This paper proposes to perform online clustering by conducting twin contrastive learning (TCL) at the instance and cluster level. Specifically, we find that when the data is projected into a feature space with a dimensionality of the target cluster number, the rows and columns of its feature matrix correspond to the instance and cluster representation, respectively. Based on the observation, for a given dataset, the proposed TCL first constructs positive and negative pairs through data augmentations. Thereafter, in the row and column space of the feature matrix, instance- and cluster-level contrastive learning are respectively conducted by pulling together positive pairs while pushing apart the negatives. To alleviate the influence of intrinsic false-negative pairs and rectify cluster assignments, we adopt a confidence-based criterion to select pseudo-labels for boosting both the instance- and cluster-level contrastive learning. As a result, the clustering performance is further improved. Besides the elegant idea of twin contrastive learning, another advantage of TCL is that it could independently predict the cluster assignment for each instance, thus effortlessly fitting online scenarios. Extensive experiments on six widely-used image and text benchmarks demonstrate the effectiveness of TCL. The code will be released on GitHub.

In this paper, we address the dichotomy between heterogeneous models and simultaneous training in Federated Learning (FL) via a clustering framework. We define a new clustering model for FL based on the (optimal) local models of the users: two users belong to the same cluster if their local models are close; otherwise they belong to different clusters. A standard algorithm for clustered FL is proposed in \cite{ghosh_efficient_2021}, called \texttt{IFCA}, which requires \emph{suitable} initialization and the knowledge of hyper-parameters like the number of clusters (which is often quite difficult to obtain in practical applications) to converge. We propose an improved algorithm, \emph{Successive Refine Federated Clustering Algorithm} (\texttt{SR-FCA}), which removes such restrictive assumptions. \texttt{SR-FCA} treats each user as a singleton cluster as an initialization, and then successively refine the cluster estimation via exploiting similar users belonging to the same cluster. In any intermediate step, \texttt{SR-FCA} uses a robust federated learning algorithm within each cluster to exploit simultaneous training and to correct clustering errors. Furthermore, \texttt{SR-FCA} does not require any \emph{good} initialization (warm start), both in theory and practice. We show that with proper choice of learning rate, \texttt{SR-FCA} incurs arbitrarily small clustering error. Additionally, we validate the performance of our algorithm on standard FL datasets in non-convex problems like neural nets, and we show the benefits of \texttt{SR-FCA} over baselines.

With the rapid development of machine learning, improving its explainability has become a crucial research goal. We study the problem of making the clusters more explainable by investigating the cluster descriptors. Given a set of objects $S$, a clustering of these objects $\pi$, and a set of tags $T$ that have not participated in the clustering algorithm. Each object in $S$ is associated with a subset of $T$. The goal is to find a representative set of tags for each cluster, referred to as the cluster descriptors, with the constraint that these descriptors we find are pairwise disjoint, and the total size of all the descriptors is minimized. In general, this problem is NP-hard. We propose a novel explainability model that reinforces the previous models in such a way that tags that do not contribute to explainability and do not sufficiently distinguish between clusters are not added to the optimal descriptors. The proposed model is formulated as a quadratic unconstrained binary optimization problem which makes it suitable for solving on modern optimization hardware accelerators. We experimentally demonstrate how a proposed explainability model can be solved on specialized hardware for accelerating combinatorial optimization, the Fujitsu Digital Annealer, and use real-life Twitter and PubMed datasets for use cases.

While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and social network analysis, clustering directed graphs remains notoriously difficult. Two of the main challenges are that the eigenvalues and eigenvectors of graph Laplacians associated with directed graphs are in general complex-valued and that there is no universally accepted definition of clusters in directed graphs. We first exploit relationships between the graph Laplacian and transfer operators and in particular between clusters in undirected graphs and metastable sets in stochastic dynamical systems and then use a generalization of the notion of metastability to derive clustering algorithms for directed and time-evolving graphs. The resulting clusters can be interpreted as coherent sets, which play an important role in the analysis of transport and mixing processes in fluid flows.

We propose a method for computing binary orthogonal non-negative matrix factorization (BONMF) for clustering and classification. The method is tested on several representative real-world data sets. The numerical results confirm that the method has improved accuracy compared to the related techniques. The proposed method is fast for training and classification and space efficient.

Approximate Nearest Neighbor Search (ANNS) in high dimensional spaces is crucial for many real-life applications (e.g., e-commerce, web, multimedia, etc.) dealing with an abundance of data. This paper proposes an end-to-end learning framework that couples the partitioning (one critical step of ANNS) and learning-to-search steps using a custom loss function. A key advantage of our proposed solution is that it does not require any expensive pre-processing of the dataset, which is one of the critical limitations of the state-of-the-art approach. We achieve the above edge by formulating a multi-objective custom loss function that does not need ground truth labels to quantify the quality of a given data-space partition, making it entirely unsupervised. We also propose an ensembling technique by adding varying input weights to the loss function to train an ensemble of models to enhance the search quality. On several standard benchmarks for ANNS, we show that our method beats the state-of-the-art space partitioning method and the ubiquitous K-means clustering method while using fewer parameters and shorter offline training times. We also show that incorporating our space-partitioning strategy into state-of-the-art ANNS techniques such as ScaNN can improve their performance significantly. Finally, we present our unsupervised partitioning approach as a promising alternative to many widely used clustering methods, such as K-means clustering and DBSCAN.

Human activity discovery aims to cluster the activities performed by humans without any prior information on what defines each activity. Most methods presented in human activity recognition are supervised, where there are labeled inputs to train the system. In reality, it is difficult to label activities data because of its huge volume and the variety of human activities. This paper proposes an unsupervised framework to perform human activity discovery in 3D skeleton sequences. First, an approach for data pre-processing is presented. In this stage, important frames are selected based on kinetic energy. Next, the displacement of joints, statistical displacements, angles, and orientation features are extracted to represent the activities information. Since not all extracted features have useful information, the dimension of features is reduced using PCA. Most methods proposed for human activity discovery are not fully unsupervised. They use pre-segmented videos before categorizing activities. To deal with this, we have used a sliding time window to segment the time series of activities with some overlapping. Then, activities are discovered by our proposed Hybrid Particle swarm optimization (PSO) with Gaussian Mutation and K-means (HPGMK) algorithm to provide diverse solutions. PSO is used due to its straightforward idea and powerful global search capability which can identify the ideal solution in a few iterations. Finally, k-means is applied to the outcome centroids from each iteration of the PSO to overcome the slow convergence rate of PSO. The experiment results on five datasets show that the proposed framework has superior performance in discovering activities compared to the other state-of-the-art methods and has increased accuracy of at least 4% on average.

In this paper, we propose an ensemble learning algorithm named \textit{bagged $k$-distance for mode-based clustering} (\textit{BDMBC}) by putting forward a new measurement called the \textit{probability of localized level sets} (\textit{PLLS}), which enables us to find all clusters for varying densities with a global threshold. On the theoretical side, we show that with a properly chosen number of nearest neighbors $k_D$ in the bagged $k$-distance, the sub-sample size $s$, the bagging rounds $B$, and the number of nearest neighbors $k_L$ for the localized level sets, BDMBC can achieve optimal convergence rates for mode estimation. It turns out that with a relatively small $B$, the sub-sample size $s$ can be much smaller than the number of training data $n$ at each bagging round, and the number of nearest neighbors $k_D$ can be reduced simultaneously. Moreover, we establish optimal convergence results for the level set estimation of the PLLS in terms of Hausdorff distance, which reveals that BDMBC can find localized level sets for varying densities and thus enjoys local adaptivity. On the practical side, we conduct numerical experiments to empirically verify the effectiveness of BDMBC for mode estimation and level set estimation, which demonstrates the promising accuracy and efficiency of our proposed algorithm.

Predicting the behaviour of shoppers provides valuable information for retailers, such as the expected spend of a shopper or the total turnover of a supermarket. The ability to make predictions on an individual level is useful, as it allows supermarkets to accurately perform targeted marketing. However, given the expected number of shoppers and their diverse behaviours, making accurate predictions on an individual level is difficult. This problem does not only arise in shopper behaviour, but also in various business processes, such as predicting when an invoice will be paid. In this paper we present CAPiES, a framework that focuses on this trade-off in an online setting. By making predictions on a larger number of entities at a time, we improve the predictive accuracy but at the potential cost of usefulness since we can say less about the individual entities. CAPiES is developed in an online setting, where we continuously update the prediction model and make new predictions over time. We show the existence of the trade-off in an experimental evaluation in two real-world scenarios: a supermarket with over 160 000 shoppers and a paint factory with over 171 000 invoices.

Luke Swanson, Field Day Lab, University of Wisconsin-Madison David Gagnon, Field Day Lab, University of Wisconsin-Madison Jennifer Scianna, Field Day Lab, University of Wisconsin-Madison John McCloskey, Field Day Lab, University of Wisconsin-Madison Nicholas Spevacek, Field Day Lab, University of Wisconsin-Madison Stefan Slater, Graduate School of Education, University of Pennsylvania Erik Harpstead, Human-Computer Interaction Institute, Carnegie Mellon University Abstract: The ability for an educational game designer to understand their audience's play styles and resulting experience is an essential tool for improving their game's design. As a game is subjected to large-scale player testing, the designers require inexpensive, automated methods for categorizing patterns of player-game interactions. In this paper we present a simple, reusable process using best practices for data clustering, feasible for use within a small educational game studio. We utilize the method to analyze a real-time strategy game, processing game telemetry data to determine categories of players based on their in-game actions, the feedback they received, and their progress through the game. Introduction Playtesting is a well-adopted method for iteratively testing and improving educational games. As a game moves through development phases, members of the target audience are given versions of the game to play, and in exchange generate feedback. This feedback can then be used to validate the design decisions made during the game's development, and to direct the next iterations of work.