# A Review on Head-Related Transfer Function Generation for Spatial Audio
## 5 Anthropometric and Morphological Approaches for HRTF Personalisation
### Regression
#### 5.3.1 Sparse Measurements  
When speaking of anthropometric features in terms of sparse measurements, one of the first works is [PERSON] et al. 's 2007 study [156]. They employ a regression model to map anthropometric features to the \"people\" vector space generated by N-mode SVD. Subsequently, when anatomical measurements from a subject not present in the database are provided, this regression model is used to determine that individual's position in the people space. This representation is then combined with the N-mode SVD results to produce a customised set of HRTFs. In 2008, [PERSON] et al. [157] introduced a method for customising HRTFs using a neural network approach based on specific anatomical measurements. The model maps selected anthropometric parameters to estimate individualised HRTFs without requiring complex setups. Selected parameters for the model include head width, head depth, shoulder width, cavum concha height and width, fossa height, pinna height, and pinna width. A three-layer feed-forward neural network is used to capture the non-linear relationship between these parameters and key HRTF characteristics like principal components and ITD. Results indicate that the localisation accuracy of the personalised HRTFs is increased compared to non-individualised HRTFs. In 2013, to develop a personalised model, [PERSON] et al. [158] applied High-Order Singular-Value Decomposition (HOSVD) to extract an individual core tensor representing an HRTF,which serves as the output. Key anthropometric parameters are selected using the Laplacian score and correlation analysis, which act as inputs for a Radial Basis Function (RBF) neural network. The RBF-based model is then employed to predict individual HRTFs using these selected anthropometric features. In 2014, [PERSON] et al. [159] proposed a method for synthesising HRTF magnitudes using a sparse representation of anthropometric features. The proposed method tackles the problem of HRTF synthesis by determining a sparse representation of a subject's anthropometric data relative to the original ones present in the training set. By learning a sparse vector that expresses a subject's features as a linear combination of the training data, this method then utilises the same representation to generate the corresponding HRTF magnitudes. This approach has been benchmarked against ridge regression, a generic man-nequin model, and various classifiers, showing enhanced localisation accuracy compared to non-individuals HRTFs. Later, in the era of deep learning, [PERSON] et al. [160] introduced a deep neural network (DNN) approach for personalising HRTFs using all measurements from the CIPIC dataset. The model outputs a personalised HRIR and demonstrates improved accuracy over averaged HRTFs, validated through root mean square error (RMSE) and log-spectral distortion (LSD) metrics. In 2019, [PERSON] et al. [161] proposed a model based on an autoencoder and a multilayer perceptron (MLP). First, the autoencoder is trained on HRTF data to extract a bottleneck vector representing key features. This bottleneck vector is then used, like in a distillation task, as a target to train the MLP, with anthropometric features as input. During the test phase, the MLP generates the bottleneck vector for a new subject's anthropometric features, and the decoder reconstructs the corresponding HRTFs. The model mitigates the overfitting observed in direct MLP-based estimation by using the autoencoder to reduce the dimensionality of the data and augmenting the training set with additional HRTF samples. The model leverages 27 anthropometric features derived from the CIPIC database, focusing on left ear measurements while excluding data related to the right pinna. Although the CIPIC database includes ITD, HRIRs, and anthropometry data, only magnitude HRTFs are considered in this work. In 2020, [PERSON] and [PERSON] expanded upon and improved these ideas in a similar investigation [162]. Still in 2020, ref. [163] introduced a method for global HRTF personalisation using spherical harmonics (SHs).