This paper presents the design and implementation of FLIPS, a middleware system to manage data and participant heterogeneity in federated learning (FL) training workloads. In particular, we examine the benefits of label distribution clustering on participant selection in federated learning. FLIPS clusters parties involved in an FL training job based on the label distribution of their data apriori, and during FL training, ensures that each cluster is equitably represented in the participants selected. FLIPS can support the most common FL algorithms, including FedAvg, FedProx, FedDyn, FedOpt and FedYogi. To manage platform heterogeneity and dynamic resource availability, FLIPS incorporates a straggler management mechanism to handle changing capacities in distributed, smart community applications. Privacy of label distributions, clustering and participant selection is ensured through a trusted execution environment (TEE). Our comprehensive empirical evaluation compares FLIPS with random participant selection, as well as three other "smart" selection mechanisms - Oort, TiFL and gradient clustering using two real-world datasets, two benchmark datasets, two different non-IID distributions and three common FL algorithms (FedYogi, FedProx and FedAvg). We demonstrate that FLIPS significantly improves convergence, achieving higher accuracy by 17 - 20 % with 20 - 60 % lower communication costs, and these benefits endure in the presence of straggler participants.

Federated learning (FL) is an emerging machine learning (ML) paradigm that enables heterogeneous edge devices to collaboratively train ML models without revealing their raw data to a logically centralized server. However, beyond the heterogeneous device capacity, FL participants often exhibit differences in their data distributions, which are not independent and identically distributed (Non-IID). Many existing works present point solutions to address issues like slow convergence, low final accuracy, and bias in FL, all stemming from client heterogeneity. In this paper, we explore an additional layer of complexity to mitigate such heterogeneity by grouping clients with statistically similar data distributions (cohorts). We propose Auxo to gradually identify such cohorts in large-scale, low-availability, and resource-constrained FL populations. Auxo then adaptively determines how to train cohort-specific models in order to achieve better model performance and ensure resource efficiency. Our extensive evaluations show that, by identifying cohorts with smaller heterogeneity and performing efficient cohort-based training, Auxo boosts various existing FL solutions in terms of final accuracy (2.1% - 8.2%), convergence time (up to 2.2x), and model bias (4.8% - 53.8%).

Previous statistical approaches to hierarchical clustering for social network analysis all construct an "ultrametric" hierarchy. While the assumption of ultrametricity has been discussed and studied in the phylogenetics literature, it has not yet been acknowledged in the social network literature. We show that "non-ultrametric structure" in the network introduces significant instabilities in the existing top-down recovery algorithms. To address this issue, we introduce an instability diagnostic plot and use it to examine a collection of empirical networks. These networks appear to violate the "ultrametric" assumption. We propose a deceptively simple and yet general class of probabilistic models called $\mathbb{T}$-Stochastic Graphs which impose no topological restrictions on the latent hierarchy. To illustrate this model, we propose six alternative forms of hierarchical network models and then show that all six are equivalent to the $\mathbb{T}$-Stochastic Graph model. These alternative models motivate a novel approach to hierarchical clustering that combines spectral techniques with the well-known Neighbor-Joining algorithm from phylogenetic reconstruction. We prove this spectral approach is statistically consistent.

There is no, nor will there ever be, single best clustering algorithm, but we would still like to be able to distinguish between methods which work well on certain task types and those that systematically underperform. Clustering algorithms are traditionally evaluated using either internal or external validity measures. Internal measures quantify different aspects of the obtained partitions, e.g., the average degree of cluster compactness or point separability. Yet, their validity is questionable, because the clusterings they promote can sometimes be meaningless. External measures, on the other hand, compare the algorithms' outputs to the reference, ground truth groupings that are provided by experts. In this paper, we argue that the commonly-used classical partition similarity scores, such as the normalised mutual information, Fowlkes-Mallows, or adjusted Rand index, miss some desirable properties, e.g., they do not identify worst-case scenarios correctly or are not easily interpretable. This makes comparing clustering algorithms across many benchmark datasets difficult. To remedy these issues, we propose and analyse a new measure: a version of the optimal set-matching accuracy, which is normalised, monotonic, scale invariant, and corrected for the imbalancedness of cluster sizes (but neither symmetric nor adjusted for chance).

Machine Learning approaches like clustering methods deal with massive datasets that present an increasing challenge. We devise parallel algorithms to compute the Multi-Slice Clustering (MSC) for 3rd-order tensors. The MSC method is based on spectral analysis of the tensor slices and works independently on each tensor mode. Such features fit well in the parallel paradigm via a distributed memory system. We show that our parallel scheme outperforms sequential computing and allows for the scalability of the MSC method.

Recent works show that the data distribution in a network's latent space is useful for estimating classification uncertainty and detecting Out-of-distribution (OOD) samples. To obtain a well-regularized latent space that is conducive for uncertainty estimation, existing methods bring in significant changes to model architectures and training procedures. In this paper, we present a lightweight, fast, and high-performance regularization method for Mahalanobis distance-based uncertainty prediction, and that requires minimal changes to the network's architecture. To derive Gaussian latent representation favourable for Mahalanobis Distance calculation, we introduce a self-supervised representation learning method that separates in-class representations into multiple Gaussians. Classes with non-Gaussian representations are automatically identified and dynamically clustered into multiple new classes that are approximately Gaussian. Evaluation on standard OOD benchmarks shows that our method achieves state-of-the-art results on OOD detection with minimal inference time, and is very competitive on predictive probability calibration. Finally, we show the applicability of our method to a real-life computer vision use case on microorganism classification.

$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Semidefinite programming (SDP) relaxations have recently been proposed for solving the $K$-means optimization problem that enjoy strong statistical optimality guarantees, but the prohibitive cost of implementing an SDP solver renders these guarantees inaccessible to practical datasets. By contrast, nonnegative matrix factorization (NMF) is a simple clustering algorithm that is widely used by machine learning practitioners, but without a solid statistical underpinning nor rigorous guarantees. In this paper, we describe an NMF-like algorithm that works by solving a nonnegative low-rank restriction of the SDP relaxed $K$-means formulation using a nonconvex Burer--Monteiro factorization approach. The resulting algorithm is just as simple and scalable as state-of-the-art NMF algorithms, while also enjoying the same strong statistical optimality guarantees as the SDP. In our experiments, we observe that our algorithm achieves substantially smaller mis-clustering errors compared to the existing state-of-the-art.

Contrastive deep graph clustering (CDGC) utilizes contrastive learning to group nodes into different clusters. Better augmentation techniques benefit the quality of the contrastive samples, thus being one of key factors to improve performance. However, the augmentation samples in existing methods are always predefined by human experiences, and agnostic from the downstream task clustering, thus leading to high human resource costs and poor performance. To this end, we propose an Attribute Graph Clustering method via Learnable Augmentation (\textbf{AGCLA}), which introduces learnable augmentors for high-quality and suitable augmented samples for CDGC. Specifically, we design two learnable augmentors for attribute and structure information, respectively. Besides, two refinement matrices, including the high-confidence pseudo-label matrix and the cross-view sample similarity matrix, are generated to improve the reliability of the learned affinity matrix. During the training procedure, we notice that there exist differences between the optimization goals for training learnable augmentors and contrastive learning networks. In other words, we should both guarantee the consistency of the embeddings as well as the diversity of the augmented samples. Thus, an adversarial learning mechanism is designed in our method. Moreover, a two-stage training strategy is leveraged for the high-confidence refinement matrices. Extensive experimental results demonstrate the effectiveness of AGCLA on six benchmark datasets.

The $k$-means++ algorithm of Arthur and Vassilvitskii (SODA 2007) is often the practitioners' choice algorithm for optimizing the popular $k$-means clustering objective and is known to give an $O(\log k)$-approximation in expectation. To obtain higher quality solutions, Lattanzi and Sohler (ICML 2019) proposed augmenting $k$-means++ with $O(k \log \log k)$ local search steps obtained through the $k$-means++ sampling distribution to yield a $c$-approximation to the $k$-means clustering problem, where $c$ is a large absolute constant. Here we generalize and extend their local search algorithm by considering larger and more sophisticated local search neighborhoods hence allowing to swap multiple centers at the same time. Our algorithm achieves a $9 + \varepsilon$ approximation ratio, which is the best possible for local search. Importantly we show that our approach yields substantial practical improvements, we show significant quality improvements over the approach of Lattanzi and Sohler (ICML 2019) on several datasets.

Time series data can be found in almost every domain, ranging from the medical field to manufacturing and wireless communication. Generating realistic and useful exemplars and prototypes is a fundamental data analysis task. In this paper, we investigate a novel approach to generating realistic and useful exemplars and prototypes for time series data. Our approach uses a new form of time series average, the ShapeDTW Barycentric Average. We therefore turn our attention to accurately generating time series prototypes with a novel approach. The existing time series prototyping approaches rely on the Dynamic Time Warping (DTW) similarity measure such as DTW Barycentering Average (DBA) and SoftDBA. These last approaches suffer from a common problem of generating out-of-distribution artifacts in their prototypes. This is mostly caused by the DTW variant used and its incapability of detecting neighborhood similarities, instead it detects absolute similarities. Our proposed method, ShapeDBA, uses the ShapeDTW variant of DTW, that overcomes this issue. We chose time series clustering, a popular form of time series analysis to evaluate the outcome of ShapeDBA compared to the other prototyping approaches. Coupled with the k-means clustering algorithm, and evaluated on a total of 123 datasets from the UCR archive, our proposed averaging approach is able to achieve new state-of-the-art results in terms of Adjusted Rand Index.