Self-supervised learning (SSL) as an effective paradigm of representation learning has achieved tremendous success on various curated datasets in diverse scenarios. Nevertheless, when facing the long-tailed distribution in real-world applications, it is still hard for existing methods to capture transferable and robust representation. Conventional SSL methods, pursuing sample-level uniformity, easily leads to representation learning disparity where head classes dominate the feature regime but tail classes passively collapse. To address this problem, we propose a novel Geometric Harmonization (GH) method to encourage category-level uniformity in representation learning, which is more benign to the minority and almost does not hurt the majority under long-tailed distribution. Specially, GH measures the population statistics of the embedding space on top of self-supervised learning, and then infer an fine-grained instance-wise calibration to constrain the space expansion of head classes and avoid the passive collapse of tail classes. Our proposal does not alter the setting of SSL and can be easily integrated into existing methods in a low-cost manner. Extensive results on a range of benchmark datasets show the effectiveness of GH with high tolerance to the distribution skewness.

We design replicable algorithms in the context of statistical clustering under the recently introduced notion of replicability from Impagliazzo et al. [2022]. According to this definition, a clustering algorithm is replicable if, with high probability, its output induces the exact same partition of the sample space after two executions on different inputs drawn from the same distribution, when its internal randomness is shared across the executions. We propose such algorithms for the statistical $k$-medians, statistical $k$-means, and statistical $k$-centers problems by utilizing approximation routines for their combinatorial counterparts in a black-box manner. In particular, we demonstrate a replicable $O(1)$-approximation algorithm for statistical Euclidean $k$-medians ($k$-means) with $\operatorname{poly}(d)$ sample complexity. We also describe an $O(1)$-approximation algorithm with an additional $O(1)$-additive error for statistical Euclidean $k$-centers, albeit with $\exp(d)$ sample complexity. In addition, we provide experiments on synthetic distributions in 2D using the $k$-means++ implementation from sklearn as a black-box that validate our theoretical results.

Within network science, a widely applicable and important inference task is to understand how the behavior of interactions between different units (nodes) within the network depend on their latent characteristics. This occurs within a wide array of disciplines, from sociological (Freeman, 2004) to biological (Luo et al., 2007) networks. One simple and interpretable model for such a task is the stochastic block model (SBM) (Holland et al., 1983) which assumes that nodes within the network are assigned a discrete community label. Edges between nodes in the network are then formed independently across all pairs of edges, conditional on these community assignments. While such a model is simplistic, it and various extensions, such as the degree corrected SBM (DCSBM), used to handle degree heterogenity (Karrer and Newman, 2011), and mixed-membership SBMs, to allow for more complex community structures (Airoldi, Blei, Fienberg, and Xing, 2008), have seen a wide degree of empirical success (Latouche et al., 2011; Legramanti et al., 2022; Airoldi, Blei, Fienberg, Xing, and Jaakkola, 2006). One restriction of the stochastic block model and its generalizations is the requirement for a discrete community assignment as a latent representation of the units within the network. While the statistical community has previously considered more flexible latent representations (Hoff et al., 2002), over the past decade, there have been significant advancements in general embedding methods for networks, which produce general vector representations of units within a network, and generally achieve start-of-the-art performance in downstream tasks for node classification and link prediction. An early example of such a method is spectral clustering (Ng et al., 2001), which constructs an embedding of the nodes in the network from an eigendecomposition of the graph Laplacian. The k smallest non zero eigenvectors provides a k dimensional representation of each of the nodes in the network.

Data is increasingly being collected from multiple sources and described by multiple views. These multi-view data provide richer information than traditional single-view data. Fusing the former for specific tasks is an essential component of multi-view clustering. Since the goal of multi-view clustering algorithms is to discover the common latent structure shared by multiple views, the majority of proposed solutions overlook the advantages of incorporating knowledge derived from horizontal collaboration between multi-view data and the final consensus. To fill this gap, we propose the Joint Multi-View Collaborative Clustering (JMVCC) solution, which involves the generation of basic partitions using Non-negative Matrix Factorization (NMF) and the horizontal collaboration principle, followed by the fusion of these local partitions using ensemble clustering. Furthermore, we propose a weighting method to reduce the risk of negative collaboration (i.e., views with low quality) during the generation and fusion of local partitions. The experimental results, which were obtained using a variety of data sets, demonstrate that JMVCC outperforms other multi-view clustering algorithms and is robust to noisy views.

Clustering is a data analysis method for extracting knowledge by discovering groups of data called clusters. Among these methods, state-of-the-art density-based clustering methods have proven to be effective for arbitrary-shaped clusters. Despite their encouraging results, they suffer to find low-density clusters, near clusters with similar densities, and high-dimensional data. Our proposals are a new characterization of clusters and a new clustering algorithm based on spatial density and probabilistic approach. First of all, sub-clusters are built using spatial density represented as probability density function ($p.d.f$) of pairwise distances between points. A method is then proposed to agglomerate similar sub-clusters by using both their density ($p.d.f$) and their spatial distance. The key idea we propose is to use the Wasserstein metric, a powerful tool to measure the distance between $p.d.f$ of sub-clusters. We show that our approach outperforms other state-of-the-art density-based clustering methods on a wide variety of datasets.

We introduce a transformation framework that can be utilized to develop online algorithms with low $\epsilon$-approximate regret in the random-order model from offline approximation algorithms. We first give a general reduction theorem that transforms an offline approximation algorithm with low average sensitivity to an online algorithm with low $\epsilon$-approximate regret. We then demonstrate that offline approximation algorithms can be transformed into a low-sensitivity version using a coreset construction method. To showcase the versatility of our approach, we apply it to various problems, including online $(k,z)$-clustering, online matrix approximation, and online regression, and successfully achieve polylogarithmic $\epsilon$-approximate regret for each problem. Moreover, we show that in all three cases, our algorithm also enjoys low inconsistency, which may be desired in some online applications.

Agglomerative hierarchical clustering based on Ordered Weighted Averaging (OWA) operators not only generalises the single, complete, and average linkages, but also includes intercluster distances based on a few nearest or farthest neighbours, trimmed and winsorised means of pairwise point similarities, amongst many others. We explore the relationships between the famous Lance-Williams update formula and the extended OWA-based linkages with weights generated via infinite coefficient sequences. Furthermore, we provide some conditions for the weight generators to guarantee the resulting dendrograms to be free from unaesthetic inversions.

The evaluation of clustering algorithms can involve running them on a variety of benchmark problems, and comparing their outputs to the reference, ground-truth groupings provided by experts. Unfortunately, many research papers and graduate theses consider only a small number of datasets. Also, the fact that there can be many equally valid ways to cluster a given problem set is rarely taken into account. In order to overcome these limitations, we have developed a framework whose aim is to introduce a consistent methodology for testing clustering algorithms. Furthermore, we have aggregated, polished, and standardised many clustering benchmark dataset collections referred to across the machine learning and data mining literature, and included new datasets of different dimensionalities, sizes, and cluster types. An interactive datasets explorer, the documentation of the Python API, a description of the ways to interact with the framework from other programming languages such as R or MATLAB, and other details are all provided at .

Short-term load forecasting (STLF) is crucial for the daily operation of power grids. However, the non-linearity, non-stationarity, and randomness characterizing electricity demand time series renders STLF a challenging task. Various forecasting approaches have been proposed for improving STLF, including neural network (NN) models which are trained using data from multiple electricity demand series that may not necessary include the target series. In the present study, we investigate the performance of this special case of STLF, called transfer learning (TL), by considering a set of 27 time series that represent the national day-ahead electricity demand of indicative European countries. We employ a popular and easy-to-implement NN model and perform a clustering analysis to identify similar patterns among the series and assist TL. In this context, two different TL approaches, with and without the clustering step, are compiled and compared against each other as well as a typical NN training setup. Our results demonstrate that TL can outperform the conventional approach, especially when clustering techniques are considered.

Single-cell RNA sequencing (scRNA-seq) is a relatively new technology that has stimulated enormous interest in statistics, data science, and computational biology due to the high dimensionality, complexity, and large scale associated with scRNA-seq data. Nonnegative matrix factorization (NMF) offers a unique approach due to its meta-gene interpretation of resulting low-dimensional components. However, NMF approaches suffer from the lack of multiscale analysis. This work introduces two persistent Laplacian regularized NMF methods, namely, topological NMF (TNMF) and robust topological NMF (rTNMF). By employing a total of 12 datasets, we demonstrate that the proposed TNMF and rTNMF significantly outperform all other NMF-based methods. We have also utilized TNMF and rTNMF for the visualization of popular Uniform Manifold Approximation and Projection (UMAP) and t-distributed stochastic neighbor embedding (t-SNE).