Dimensionality Reduction in HRTF by Using Multiway Array Analysis

In a human centered robotic system, it is important to provide the robotic platform with multimodal human-like sensing, e.g. haptic, vision and audition, in order to improve interactions between the human and the robot. Recently, Head Related Transfer Functions (HRTFs) based techniques have become a promising methodology for robotic binaural hearing, which is a most prominent concept in human robot communication. In complex and dynamical applications, due to its high dimensionality, it is inefficient to utilize the originial HRTFs. To cope with this difficulty, Principle Component Analysis (PCA) has been successfully used to reduce the dimensionality of HRTF datasets. However, it requires in general a vectorization process of the original dataset, which is a three-way array, and consequently might cause loss of structure information of the dataset. In this paper we apply two multi-way array analysis methods, namely the Generalized Low Rank Approximations of Matrices (GLRAM) and the Tensor Singular Value Decomposition (Tensor-SVD), to dimensionality reductions in HRTF based applications. Our experimental results indicate that an optimized GLRAM outperforms significantly the PCA and performs nearly as well as Tensor-SVD with less computational complexity.