictive model for the determination of the surface roughness. According to the comprehensive reviews reported in [4; 5; 6], a classifier/regressive modeling system has been used to classify/predict the surface roughness. However, the remaining five uncontrollable factors of tool properties, work piece properties, machine tool properties, dynamic properties, and thermal properties also affect the surface roughness and thus cannot be neglected during in-process machine milling; this interrelationships makes surface roughness prediction difficult. The above-described predictive models describing the internal representations between the inputs and outputs are formulated using the so-called physics-based or deterministic approach [7; 8; 9]. [PERSON] [7] presented the highly nonlinear relationships between processing conditions and the specific cutting energy, arithmetical mean roughness, and means roughness depth. [PERSON] [8] presented the modelling of surface roughness in inclined milling operations with circle-segment end mills. This study used the most important mechanical and kinematic parameters during cutting. The kinematic parameters include the tool geometry, feed rate, radial immersion, and tool runout. [PERSON] et al. [9] explored the metrological relationships between instant tool displacements and surface roughness during precise ball end milling. An alternative approach, named the data-driven approach, which involves directly adopting sensor signals' input data to correlate surface roughness using a statistical and machine learning model, is an approach for predicting the roughness that achieves high accuracy and effectiveness. The crucial factors affecting the performance of the data-driven approach are two-fold: the features extracted for model inputs and the selection of the model used for prediction. Regarding the feature extraction aspects, surface roughness prediction can be achieved directly or indirectly based on various sensor inputs, including images [10; 11; 12; 13], accelerometers [14; 15; 16; 17], and dynamometers [18; 19; 20; 21; 22]. [PERSON] et al. [11] utilized an image profilometry approach to measure the surface roughness of metallic samples and achieved a highly accurate result. [PERSON] [12] used 2-D images to evaluate the surface profile in the finish machining and successfully forecasted the final surface profile. [PERSON] [13] applied an image processing technique to measure the surface roughness and explored the effects of the camera resolution and position setting with respect to the measured surfaces. [PERSON], [PERSON] [14] proposed the use of singular spectrum analysis (SSA) to perform surface roughness monitoring based on vibration signals. [PERSON] et al. [15] proposed the use of multiple regression results to predict the surface roughness and found that the features extracted from the signals were an important index to enhance the reliability of the regression model. [PERSON] et al. [16] applied Singular spectrum analysis (SSA) to extract the raw vibration signals and found a correlation between the surface roughnesses in end-milling processing.