FedSpectral+: Spectral Clustering using Federated Learning

Clustering in graphs has been a well-known research problem, particularly because most Internet and social network data is in the form of graphs. Organizations widely use spectral clustering algorithms to find clustering in graph datasets. However, applying spectral clustering to a large dataset is challenging due to computational overhead. While the distributed spectral clustering algorithm exists, they face the problem of data privacy and increased communication costs between the clients. Thus, in this paper, we propose a spectral clustering algorithm using federated learning (FL) to overcome these issues. FL is a privacy-protecting algorithm that accumulates model parameters from each local learner rather than collecting users' raw data, thus providing both scalability and data privacy. We developed two approaches: FedSpectral and FedSpectral+. FedSpectral is a baseline approach that uses local spectral clustering labels to aggregate the global spectral clustering by creating a similarity graph. FedSpectral+, a state-of-the-art approach, uses the power iteration method to learn the global spectral embedding by incorporating the entire graph data without access to the raw information distributed among the clients. We further designed our own similarity metric to check the clustering quality of the distributed approach to that of the original/non-FL clustering. The proposed approach FedSpectral+ obtained a similarity of 98.85% and 99.8%, comparable to that of global clustering on the ego-Facebook and email-Eu-core dataset.

k-Means SubClustering: A Differentially Private Algorithm with Improved Clustering Quality

In today's data-driven world, the sensitivity of information has been a significant concern. With this data and additional information on the person's background, one can easily infer an individual's private data. Many differentially private iterative algorithms have been proposed in interactive settings to protect an individual's privacy from these inference attacks. The existing approaches adapt the method to compute differentially private(DP) centroids by iterative Llyod's algorithm and perturbing the centroid with various DP mechanisms. These DP mechanisms do not guarantee convergence of differentially private iterative algorithms and degrade the quality of the cluster. Thus, in this work, we further extend the previous work on 'Differentially Private k-Means Clustering With Convergence Guarantee' by taking it as our baseline. The novelty of our approach is to sub-cluster the clusters and then select the centroid which has a higher probability of moving in the direction of the future centroid. At every Lloyd's step, the centroids are injected with the noise using the exponential DP mechanism. The results of the experiments indicate that our approach outperforms the current state-of-the-art method, i.e., the baseline algorithm, in terms of clustering quality while maintaining the same differential privacy requirements. The clustering quality significantly improved by 4.13 and 2.83 times than baseline for the Wine and Breast_Cancer dataset, respectively.

Merged-GHCIDR: Geometrical Approach to Reduce Image Data

The computational resources required to train a model have been increasing since the inception of deep networks. Training neural networks on massive datasets have become a challenging and time-consuming task. So, there arises a need to reduce the dataset without compromising the accuracy. In this paper, we present novel variations of an earlier approach called reduction through homogeneous clustering for reducing dataset size. The proposed methods are based on the idea of partitioning the dataset into homogeneous clusters and selecting images that contribute significantly to the accuracy. We propose two variations: Geometrical Homogeneous Clustering for Image Data Reduction (GHCIDR) and Merged-GHCIDR upon the baseline algorithm - Reduction through Homogeneous Clustering (RHC) to achieve better accuracy and training time. The intuition behind GHCIDR involves selecting data points by cluster weights and geometrical distribution of the training set. Merged-GHCIDR involves merging clusters having the same labels using complete linkage clustering. We used three deep learning models- Fully Connected Networks (FCN), VGG1, and VGG16. We experimented with the two variants on four datasets- MNIST, CIFAR10, Fashion-MNIST, and Tiny-Imagenet. Merged-GHCIDR with the same percentage reduction as RHC showed an increase of 2.8%, 8.9%, 7.6% and 3.5% accuracy on MNIST, Fashion-MNIST, CIFAR10, and Tiny-Imagenet, respectively.

Geometrical Homogeneous Clustering for Image Data Reduction

In this paper, we present novel variations of an earlier approach called homogeneous clustering algorithm for reducing dataset size. The intuition behind the approaches proposed in this paper is to partition the dataset into homogeneous clusters and select some images which contribute significantly to the accuracy. Selected images are the proper subset of the training data and thus are human-readable. We propose four variations upon the baseline algorithm-RHC. The intuition behind the first approach, RHCKON, is that the boundary points contribute significantly towards the representation of clusters. It involves selecting k farthest and one nearest neighbour of the centroid of the clusters. In the following two approaches (KONCW and CWKC), we introduce the concept of cluster weights. They are based on the fact that larger clusters contribute more than smaller sized clusters. The final variation is GHCIDR which selects points based on the geometrical aspect of data distribution. We performed the experiments on two deep learning models- Fully Connected Networks (FCN) and VGG1. We experimented with the four variants on three datasets- MNIST, CIFAR10, and Fashion-MNIST. We found that GHCIDR gave the best accuracy of 99.35%, 81.10%, and 91.66% and a training data reduction of 87.27%, 32.34%, and 76.80% on MNIST, CIFAR10, and Fashion-MNIST respectively.