# A Comparison of Deep Transfer Learning Methods for Land Use and Land Cover Classification
## 2 Materials and Methods
### Methods
#### 2.2.2 Deep Transfer Learning Methods  
A domain consists of two components: a feature space, denoted as \(\mathcal{X}\), and a marginal probability distribution \(P(X)\), where \(X=\{x_{1},\ldots,x_{n}\}\in\mathcal{X}\). For instance, consider a machine learning application for software module defect classification, where each software metric serves as a feature. Here, \(x_{i}\) represents the \(i\)-th feature vector, or instance, corresponding to the \(i\)-th software module. The total number of feature vectors is denoted as \(n\), while \(\mathcal{X}\) represents the space of all possible feature vectors, and a specific learning sample is represented by \(X\)[53]. In a given domain \(\mathcal{D}\), a task \(\mathcal{T}\) is defined by a label space \(\mathcal{Y}\) and a predictive function \(f(\cdot)\), which is learned from the pairs of feature vectors and labels \(\{x_{i},y_{i}\}\), where \(x_{i}\in X\) and \(y_{i}\in\mathcal{Y}\). In the software module defect classification application, for example, \(\mathcal{Y}\) comprises true and false labels, with \(y_{i}\) taking on either of these values. The learner function \(f(x)\) predicts the label value for a given software module \(x\). The domain \(\mathcal{D}\) is represented as \(\mathcal{D}=\{\mathcal{X},\ P(X)\}\), while the task \(\mathcal{T}\) is denoted as \(\mathcal{T}=\{\mathcal{Y},\ f(\cdot)\}\)[53]. \(\mathcal{D}_{\mathcal{S}}\) rep resents the source domain data, where \(\mathcal{D}_{\mathcal{S}}=\{(x_{s,1},\ y_{s,1}),\ldots,(x_{s,n},\ y_{s,n})\}\), with \(x_{s,i}\in\mathcal{X}_{\mathcal{S}}\) as the \(i\)-th data instance of \(\mathcal{D}_{\mathcal{S}}\), and \(y_{s,i}\in\mathcal{Y}_{\mathcal{S}}\) as the corresponding class label for \(xs_{i}\). Similarly, \(\mathcal{D}_{\mathcal{T}}\) represents the target domain data, where \(\mathcal{D}_{\mathcal{T}}=\{(x_{\tau,1},\ y_{\tau,1}),\ldots,(x_{\tau,n},\ y_{ \tau,n})\}\), with \(x_{T,i}\in\mathcal{X}_{\mathcal{T}}\) as the \(i\)-th data instance of \(\mathcal{D}_{\mathcal{T}}\), and \(y_{T,i}\in\mathcal{Y}_{\mathcal{T}}\) as the corresponding class label for \(x_{T,i}\). The source task is represented as \(\mathcal{T}_{\mathcal{S}}\), the target task is represented as \(\mathcal{T}_{\mathcal{T}}\), the source predictive function is represented as \(f_{\mathbb{S}}(\cdot)\), and the target predictive function is represented as \(f_{\mathbb{T}}(\cdot)\)[53]. The formal definition of transfer learning states that it involves improving the predictive function \(f(\cdot)\) for a target domain \(\mathcal{D}_{\mathcal{T}}\) and task \(\mathcal{T}_{\mathcal{T}}\) by leveraging related information from a source domain \(\mathcal{D}_{\mathcal{S}}\) and task \(\mathcal{T}_{\mathcal{S}}\), where either \(\mathcal{D}_{\mathcal{S}}\
eq\mathcal{D}_{\mathcal{T}}\) or \(\mathcal{T}_{\mathcal{S}}\
eq\mathcal{T}_{\mathcal{T}}\)[53]. It is possible to extend the single source domain to multiple source domains. When \(\mathcal{D}_{\mathcal{S}}=\{\mathcal{X}_{\mathcal{S}},\ P(X_{\mathcal{S}})\}\) and \(\mathcal{D}_{\mathcal{T}}=\{\mathcal{X}_{\mathcal{T}},\ P(X_{T})\}\), the condition where \(\mathcal{D}_{\mathcal{S}}\
eq\mathcal{D}_{\mathcal{T}}\) means that \(\mathcal{X}_{\mathcal{S}}\
eq\mathcal{X}_{\mathcal{T}}\) and/or \(P(X_{\mathcal{S}})\
eq P(X_{\mathcal{T}})\)[53]. Contrary to standard deep learning approaches, transfer learning techniques leverage knowledge accumulated from data in related domains (source domain) to enable predictive modeling comprising multiple data patterns in the target domain. To perform deep transfer learning, a pre-trained neural network is adjusted to tackle a different task by fine-tuning its parameters. The pre-trained model is usually trained on an extensive dataset such as ImageNet, and its knowledge can be applied to new tasks with similar characteristics. This process entails freezing the pre-trained layers' weights and training new layers to tailor the model to the new task [18; 47].