## 3 Results
### System's Robustness  
Thermography is usually affected by noise, as one of the undeniable facts of using infrared imagery induced by environmental conditions surrounding the breast cancer screening exam. Robustness of the model versus noise can be vital for the system, particularly on the imaging acquisition and decision-making system. This problem is highlighted especially for our study cohort with different ages, races, family histories, and body shapes. The proposed SPAER model is presumably robust against noise because of the nature of the low-rank matrix approximation and latent space representation of the input image. To show such stability in the SPAER model, we measured the signal-to-noise ratio (SNR) of the model with additive Gaussian noise in the multiple channels of input of the SPEAR model. We used the following SNR equation to measure the stability of the SPAER model (from [63]):  
\[\text{SNR}=10\log_{10}\frac{\left|\mu_{S}-\mu_{N}\right|^{2}}{\sigma_{N}^{2}} \tag{5}\]  
where \(\mu_{S}\) and \(\mu_{N}\) are the signal and noise averages in the ROI, respectively, and \(\sigma_{N}\) denotes the standard deviation of the noise, obtained from the thermal referencing point in the images. The low-rank matrix approximation techniques significantly eliminated the noise of the input data (see [37; 46]). The reason we evaluated the SNR only for the multichannel input of the SPAER model was to have a separate assessment of this model. We included the additive Gaussian noise, incrementally increasing it from 3% to a 20% noise level for  
Figure 5: The receiver operating characteristic (ROC) curves of different embedding approaches used with SPAER, both with and without adding demographics.  
the multichannel input of the trained SPAER model and extracting deep thermomics, then reconstructing the image where the SNR was measured to evaluate the stability of the SPAER model. With that, we also measured the SNRs for the thermal matrix factorization techniques separately. Figure 6 presents the robustness of the model, divided into two parts: low-rank matrix approximation methods and the SPAER model. The results showed that sparse PCT and the SPAER model demonstrated the highest robustness due to additive penalty terms, inducing nonlinear behavior and limiting the domain of the solution, which increased the robustness of the model. This was also seen in sparse NMF, where non-negative constraints may have weakened the robustness occurring in NMF, with the lowest robustness among the matrix factorization algorithms. IPCT showed more robustness than PCT. This might be because of the incremental adjusting of the bases in the algorithm. We also performed statistical analysis among matrix factorization methods using a \(t\)-test between sparse PCT and other approaches. The results showed a significant difference between sparse PCT and sparse NMF, IPCT, and PCT. It may be due to the dissimilarity between PCT and IPCT and the non-negative and sparsity constraints in sparse NMF. NMF and sparse PCT showed more similarity in SNR while the noise increased, as non-negative constraints also limited the domain of the solution, similar to the sparsity penalty term in sparse PCT, despite the lower stability of NMF.