## 3 Results and Discussion
### Methodology Analysis
#### 3.2.3 Comparison with Other Transfer Learning Methodologies  
The main hypothesis of the study is that, in the development of HVAC FDD systems, the dissimilarity caused by the characteristics and particularities of each building and HVAC installation complicates the task of applying a transfer learning methodology without first studying the nature of the data that one is aiming to transfer and examine the similarity of the domains. To validate this hypothesis, this section of the results includes a comparison of several state-of-the-art transfer learning methodologies which are being applied to the field. The results of evaluating 7 different methods (in addition to the proposed one) are collected in Table 4. The techniques evaluated can be classified into two categories of transfer learning: (i) feature-based transfer learning, which consists of the use of common features with similar behaviour with respect to both the source and target domains; and (ii) instance-based, which tries to re-weight the labelled training samples to correct the difference between the distributions during the training. The feature-based methodologies compared are:  
* domain adversarial neural network (DANN), replicating the network architecture and training parameters used in [19] which consists of several dense layers fully connected, that is, a 3-layer feature extractor with 17, 14 and 11 neurons followed by a 4-layer (11, 9, 7, 5 neurons) label predictor and a 4-layer domain discriminator with 11, 8, 5 and 2 neurons. The learning rate is set to 0.001 and is trained for 400 epochs using the Adam optimizer,
* Subspace alignment, which is a classical transfer learning that tries to linearly align the source and target domain in a reduced PCA space. It has been used in [55] for activity recognition in one building using features learnt in another building. For this implementation, a 3-component PCA has been implemented as a pre-processing stage before the ANN architecture described in the proposed methodology,
* Feature augmentation, which consists of increasing the number of features by separating the existing features into three classes: specific source features, specific target features, and general features that have the same behaviour in both domains. Like in the previous approach, it consists of a pre-processing stage that is added in before the ANN defined for the proposed methodology,
* Correlation alignment (CORAL), minimizes the domain shift by aligning the second-order statistics of the distributions. This, as in the rest of the methodologies of the category performs a transformation on the input data before it is fed to the ANN of the proposed methodology. Here, the regularization hyperparameter has been set at \(1\times 10^{-5}\) which is a common value found in the literature, and
* Transfer Component analysis (TCA), which is an efficient dimensionality reduction for aligning marginal distributions. It is used in [23] in combination with an SVM for the transfer learning in FDD for chillers achieving an F-scores between 0.7 and 0.9. It is also used in [20] for the prediction of temperatures in residential buildings. Here, both TCA-SVM and TCA-ANN were tested using the radial basis function as the TCA kernel and a trade-off parameter of 0.1. The ANN variant of the TCA obtained better results and it is the one that is reported in Table 4. And the instance-based approaches included in the comparison are:
* Kullback-Leibler importance estimation procedure (KLIEP) which reweights the source samples minimizing the Kullback-Leibler divergence between the source and target domains. In [56], the authors use this methodology to estimate occupancy in smart buildings. Here the hyperparameters of the KLIEP estimator are the same used in [56] and the estimator used is the same as the one in the proposed methodology, and Transfer AdaBoost (TrAdaBoost), which applies the reverse boosting principle to reduce the weights of the poorly predicted source samples and increase the weight of the target samples.