A lot of research in federated learning is ongoing ever since it was proposed. Federated learning allows collaborative learning among distributed clients without sharing their raw data to a central aggregator (if it is present) or to other clients in a peer to peer architecture. However, each client participating in the federation shares their model information learned from their data with other clients participating in the FL process, or with the central aggregator. This sharing of information, however, makes this approach vulnerable to various attacks, including data reconstruction attacks. Our research specifically focuses on Principal Component Analysis (PCA), as it is a widely used dimensionality technique. For performing PCA in a federated setting, distributed clients share local eigenvectors computed from their respective data with the aggregator, which then combines and returns global eigenvectors. Previous studies on attacks against PCA have demonstrated that revealing eigenvectors can lead to membership inference and, when coupled with knowledge of data distribution, result in data reconstruction attacks. Consequently, our objective in this work is to augment privacy in eigenvectors while sustaining their utility. To obtain protected eigenvectors, we use k-anonymity, and generative networks. Through our experimentation, we did a complete privacy, and utility analysis of original and protected eigenvectors. For utility analysis, we apply HIERARCHICAL CLUSTERING, RANDOM FOREST regressor, and RANDOM FOREST classifier on the protected, and original eigenvectors. We got interesting results, when we applied HIERARCHICAL CLUSTERING on the original, and protected datasets, and eigenvectors. The height at which the clusters are merged declined from 250 to 150 for original, and synthetic version of CALIFORNIA-HOUSING data, respectively. For the k-anonymous version of CALIFORNIA-HOUSING data, the height lies between 150, and 250. To evaluate the privacy risks of the federated PCA system, we act as an attacker, and conduct a data reconstruction attack.

The research dedicated to the aggregation of classification trees and general trees (hierarchical structure of objects) has made enormous progress in the past decade. The problem statement for aggregation of classification trees or general trees is as follows: Given k classification or general trees for a set of objects, we aim to build a consensus tree (classification or general). That is, a representative tree for the given trees. In this paper, we explore different perspectives for the motivation to construct a single tree from multiple trees given by researchers. The survey presents the approaches for the aggregation of both the classification trees as well as general trees. We bifurcate our study of the aggregation approaches into two categories: Selecting a single tree from multiple trees and merging trees. We will discuss these categories and the aggregation approaches under these categories in the paper comprehensively. We also discuss the privacy aspects of tree aggregation approaches and the possible directions for new research like using the technique of aggregating decision trees in the field of Federated Learning, which is a booming topic.