## 1 Introduction  
The research and development of virtual reality (VR) and augmented reality (AR) have made significant progress over the last several decades. For the successful realization of VR/AR systems, it has been known that spatial sound or three-dimensional (3D) sound is an important component for enhancing the immersive quality of the systems when combined with video [1]. To generate such spatial sound, spatial cues from the human auditory system have been studied. The principle of spatial hearing is based on binaural and monaural cues [2]. Binaural cues imply the differences between two ears, including the time difference of arrival and the intensity difference between two ears, which are respectively referred to as the interaural time difference (ITD) and the interaural level difference (ILD). These binaural cues are related to the perceiving horizontal direction of a sound source. However, monaural cues contain the effects of the head, body, and pinna. They modify the magnitude spectrum of a sound source and are strongly related to perceiving the vertical direction of sound sources [3]. Another monaural cue is the reverberant factor, which is defined as the amount of reflection and reverberation relative to the direct sound and is primarily related to perceiving the distance of a sound source [4]. To date, audio rendering, which is a spatial audio processing technique, has been used to localize a sound source to an arbitrary position in 3D space. Thus, a listener perceives a sound produced from a localized position virtually. The audio rendering can be conducted in either the binaural or transaural configuration [1]. In a binaural configuration through headphones, research on spatial sound has focused primarily on finding the relationship between the position of a given sound source and the listener's ears. The relationship between such a sound source and the listener is typically called the head-related transfer function (HRTF), through which spatial sound is produced. The HRTF can be measured using a dummy head that mimics the human eardrum [5]. This measurement represents the effects of the head, body, and pinna and the pathway from a given source position to a dummy head. Therefore, HRTFs differ from person to person because sound propagation varies due to the head, torso, and eardrums of each person [6]. Applying measured HRTFs from a dummy head or other people to a specific person can degrade the performance of immersive sound effects due to the variance in personal characteristics. Therefore, HRTFs should be individually designed or measured to obtain localization performance. Figure 1 shows a possible application of the personalized HRTF when playing sound in a binaural configuration. As shown in Figure 1a, a traditional approach to generating binaural sound from monaural sound is using a pre-defined HRTF, but the proposed method shown in Figure 1b enables us to provide better sound quality to a listener with HRTF that is personalized to the listener. As HRTFs vary according to anthropometric measurements, HRTFs have been designed using statistical methods to create standard human head models [5]. However, since HRTFs are sensitive to individual characteristics, the spatial sound generated by an average HRTF model cannot be expected to produce faultless effects [6]. Therefore, it is necessary to measure the HRTF that suits the individual, but the measurement cost and time pose difficulties. To overcome these shortcomings, mathematical design methods based on measured HRTFs have also been studied in Reference [7; 8; 9]. Recently, artificial neural networks have shown meaningful results in various applications, such as temperature estimation and control [10; 11], machinery fault diagnosis [12; 13], material property prediction [14; 15], load forecasting [16], handwritten digit recognition [17], and wind-speed forecasting [18]. In particular, based on biometric information, breast cancer classification [19] and corneal power estimation [20] showed good performance.