## 2 Methodology  
HRTFs, or their time-domain counterparts, head-related impulse responses (HRIRs), describe the transmission process of sound waves scattering and reflecting through the head, torso, and pinnae in the free field [1]. Usually, an HRTF is defined as  
\[H_{L}=P_{L}(r,\theta,\phi,f,a)/P_{0}(r,f);\;H_{R}=P_{R}(r,\theta,\phi,f,a)/P_{ 0}(r,f) \tag{1}\]  
here \(P_{L}\) and \(P_{R}\) are the complex sound pressure produced by the sound source in the left and right ears of the listener, respectively; \(P_{0}\) is the complex sound pressure at the center of the head when the human head is absent; \(f\) is the sound frequency; and \(a\) represents HRTF-related anthropometric parameters. An interaural polar coordinate system is adopted in this paper. Sound localization is determined by azimuth \(\theta\) (\(-90^{\circ}\leq\theta\leq 90^{\circ}\)), elevation \(\varphi\) (\(-90^{\circ}<\varphi\leq 270^{\circ}\)), and distance \(r\).  
Equation (1) shows that an HRTF is a multivariate function that includes spatial sound localization, frequency, etc. Therefore, it is necessary to employ an appropriate decomposition method to reduce the dimensions and extract characteristics. ICA is an effective method for decomposing large amounts of data, and has been widely used in brain/speech signal processing, wireless communication, feature extraction, data mining, fault diagnosis, and other fields [26]. ICA is based on a higher-order statistical analysis (such as kurtosis), and thus yields independent base-vectors. In the structural model of HRTFs, the effects of anatomical structures were classified into three independent sub-models: effects of the head model, effects of the torso model, and pinna models [27]. Moreover, [PERSON] performed a division analysis on HRIRs, revealing head and pinna effects, torso reflection, and knee reflection [28]. The theory of the structure models and anatomical filters/effects provides the theoretical foundations for utilizing ICA for HRTF decomposition.  
As shown in Figure 1, a variety of statistical methods are combined to establish a hybrid algorithm for the customization of individualized HRTFs based on anthropometric parameters. On the one hand, ICA decomposition is applied to the magnitude of HRTFs to obtain the independent components and individual-dependent weight coefficients. The individual-dependent weight coefficient is used as the dependent variable to establish the subsequent prediction formula. On the other hand, factor analysis is applied to all anthropometric parameters to remove redundancy between these parameters. As a result, key anthropometric parameters are selected as independent variables in the subsequent prediction formula. Finally, the prediction formula relating weight coefficients to key anthropometric parameters is established by a multiple linear regression analysis. In application scenarios, the individualized coefficient weights for a specific listener are determined by substituting the measured listener's individualized anthropometric parameters into the proposed prediction formula. Then, the listener's customized HRTF can be obtained by substituting the predicted weight coefficients into an ICA-based HRTF formula. This is the basic idea of the proposed hybrid algorithm for customization of individualized HRTFs from anthropometric measurements.