## 6 Discussion
### Comparative Performance Evaluation of Feature Reduction Approaches  
The DWT is considered an excellent method for decomposing thermal images into multi-resolution frequency sub-bands, identifying biologically relevant thermal patterns (e.g., localized heat anomalies), and reducing high-frequency noise. As contrasted with the linear variance preservation by PCA, DWT gives the ability to capture spatial-frequency relationships that are vital for finding subtle thermal inconsistencies in breast thermograms. Low-frequency sub-bands capture global thermal trends, while the high-frequency bands accentuate subtle variations; these are hugely important for distinguishing benign from malignant cases.  
NNMF was selected because it is a non-negativity constrained method consistent with the physical nature of thermal data (temperature values should be non-negative). This greatly favors the interpretability of the decomposed features from an additivity perspective, important in medical diagnosis. In contrast, PCA and Autoencoders allow for the presence of negative components; this makes clinical interpretation challenging. NNMF has the ability to provide parts-based representations that help in localizing thermal signatures (e.g., tumor-induced vascular changes) that would have otherwise gone unnoticed with linear methods, such as PCA.  
* PCA: generally effective for linear dimensionality reduction; however, it also assumes Gaussian distribution with linear correlations, which may not be effective on the nonlinear and heterogeneous thermal patterns in breast thermography.
* t-SNE/UMAP: These techniques are best suited for visualization through local structure preservation. However, these are computationally very expensive and do not fit well for learning an effective subspace of features for further classification tasks. Their stochastic nature can also affect reproducibility by introducing variability.
* Autoencoders: Though powerful in producing nonlinear embeddings, they require huge amounts of training data and significant computational resources to get them to perform well. This is opposed to what could be achieved by accomplishing a light, efficient deployment in the resource-limited context.  
Table 9 shows a comparative performance evaluation with dimensionality reduction approaches including NNMF, PCA, and Autoencoders. The outcomes indicate that NNMF performs better than PCA and Autoencoders in all models and layers tested. For instance,  
with EfficientNetB0 Layer 1 deep features, NNMF achieved a classification accuracy of 98.1% with LSVM, whereas PCA and Autoencoders achieved 97.2% and 97.9%, respectively. Similarly, in Layer 2, NNMF achieved an accuracy of 98.9% with LSVM, whereas PCA and Autoencoders both achieved 98.7%. This trend is also seen in other architectures like MobileNet and ShuffleNet. Notably, NNMF yielded equal or better performance across all classifiers, i.e., QSVM, CSVM, MGSVM, and CGSVM. The advantage of NNMF is that it has the ability to factorize data into non-negative components without loss of additivity of features and with enhanced interpretability. These results show how well NNMF reduces dimensions and captures the most discriminative features--qualities especially important for higher classification accuracy. The method guarantees that only non-redundant and highly relevant features are extracted by means of the integration of NNMF and MRMR, so augmenting the resilience of our suggested method.