Testing Deep Learning (DL)-based systems is an open challenge. Although it is relatively easy to find inputs that cause a DL model to misbehave, the grouping of inputs by features that make the DL model under test fail is largely unexplored. Existing approaches for DL testing introduce perturbations that may focus on specific failure-inducing features, while neglecting others that belong to different regions of the feature space. In this paper, we create an explicit topographical map of the input feature space. Our approach, named TopoMap, is both black-box and model-agnostic as it relies solely on features that characterise the input space. To discriminate the inputs according to the specific features they share, we first apply dimensionality reduction to obtain input embeddings, which are then subjected to clustering. Each DL model might require specific embedding computations and clustering algorithms to achieve a meaningful separation of inputs into discriminative groups. We propose a novel way to evaluate alternative configurations of embedding and clustering techniques. We used a deep neural network (DNN) as an approximation of a human evaluator who could tell whether a pair of clusters can be discriminated based on the features of the included elements. We use such a DNN to automatically select the optimal topographical map of the inputs among all those that are produced by different embedding/clustering configurations. The evaluation results show that the maps generated by TopoMap consist of distinguishable and meaningful regions. In addition, we evaluate the effectiveness of TopoMap using mutation analysis. In particular, we assess whether the clusters in our topographical map allow for an effective selection of mutation-killing inputs. Experimental results show that our approach outperforms random selection by 35% on average on killable mutants; by 61% on non-killable ones.

We examine federated learning (FL) with over-the-air (OTA) aggregation, where mobile users (MUs) aim to reach a consensus on a global model with the help of a parameter server (PS) that aggregates the local gradients. In OTA FL, MUs train their models using local data at every training round and transmit their gradients simultaneously using the same frequency band in an uncoded fashion. Based on the received signal of the superposed gradients, the PS performs a global model update. While the OTA FL has a significantly decreased communication cost, it is susceptible to adverse channel effects and noise. Employing multiple antennas at the receiver side can reduce these effects, yet the path-loss is still a limiting factor for users located far away from the PS. To ameliorate this issue, in this paper, we propose a wireless-based hierarchical FL scheme that uses intermediate servers (ISs) to form clusters at the areas where the MUs are more densely located. Our scheme utilizes OTA cluster aggregations for the communication of the MUs with their corresponding IS, and OTA global aggregations from the ISs to the PS. We present a convergence analysis for the proposed algorithm, and show through numerical evaluations of the derived analytical expressions and experimental results that utilizing ISs results in a faster convergence and a better performance than the OTA FL alone while using less transmit power. We also validate the results on the performance using different number of cluster iterations with different datasets and data distributions. We conclude that the best choice of cluster aggregations depends on the data distribution among the MUs and the clusters.

Clustering aggregation has emerged as an important extension of the classical clustering problem. It refers to the situation in which a number of different (input) clusterings have been obtained for a particular data set and it is desired to aggregate those clustering results to get a better clustering solution. In this paper, we propose a unified framework to solve the clustering aggregation problem, where the aggregated clustering result is obtained by minimizing the (weighted) sum of the Bregman divergence between it and all the input clusterings. Moreover, under our algorithm framework, we also propose a novel cluster aggregation problem where some must-link and cannot-link constraints are given in addition to the input clusterings. Finally the experimental results on some real world data sets are presented to show the effectiveness of our method.