## 5 Materials and Methods
### Domain-Specific Classifier Alignment  
A domain-specific classifier is a classification model trained on a paired source domain with a target domain and optimized for classifying unseen samples from the target domain. It is specifically designed to handle domain shifts, ensuring good generalization to the target domain despite differences in data distribution. The adversarial models trained for shifting domains usually tend to produce a one-to-one mapping between two distinct feature spaces. However, this approach is effective for coarse-grained applications when the two feature vectors are not significantly different. As the considered domain-transforming tasks in our case are being applied to fine-grained variations where the subject, environment, and/or atmospheric conditions are fully changed from the source to the target domain, such models are not expected to be very efficient in achieving good recognition accuracy for fine-grained domain shifting tasks in device-free HAR. These significant variations may have impact near to the decision boundaries of the classifier output and can misclassify similar source and target data features owing to dissimilarities created near to the decision boundaries.Models trained to transform a single source domain into a target domain often struggle to classify distinct classes near decision boundaries due to overlapping feature distributions. Data points near these overlaps exhibit characteristics of both classes, making it difficult for the model to assign high-confidence predictions. In our case, the source samples come from a diverse distribution which is highly likely to suffer from overlapping feature distributions and uncertainties in classifying target classes near decision boundaries. To address this, the third stage of our proposed model involves \(N\) domain-specific predictors. Each of them receives a pair of source and target domain-specific invariant data features from the Stage 2 output of \(N\) unshared domain-specific feature extractors. Each classifier uses a softmax layer to classify the probability distribution into \(K\) classes. We exploit the disagreement of multiple classifiers in order to minimize the discrepancy near to the decision boundaries. Suppose \(C_{i}(\bullet)\) is the \(i\)-\(th\) domain-specific classifier mapping function with a mapping parameter \(\theta_{c_{i}}\) introduced with the Stage 2 paired \(j\)-\(th\) source and the target-generated domain-specific data features \(Z_{h_{is}}^{j}\) and \(Z_{h_{iL}}\), respectively. The domain-specific classifier produces the probability distribution divided among \(K\) classes such that \(Z_{c_{is}}^{j}=C_{i}(Z_{h_{is}}^{j};\theta_{c_{i}})\) and \(Z_{c_{t}}=C_{i}(Z_{h_{iL}};\theta_{c_{i}})\). Suppose there are such \(N\) classifiers trained on a pair of source and target domain-specific data features of \(N\) total such distinct source domains. In that case, they are more likely to produce disagreement in the classifiers' outputs for the unseen target samples due to their mismatch near to the class boundaries. Since the classifiers are trained on different source domains paired with a target domain, they are supposed to create this disagreement intuitively. Our objective is to minimize the discrepancy among classifiers' outputs as much as possible and then take the average of all the classifiers' outputs as the model's final outcome. This final prediction has more confidence due to its weightage taken from the mutual agreement of \(N\) aligned classifiers on the target domain. To minimize this discrepancy, we utilize discrepancy loss as the absolute values of the differences among all pairs of classifiers' probabilistic outputs. Suppose \(P_{c_{i1}}(y_{i1}|x_{i1})\) and \(P_{c_{2}}(y_{i2}|x_{i2})\) are the softmax layer probabilistic outputs for \(i1\)-\(th\) and \(i2\)-\(th\) classifiers of \(K\) total classes.