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Hierarchical federated learning (HFL) is a promising distributed deep learning model training paradigm, but it has crucial security concerns arising from adversarial attacks. This research investigates and assesses the security of HFL using a novel methodology by focusing on its resilience against adversarial attacks inference-time and training-time. Through a series of extensive experiments across diverse datasets and attack scenarios, we uncover that HFL demonstrates robustness against untargeted training-time attacks due to its hierarchical structure. However, targeted attacks, particularly backdoor attacks, exploit this architecture, especially when malicious clients are positioned in the overlapping coverage areas of edge servers. Consequently, HFL shows a dual nature in its resilience, showcasing its capability to recover from attacks thanks to its hierarchical aggregation that strengthens its suitability for adversarial training, thereby reinforcing its resistance against inference-time attacks. These insights underscore the necessity for balanced security strategies in HFL systems, leveraging their inherent strengths while effectively mitigating vulnerabilities.

Random Forest is an ensemble of decision trees based on the bagging and random subspace concepts. As suggested by Breiman, the strength of unstable learners and the diversity among them are the ensemble models' core strength. In this paper, we propose two approaches known as oblique and rotation double random forests. In the first approach, we propose rotation based double random forest. In rotation based double random forests, transformation or rotation of the feature space is generated at each node. At each node different random feature subspace is chosen for evaluation, hence the transformation at each node is different. Different transformations result in better diversity among the base learners and hence, better generalization performance. With the double random forest as base learner, the data at each node is transformed via two different transformations namely, principal component analysis and linear discriminant analysis. In the second approach, we propose oblique double random forest. Decision trees in random forest and double random forest are univariate, and this results in the generation of axis parallel split which fails to capture the geometric structure of the data. Also, the standard random forest may not grow sufficiently large decision trees resulting in suboptimal performance. To capture the geometric properties and to grow the decision trees of sufficient depth, we propose oblique double random forest. The oblique double random forest models are multivariate decision trees. At each non-leaf node, multisurface proximal support vector machine generates the optimal plane for better generalization performance. Also, different regularization techniques are employed for tackling the small sample size problems in the decision trees of oblique double random forest.

Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a representative of these codes, is used for compressing small numbers. Time consumption of a decompression algorithm is not usually as important as the time of a compression algorithm. However, efficiency of the decompression may be a critical issue in some cases. For example, a real-time compression of tree data structures follows this issue. Tree's pages are decompressed during every reading from a secondary storage into the main memory. In this case, the efficiency of a decompression algorithm is extremely important. We have developed a Fast Fibonacci decompression for this purpose. Our approach is up to $3.5\times$ faster than the original implementation.