## 3 Results
### Classification Outcome  
The extracted deep thermomics generated by the SPAER model were used to train a random forest model and distinguish symptomatic patients from asymptomatic participants. The accuracy of this model was evaluated by comparing the model's suggested cohort versus the ground truth, which was obtained by mammography and breast biopsy. We benchmarked the model using 16 extracted deep thermomics biomarkers and other  
Figure 4: Some examples of low-rank thermal matrix approximation for six cases (healthy, healthy with symptoms, and symptomatic) using different matrix factorization techniques. (**i. **ii) The regions of interest (ROIs) of low-rank approximate representations of healthy cases. (**iii) A healthy case with pain and changes in the nipple of the patient. (**iv)** Case in which a patient experienced pain in the breast and the results of the biopsy indicated a noncancerous lesion. (**v**,**vi)** Cases representing cancer patients. Their columns show low-rank thermal matrix representation for the targeted ROI. Columns (**a**–**e**) represent the matrix factorization techniques used to extract the low-rank representation IPCT, PCT, Sparse PCT, NMF, and Sparse NMF, respectively. clinical and demographic information (e.g., age, marital status, and family history) through leave-one-out cross-validation. The accuracy of the maximal multivariate model yielded 78.2% (74.3-82.5%) for NMF deep thermomics and clinical information, which was challenged by NMF-SPAER, PCT-SPAER and sparse PCT-SPAER with clinical information, having accuracies of 77.7% (70.9-82.1%), 77.7% (73.3-82.1%), and 77.7% (72.3-81.6%), respectively. IPCT-SPAER, PCT-SPAER, and sparse PCT-SPAER showed considerably similar accuracies of diagnosis, yielding 85.4% (79.6-88.8%) and 86.4% (81.1-88.8%) with and without clinical information, respectively. IPCT-SPAER showed the lowest diagnostic accuracy of 74.3% (69.4-80.1%), 74.3% (70.4-79.1%), and 74.3% (69.9-79.6%), respectively. IPCT-SPAER's accuracy slightly increased to 76.2% (71.4-79.6%) with demographics. The minimal full multivariate model, which was for sparse NMF-SPAER with clinical information, showed an accuracy of 74.8% (70.9-77.2%), indicating lower performance, probably due to dual sparsity and non-negative matrix factorization with the models (see Table 2). The sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) were calculated using the optimum point in the receiver operating characteristic (ROC) for the trained model (Table 2). Sparse NMF-SPAER + Clinical showed the maximum sensitivity (87.5%) among the other methods, where IPCT-SPAER + Clinical and Sparse PCT-SPAER at 86.3% were the second-best sensitivities among the methods. Clinical covariates alone showed the minimum sensitivity (73.8%) compared with the other approaches. The sparse NMF-SPAER (91.4%) and NMF-SPAER + Clinical (87.5%) showed the maximum specificities, while clinical alone showed the worst specificity of 70.3%. The sparsity in the model might be the key to having higher specificity and indicating which cases are not symptomatic. Similarly, sparse NMF-SPAER showed the maximum PPV (85.5%), while sparse NMF-SPAER + Clinical had the highest NPV among the rest of the algorithms (91.2%). The clinical covariate was the least significant for the PPV and NPV. A multivariate model consisting of clinical information and demographics alone provided an accuracy of 72.8% (70.4-75.3%). We also calculated the statistical difference of the maximal accuracy (NMF-SPAER + Clinical), with other approaches using a two-tailed \(t\)-test (see Table 2). NMF-SPAER + Clinical showed considerable similarity to NMF-SPAER with clinical covariates (t-statistic = 1.1, \(p\)-value = 0.27) as well as sparse PCT-SPAER + Clinical (\(t\)-statistic = 0.2, \(p\)-value = 0.8) and PCT-SPAER+ Clinical (t-statistic = 0.6,