## 4 Physical Audio Features Extraction Techniques
### Other Domains  
The literature contains other approaches to audio feature extraction that operate on domains different to the ones just reviewed. Some of the most significant physical-based features are the eigenspace domain, the phase space domain, and the acoustic environment domain. The following paragraphs briefly describe these approaches.  
* **Eigenspace:** audio features expressed in the eigenspace are usually obtained from sound segments of several seconds of duration, which are postprocessed by dimensionality reduction algorithms in order to obtain a compact representation of the main signal information. This dimensionality reduction is normally performed by means of Principal Component Analysis (PCA) (or alternatively, via Singular Value Decomposition or SVD), which is equivalent to a projection of the original data onto a subspace defined by its eigenvectors (or eigenspace), or Independent Component Analysis (ICA). Some of the most relevant eigendomain physical features found in the literature are: i) MPEG-7 audio spectrum basis/projection feature, which is a combination of two descriptors (audio spectrum basis or ASB-and audio spectrum projection or ASP) conceived for audio retrieval and classification [45,76]. ASB feature is a compact representation of the signal spectrogram obtained through SVD, while ASP is the spectrogram projection against a given audio spectrum basis. ASB and ASP have been used for environmental sound recognition, as in [PERSON] and [PERSON] [47]; and ii) Distortion discriminant analysis (DDA) feature, which is a compact time-invariant and noise-robust representation of an audio signal, that is based on applying hierarchical PCA to a time-frequency representation derived from a modulated complex lumped transform (MCLT) (see [PERSON] _et al._[148], or [PERSON] [149]). Therefore, this feature serves as a robust audio representation against many signal distortions (time-shifts, compression artifacts and frequency and noise distortions).
* **Phase space:** this type of features emerge as a response to the linear approach that has usually been employed to model speech. However, linear models do not take into account nonlinear effects occurring during speech production, thus constituting a simplification of reality. This is why approaches based on nonlinear dynamics try to bridge this gap. A first example are the nonlinear features for speech recognition presented in the work by [PERSON] _et al._[150], which are based on the so-called reconstructed phase space generated from time-lagged versions of the original time series. The idea is that reconstructed phase spaces have been proven to recover the full dynamics of the generating system, which implies that features extracted from it can potentially contain more and/or different information than a spectral representation. In the worksby [PERSON] and [PERSON] [151] and by [PERSON] and [PERSON] [152], a similar idea is employed to compute for short time series of speech sounds useful features like Lyapunov exponents.
* **Acoustic environment features:** this type of features try to capture information from the acoustic environment where the sound is measured. As an example, in the work by [PERSON] _et al._[153], the authors propose the use of Direct-to-Reverberant Ratio (DRR), the ratio between the Room Impulse response (RIR) energy of the direct path and the reverberant components, to perform speaker diarization. In this approach, they don't use a direct measure of the RIR, but a Non-intrusive Room Acoustic parameter estimator (NIRA) (see [PERSON] _et al._[154]). This estimator is a data-driven approach that uses 106 features derived from pitch period importance weighted signal to noise ratio, zero-crossing rate, Hilbert transformation, power spectrum of long term deviation, MFCCs, line spectrum frequency and modulation representation.