## 2 Review of HRTF Modeling Using Anthropometrics  
In this section, we briefly review a method for generating personalized HRTFs based on DNNs using anthropometric measurements, as shown in Figure 2[22]. In the process of designing personalized HRTFs, the public HRTF database was provided by the Center for Image Processing and Integrated Computing (CIPIC) of the University of California at Davis [24]. This database included head-related impulse responses (HRIRs), another representation of HRTFs, for 45 subjects at 25 different azimuths and 50 different elevations with anthropometric measurements and ear images of each subject. The specifications of the anthropometric measurements included in the database are as shown in Figure 3 and Table 1. In the CIPIC database, there were 17 parameters for head and torso measurements and 10 for pinna measurements. In particular, elevation and azimuth were sampled using a head-centered polar coordinate system. The elevations were uniformly sampled at intervals of \(5.625^{\circ}\) from \(-45^{\circ}\) to \(230.625^{\circ}\) while the azimuths were sampled at 25 different angles from \(-80^{\circ}\) to \(80^{\circ}\) with different steps of \(5^{\circ}\) to \(15^{\circ}\). There were 1250 HRTFs of length 200 samples, corresponding to a duration of approximately 4.5 msec at a sampling rate of 44.1 kHz. Figure 2: Block diagram of a deep neural network (DNN)-based HRTF estimation method using anthropometric measurements. To compare the performance of our proposed method in Section 3 with the neural network model described in this section, a DNN is constructed as shown at the upper block of Figure 2. The DNN model here is composed of one input layer, five hidden layers, and one output layer. There are 37 input units (17 parameters for the height and circumference measurements and 20 for the pinna measurements for both ears), as described in Table 1, and the number of output nodes is set to 200, corresponding to the length of the HRTFs. In addition, the number of each hidden layer's nodes is set to 64 and the rectified linear unit (ReLU) is applied as an activation function for each layer because the ReLU activation function is known to be effective for solving gradient-vanishing problems [25]. Moreover, since the range of anthropometric measurement is different between measurements, a measurement with a small range may not influence learning. Thus, each input feature for the DNN is normalized using the mean and variance for all training data without regard for the subjects, such as  
\[\overline{z}_{i}=\left(1+e^{-\frac{(\overline{z}_{i}-\overline{z}_{i})}{ \overline{\sigma}_{i}^{2}}}\right)^{-1} \tag{1}\]  
where \(z_{i}\) and \(\overline{z}_{i}\) are the \(i\)-th component of the input and normalized feature vector, respectively, and \(\mu_{i}\) and \(\sigma_{i}\) are the mean and standard deviation of all the training data, respectively. Note that \(z_{i}\) could be \(x_{i},\ d_{i}\), or \(\theta_{i}\) in Table 1.  
For training the DNN, Xavier initialization is utilized for the initial weights of the configured model, and the biases are initialized at zero [26]. The mean square error (MSE) between the original target and the estimate target is selected as a cost function [27]. The adaptive moment estimation (Adam) optimization is utilized for the backpropagation algorithm and the first- and second-moment decay rates are set to 0.9 and 0.999, respectively, with a learning rate of 0.001 [28]. In addition, the dropout technique is utilized with the keep probability of 0.9 [29]. Finally, the model was trained for 20,000 epochs. The performance of the DNN described thus far will be discussed in Section 4.