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Principal Component Analysis is a robust statistical method for data representation. The technique projects an original dataset on an orthogonal subspace that is estimated by taking the covariance of the data into account. The technique can be used to unveil relationships between the independent variables in a dataset and in this way reduce a high-dimensional dataset into a more meaningful, low-dimensional space. It has been widely used in computer vision and pattern recognition to find relevant structure in data and neglect redundant information. Usually the input data is pre-processed and aligned prior PCA to increase the performance. The resulting model parameters can be calculated directly from the input data through Singular Value Decomposition (SVD). Through a linear combination of the new basis and their corresponding principal weights, the original dataset can be reconstructed with a controllable accuracy, because the orthogonal principal components are sorted according to their variance describing the original data.

Spherical Harmonic Decomposition, primary intended for the modeling and approximation of continuous functions on the sphere, has also been applied to model HRTFs. As HRTF measurements occur for positions distributed on a sphere, or spherical sections, such an approach is inherently appropriate. The dataset is projected onto spherical basis functions of a desired order, whose weighted combination can be used for modeling or approximation purposes. In contrast to PCA, where the basis functions are computed from the dataset, the spherical harmonic functions are fixed and defined hierarchically. On the basis of the Fourier Transform which decomposes a function f(x) into an infinite sum of sin(nx) and cos(nx), the spherical harmonic decomposition expands a function f(θ,φ) into an infinite sum of spherical harmonics. In this way, usually a better parametric description of a geometric body can be obtained [@KSG99]. The spherical harmonics originate by solving the angular part of Laplace’s equation in spherical coordinates.

[@KSG99]: A. Kelemen, G. Székely, and G. Gerig, "Elastic model-based segmentation of 3-D neuroradiological data sets" Medical Imaging, 1999.