## 3 Materials and Methods
### Presented CAD  
The suggested CAD approach adeptly resolves the deficiencies found in previous work by presenting innovative solutions designed to overcome the constraints of current systems. Initially, it employs lightweight CNN architectures like MobileNet [31], EfficientNetB0 [32], and ShuffleNet [33], which have been tailored to minimize computational demands while preserving excellent performance. Utilizing transfer learning with pre-trained networks, the framework diminishes the necessity for comprehensive training data and mitigates the possibility of overfitting [58]. This method improves computational efficiency and guarantees outstanding results in thermogram-based breast cancer detection. Furthermore, the framework combines attributes from three disparate CNN architectures, capitalizing on the advantages of each design to formulate a more extensive and resilient feature set [34; 35]. This multi-architecture integration guarantees a more comprehensive depiction of thermal structures, enhancing the framework's overall accuracy. The proposed CAD framework implements a multi-layer feature extraction strategy designed to improve classification performance via an in-depth analysis of deep features. This study diverges from traditional methods that utilize features from individual CNNlayers by extracting features from three separate deep layers across three lightweight CNN architectures--MobileNet, EfficientNetB0, and ShuffleNet--to assess their respective and collective influence on classification accuracy. This stratified methodology facilitates enhanced feature representations, augmenting the system's responsiveness to nuanced thermal irregularities linked to breast cancer. The framework utilizes advanced feature transformation techniques, namely discrete wavelet transform (DWT) and non-negative matrix factorization (NNMF), to improve computational efficiency by effectively reducing feature dimensionality while maintaining essential diagnostic information. These transformations optimize the classification process and substantially reduce computational requirements, facilitating high accuracy with minimal resource expenditure. Moreover, the proposed paradigm streamlines the detection workflow by removing superfluous preprocessing and segmentation stages typically present in current systems. This simplification improves overall system efficiency and facilitates practical implementation in clinical environments. The Minimum Redundancy Maximum Relevance (MRMR) method is ultimately employed for feature selection, guaranteeing that solely the most informative features influence the final classification. This step enhances model performance and strengthens the reliability of the diagnostic process. The proposed CAD system consists of six successive steps: thermogram preprocessing, development and training of compact CNNs, multi-layer feature extraction, dimensionality reduction, multi-layer feature combination and selection, and breast cancer identification. During the preliminary preprocessing phase, thermal photos have their sizes changed and boosted to improve their variability and resilience. In the subsequent stage, three lightweight pre-trained CNN models--ShuffleNet, MobileNet, and EfficientNetB0--are altered and optimized, particularly for thermographic images. After retraining those CNNs, deep attributes are obtained from three separate layers (Layer 1, Layer 2, and Layer 3) across each compact CNN to assess how each one contributes to diagnostic accuracy. Layer 1 variables are significantly large, so the DWT is used to decrease their size. After that, the NNMF method is employed on the features from Layer 1 and Layer 2 to additionally reduce their dimensions. This stage involves an ablation study to evaluate the effects of various diminished feature sizes on the effectiveness of breast cancer identification. The features extracted from each layer of the compact CNNs are subsequently combined to assess the impact of feature integration on diagnostic results.