# Empirical Evidence Regarding Few-Shot Learning for Scene Classification in Remote Sensing Images
## 3 Materials and Methods
### FSL Approaches
#### 3.3.2 Transductive Approaches  
Regarding the five transductive approaches, Bias Diminishing Cosine Similarity-based Prototypical Network (BD-CSPN) [42] was the first selected. The motivation for their research was the fact that PNs trained on a narrow-size distribution of scarce data usually tend to obtain biased prototypes. They then identified two major factors influencing such a process: intra-class bias and cross-class bias. To address these, a straightforward yet effective technique for prototype rectification in a transductive setting was proposed. This approach leverages label propagation to reduce intra-class bias and feature shifting to mitigate cross-class bias. Their goal was to find the expected prototypes that maximise cosine similarity with all data points within the same class. To achieve this, CSPN was proposed, which is designed to extract discriminative features and compute fundamental prototypes from limited samples.  
In [43], the authors presented a transductive Laplacian-regularised inference for few-shot tasks. Given any feature embedding learned from the base classes (classes of the base dataset), they minimise a quadratic binary-assignment function containing two terms: (1) a unary term assigning query samples to the nearest class prototype, and (2) a pairwise Laplacian term encouraging nearby query samples to have consistent label assignments. Their transductive inference does not re-train the base model and can be seen as a graph clustering of \(Q\), subject to supervision constraints from \(S\). This technique is called here as LaplacianShot (LS).  
With Power Transform Maximum A Posteriori (PT-MAP) [44], the authors addressed the challenge of transfer-based FSL with a twofold approach: (1) preprocessing the data extracted from the backbone to align them with a specific distribution (e.g., Gaussian-like), and (2) exploiting this distribution using a carefully designed algorithm based on maximum a posteriori estimation and optimal transport, applicable specifically in the transductive few-shot setting.  
Transductive Information Maximisation (TIM) [45] maximises the mutual information between the query features and their label predictions for a certain few-shot task, in conjunction with a supervision loss based on \(S\). Moreover, the authors also derived a new alternating-direction solver for the mutual-information loss, which substantially accelerates transductive inference convergence over gradient-based optimisation whileyielding a similar performance. TIM inference is modular and can be applied on top of any base-trained feature extractor.  
To propose Transductive Fine-Tuning (TFT) [46], the authors claimed that fine-tuning a deep neural network trained using standard cross-entropy loss serves as a strong baseline for FSL. When fine-tuned in a transductive manner, it surpasses up-to-date FSL approaches on non-RS datasets such as mini-ImageNet [54], tiered-ImageNet [56], and others, all while using the same hyperparameters.  
It is important to emphasise that all such solutions, whether inductive or transductive, have been proposed and evaluated on diverse datasets but not with RS images/patches. Hence, one of the relevant points of this research is precisely to realise their performances considering the characteristics of several RS datasets.