Building on recent advances in speeding up t-SNE and obtaining finer-grained structure, we combine the two to create tree-SNE, a hierarchical clustering and visualization algorithm based on stacked one-dimensional t-SNE embeddings. We also introduce alpha-clustering, which recommends the optimal cluster assignment, without foreknowledge of the number of clusters, based off of the cluster stability across multiple scales. We demonstrate the effectiveness of tree-SNE and alphaclustering on images of handwritten digits, mass cytometry (CyTOF) data from blood cells, and single-cell RNAsequencing (scRNA-seq) data from retinal cells. Furthermore, to demonstrate the validity of the visualization, we use alpha-clustering to obtain unsupervised clustering results competitive with the state of the art on several image data sets. Software is available at https: //github.com/isaacrob/treesne.

Recently, federated learning (FL) has drawn significant attention due to its capability of training a model over the network without knowing the client's private raw data. In this paper, we study the unsupervised clustering problem under the FL setting. By adopting a generalized matrix factorization model for clustering, we propose two novel (first-order) federated clustering (FedC) algorithms based on principles of model averaging and gradient sharing, respectively, and present their theoretical convergence conditions. We show that both algorithms have a O(1/T) convergence rate, where T is the total number of gradient evaluations per client, and the communication cost can be effectively reduced by controlling the local epoch length and allowing partial client participation within each communication round. Numerical experiments show that the FedC algorithm based on gradient sharing outperforms that based on model averaging, especially in scenarios with non-i.i.d. I. INTRODUCTION As one of the most fundamental data mining tasks, unsupervised clustering has a vast range of applications [1]. In view of the increasing volume of real-life data, distributed clustering methods that can process large-scale datasets in parallel computing environments have gained significant interests in the last decade [2], [3], [4]. However, recent emphasis on user privacy has called for new distributed schemes that can perform clustering without directly accessing the users' raw data.

Clustering is a fundamental task in data analysis. Recently, deep clustering, which derives inspiration primarily from deep learning approaches, achieves state-of-the-art performance and has attracted considerable attention. Current deep clustering methods usually boost the clustering results by means of the powerful representation ability of deep learning, e.g., autoencoder, suggesting that learning an effective representation for clustering is a crucial requirement. The strength of deep clustering methods is to extract the useful representations from the data itself, rather than the structure of data, which receives scarce attention in representation learning. Motivated by the great success of Graph Convolutional Network (GCN) in encoding the graph structure, we propose a Structural Deep Clustering Network (SDCN) to integrate the structural information into deep clustering. Specifically, we design a delivery operator to transfer the representations learned by autoencoder to the corresponding GCN layer, and a dual self-supervised mechanism to unify these two different deep neural architectures and guide the update of the whole model. In this way, the multiple structures of data, from low-order to high-order, are naturally combined with the multiple representations learned by autoencoder. Furthermore, we theoretically analyze the delivery operator, i.e., with the delivery operator, GCN improves the autoencoder-specific representation as a high-order graph regularization constraint and autoencoder helps alleviate the over-smoothing problem in GCN. Through comprehensive experiments, we demonstrate that our propose model can consistently perform better over the state-of-the-art techniques.

Let's quickly look at types of clustering algorithms and when you should choose each type. When choosing a clustering algorithm, you should consider whether the algorithm scales to your dataset. Datasets in machine learning can have millions of examples, but not all clustering algorithms scale efficiently. Many clustering algorithms work by computing the similarity between all pairs of examples. This means their runtime increases as the square of the number of examples \(n\), denoted as \(O(n 2)\) in complexity notation.

K-means clustering is one of the simplest and popular unsupervised machine learning algorithms. Unsupervised algorithms make inferences from data sets using only input vectors without referring to known, or labeled, outcomes. Unsupervised learning allows us to approach problems with little or no idea what our results should look like. Unsupervised algorithms find patterns based only on input data. The technique is useful when we're not quite sure what to look for.

In this paper, we analyse classical variants of the Spectral Clustering (SC) algorithm in the Dynamic Stochastic Block Model (DSBM). Existing results show that, in the relatively sparse case where the expected degree grows logarithmically with the number of nodes, guarantees in the static case can be extended to the dynamic case and yield improved error bounds when the DSBM is sufficiently smooth in time, that is, the communities do not change too much between two time steps. We improve over these results by drawing a new link between the sparsity and the smoothness of the DSBM: the more regular the DSBM is, the more sparse it can be, while still guaranteeing consistent recovery. In particular, a mild condition on the smoothness allows to treat the sparse case with bounded degree. We also extend these guarantees to the normalized Laplacian, and as a by-product of our analysis, we obtain to our knowledge the best spectral concentration bound available for the normalized Laplacian of matrices with independent Bernoulli entries.

Driving behaviour has a great impact on road safety. A popular way of analysing driving behaviour is to move the focus to the manoeuvres as they give useful information about the driver who is performing them. In this paper, we investigate a new way of identifying manoeuvres from vehicle telematics data, through motif detection in time-series. We implement a modified version of the Extended Motif Discovery (EMD) algorithm, a classical variable-length motif detection algorithm for time-series and we applied it to the UAH-DriveSet, a publicly available naturalistic driving dataset. After a systematic exploration of the extracted motifs, we were able to conclude that the EMD algorithm was not only capable of extracting simple manoeuvres such as accelerations, brakes and curves, but also more complex manoeuvres, such as lane changes and overtaking manoeuvres, which validates motif discovery as a worthwhile line for future research.

We study the problem of community detection in multi-layer networks, where pairs of nodes can be related in multiple modalities. We introduce a general framework, i.e., mixture multi-layer stochastic block model (MMSBM), which includes many earlier models as special cases. We propose a tensor-based algorithm (TWIST) to reveal both global/local memberships of nodes, and memberships of layers. We show that the TWIST procedure can accurately detect the communities with small misclassification error as the number of nodes and/or the number of layers increases. Numerical studies confirm our theoretical findings. To our best knowledge, this is the first systematic study on the mixture multi-layer networks using tensor decomposition. The method is applied to two real datasets: worldwide trading networks and malaria parasite genes networks, yielding new and interesting findings.

Data scientists have nowadays to deal with massive and complex datasets, that are often corrupted by outliers. Classical data mining procedures such as K-means or more general EM algorithms for instance are however sensitive to the presence of outliers, which can induce a time consuming pre-processing of the data. In this context, robust versions of data mining procedures are particularly relevant and we investigate a way to produce a Lloyd-type algorithm for hard clustering that is robust to the presence of ouliers. To do this, we propose to use a variant of median-of-means (MOM) statistics, that we call bootstrap median-of-means (bMOM). MOM principle has been the object of recent active research in mean estimation, regression, highdimensional framework and also supervised classification and machine learning ([17, 9, 15, 16, 19, 18, 20, 22]). Note that other approaches to robustness for K-means exist in the literature, such as for instance K-median or trimmed K-means (see for instance the survey [10] and references therein; see also [5]). Given a dataset, the boostrap median-of-means consists in first generating a (large) bootstrap sample and then perform a classical median-of-means on this bootstrap sample. We prove in Section 2 that if enough blocks are generated from the bootstrap sampling, then for a fixed block size, bMOM has a higher breakdown point than MOM.

The goal of this research project is to analyze the dynamics of social networks using machine learning techniques to locate maximal cliques and to find clusters for the purpose of identifying a target demographic. Unsupervised machine learning techniques are designed and implemented in this project to analyze a dataset from YouTube to discover communities in the social network and find central nodes. Different clustering algorithms are implemented and applied to the YouTube dataset. The well-known Bron-Kerbosch algorithm is used effectively in this research to find maximal cliques. The results obtained from this research could be used for advertising purposes and for building smart recommendation systems. All algorithms were implemented using Python programming language. The experimental results show that we were able to successfully find central nodes through clique-centrality and degree centrality. By utilizing clique detection algorithms, the research shown how machine learning algorithms can detect close knit groups within a larger network.