Y. SarcheshmehPour

Y. SarcheshmehPour, Y. Tian, L. Zhang et al.

We propose and study a novel graph clustering method for data with an intrinsic network structure. Similar to spectral clustering, we exploit an intrinsic network structure of data to construct Euclidean feature vectors. These feature vectors can then be fed into basic clustering methods such as k-means or Gaussian mixture model (GMM) based soft clustering. What sets our approach apart from spectral clustering is that we do not use the eigenvectors of a graph Laplacian to construct the feature vectors. Instead, we use the solutions of total variation minimization problems to construct feature vectors that reflect connectivity between data points. Our motivation is that the solutions of total variation minimization are piece-wise constant around a given set of seed nodes. These seed nodes can be obtained from domain knowledge or by simple heuristics that are based on the network structure of data. Our results indicate that our clustering methods can cope with certain graph structures that are challenging for spectral clustering methods.

S. Abdurakhmanova, Y. SarcheshmehPour, A. Jung

We present a model-agnostic federated learning method that mirrors the operation of a smart power grid: diverse local models, like energy prosumers, train independently on their own data while exchanging lightweight signals to coordinate with statistically similar peers. This coordination is governed by a graph-based regularizer that encourages connected models to produce similar predictions on a shared, public unlabeled dataset. The resulting method is a flexible instance of regularized empirical risk minimization and supports a wide variety of local models - both parametric and non-parametric - provided they can be trained via regularized loss minimization. Such training is readily supported by standard ML libraries including scikit-learn, Keras, and PyTorch.

Y. Sarcheshmehpour, M. Leinonen, A. Jung

This paper formulates and studies a novel algorithm for federated learning from large collections of local datasets. This algorithm capitalizes on an intrinsic network structure that relates the local datasets via an undirected "empirical" graph. We model such big data over networks using a networked linear regression model. Each local dataset has individual regression weights. The weights of close-knit sub-collections of local datasets are enforced to deviate only little. This lends naturally to a network Lasso problem which we solve using a primal-dual method. We obtain a distributed federated learning algorithm via a message passing implementation of this primal-dual method. We provide a detailed analysis of the statistical and computational properties of the resulting federated learning algorithm.