# Semantically Controlled Adaptive Equalisation in Reduced Dimensionality Parameter Space +
## 6 Discussion  
For reconstruction accuracy we find that the sAE is able to outperform all pairwise combinations of dimensionality reduction and reconstruction techniques, whether the system includes parameter weighting or not (Table 4 and Table 5). Furthermore, the sAE is able to achieve the second highest _trustworthiness_ score (see Table 2, Figure 5a,c) in low-dimensional space, and performs to a high standard in the preservation of high-dimensional clusters (_continuity_), as in Table 2 and Figure 5b,d.  
Figure 6: Equalisation settings shown in reduced dimensionality space where the figure (**a**) shows the results of users recording warm and bright samples using 13 parameters; (**b**) the results of users producing the same descriptors using a sAE-based two-dimensional equaliser. Here, diamonds represent the class centroids.  
Figure 7: The reconstructed equaliser curves for the centroid of the _warm_ and _bright_ descriptors for both the high-dimensional (red) and low-dimensional (blue) datasets. (**a**) Reconstructed _warm_ equaliser curve; (**b**) Reconstructed _bright_ equaliser curve.  
Using a sAE however, the class-separability in low-dimensional space is reduced when parameter weighting is applied. Furthermore, the system is able to reconstruct the most parameters of the equaliser accurately (six for the unweighted parameters and five for the weighted parameters), while FA with SVR is the only combination able to accurately reconstruct five parameters for the weighted reconstruction. It achieves lower results for overall reconstruction accuracy (0.065), trustworthiness (0.7761), and classification (59.52%), and marginally lower for continuity (0.9359).  
Whilst the parameter reconstruction of the autoencoder is sufficiently accurate for our application, it is bound by the intrinsic dimensionality of the data, defined as the minimum number of variables required to accurately represent the variance in lower dimensional space. For the _bright_/_warm_ parameter-space data used in this experiment, we can show that the intrinsic dimensionality requires three variables when computed using Maximum Likelihood Estimation [47]. As our application requires a two-dimensional interface, this means the reconstruction accuracy is inherently limited.  
Additionally, the user tests revealed that the two-dimensional slider using a sAE is able to accurately reconstruct the equaliser curve, retaining the characteristics associated with _warm_ (boost on low-mid and cut on high-end) and _bright_ (cut on low-end and boost on high-end), as displayed in Figure 7a,b. Participants of the experiment also commented that the underlying two-dimensional map is easy to quickly learn and provides an intuitive tool for controlling an audio equaliser. Taking into account that the final audio effect should be incorporated alongside the equaliser, with the high-dimensional parameters also available to the users, and with indications as to where the semantic regions are placed, it can be expected that the resulting effect will feature a quick way of achieving the different descriptors (using the two-dimensional slider) and a further fine-tuning stage (via changing the high-dimensional equaliser parameters) if that is necessary.  
Providing the model training is applied offline, mapping techniques such as PCA, LDA, DM, pPCA, kPCA, and FA are all capable of running in real-time given the lower degree of computational complexity, as do reconstruction methods such as the interpolation techniques (LI, NaNI, NeNI) and the sAE. Similarly, while the sAE requires iterative training, which will have variable training times based on the number of iterations, the learning rate and the number of neurons and hidden layers, it still offers a fast implementation as the user-input process is relatively lightweight.