Data/1_Writing/3_Task/0_Results.qmd

# Results {#sec-ch_3}
In this chapter, the results achieved with \gls{cnmc} shall be presented and assessed.
First, in section [-@sec-sec_3_1_Tracking_Results], the tracking algorithm is evaluated by showing the outcome for 3 different dynamical model configurations .
Second, in section [-@sec-sec_3_2_MOD_CPE], statements about the performance of modeling the \glsfirst{cpevol} are made . 
They are supported with some representative outputs. 
Third, in section [-@sec-sec_3_3_SVD_NMF] the two decomposition methods are compared in terms of computational time and prediction quality in subsection [-@sec-subsec_3_3_1_SVD_Speed] and [-@sec-subsec_3_3_2_SVD_Quality], respectively .
Fourth, it has been mentioned that 3 different regressors for representing the $\boldsymbol Q / \boldsymbol T$ tensor are available. 
Their rating is given in  section [-@sec-sec_3_4_SVD_Regression].
Finally, the \gls{cnmc} predicted trajectories for different models shall be displayed and evaluated in section [-@sec-sec_3_5_Pred].\newline


For assessing the performance of \gls{cnmc} some dynamical model with a specific configuration will be used many times. 
In order not to repeat them too often, they will be defined in the following.\newline 

 **Model configurations**

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 The first model configuration is denoted as  *SLS*, which stands for \textsl{S}mall **L**orenz \textsl{S}ystem .
 It is the Lorenz system described with the sets of equations @eq-eq_6_Lorenz and the number of centroids is $K=10$. 
 Furthermore, the model was trained with $\vec{\beta }_{tr} = [\beta_0 = 28 ; \, \beta_{end} = 33], \, n_{\beta, tr} = 7$, where the training model parameter values $\vec{\beta}_{tr}$ are chosen to start from $\beta_0 = 28$ and end at $\beta_{end} = 33$, where the total number of linearly distributed model parameter values is $n_{\beta, tr} = 7$.\newline

 The second model is referred to as *LS20*. 
 It is also a Lorenz system @eq-eq_6_Lorenz, but with a higher number of centroids $K=20$ and the following model configuration: $\vec{\beta }_{tr} = [\, \beta_0 = 24.75 ; \, \beta_{end} = 53.75  \,], \, n_{\beta, tr} = 60$.\newline

The third model is designated as *FW15*. It is based on the *Four Wing* set of equations @eq-eq_10_4_Wing and an illustrative trajectory is given in figure @fig-fig_37 .
The number of centroids is $K=15$ and it is constructed with the following configuration $\vec{\beta }_{tr} = [\, \beta_0 = 8 ; \, \beta_{end} = 11 \,], \, n_{\beta, tr} = 13$.\newline

![*FW15* @eq-eq_10_4_Wing trajectory for $\beta = 8$](../../3_Figs_Pyth/3_Task/1_Tracking/10_1_Traj_8.svg){#fig-fig_37}